Document [original]

Integrated Optical Distributed Bragg

Reflector and Distributed Feedback

Lasers in Er:LiNbO3Waveguides with

Photorefractive Gratings.

Thesis

Submitted to the

Department of Physics, Faculty of Science

University of Paderborn, Germany

for the degree

Doctor of Philosophy (Ph.D/Dr.rer.nat)

Bijoy Krishna Das

Reviewers:

1. Prof. Dr. W. Sohler

2. Prof. W. von der Osten

Date of the Submission: 18.03.2003

Date of the Defence Examination: 24.04.2003

Dedicated to my friends and well wishers

Chumki Saha, B. Umapathi, Lakhsmi Bera, Bidyut Samanta, Satyajit Saha

Rajib, Makhan, Sidhu, Papu, Raju, Dilip, Bishu, Debu, and Bithika

who encouraged me to study Ph.D. in Germany

Contents

1 Introduction 1

1.1 Background ................................. 1

1.2 Motivation.................................. 2

1.3 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Photorefractive Gratings: Theoretical Analysis 5

2.1 Introduction................................. 5

2.2 Photorefractive Effect in Fe:LiNbO3.................... 5

2.3 Refractive Index Modulation

by Two-Beam Interference . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Thermal Fixing and Developing . . . . . . . . . . . . . . . . . . . . . . 12

2.5 Grating Response:

Coupled Mode Theory Analysis . . . . . . . . . . . . . . . . . . . . . . 14

2.6 Conclusions ................................. 18

3 Doped Waveguides: Fabrication and Characterization 19

3.1 Introduction................................. 19

3.2 Fabrication ................................. 19

3.2.1 Er-Diffusion Doping . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.2 Fe-Diffusion Doping . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.3 Fabrication of Ti-Indiffused Waveguides . . . . . . . . . . . . . 25

3.2.4 Annealing .............................. 25

3.3 Characterization .............................. 26

3.3.1 Waveguide Loss and Mode-Size . . . . . . . . . . . . . . . . . . 26

3.3.2 Absorption and Gain . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3.3 Amplified Spontaneous Emission (ASE) . . . . . . . . . . . . . . 30

3.4 Conclusions ................................. 31

4 Photorefractive Gratings: Fabrication and Characterization 33

4.1 Introduction................................. 33

4.2 Fabrication ................................. 34

4.2.1 Grating Definition . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2.2 Thermal Fixing and Development of Ionic Gratings . . . . . . . 39

4.3 Properties of Fixed Gratings . . . . . . . . . . . . . . . . . . . . . . . . 40

4.4 Conclusions ................................. 47

5 Lasers with Photorefractive Gratings 49

5.1 Introduction................................. 49

5.2 Basic Theory of Ti:Er:LiNbO3Waveguide Lasers . . . . . . . . . . . . . 49

5.3 DBR-Laser with One Grating . . . . . . . . . . . . . . . . . . . . . . . 53

5.4 DBR Laser with Two Gratings . . . . . . . . . . . . . . . . . . . . . . 57

5.5 DFBLaser/Amplifier............................ 62

5.6 DFB-DBR Coupled Cavity Laser . . . . . . . . . . . . . . . . . . . . . 65

5.7 Conclusions ................................. 72

6 Summary and Conclusions 73

Chapter 1

Introduction

1.1 Background

Since the invention of the transistor in 1947, the development of integrated elec-

tronic circuits has led to increased reliability with increased performance and reduced

cost, size, weight, and power requirements. With the expectation of realizing similar

benefits for optical signal processing, computing, sensing, and communications, the

research on integrated optical circuit (IOC) technology had been introduced after the

invention of laser in 1960. For the first decade or so, the field of integrated optics

research progressed very slowly, but in course of time the number of governmental,

industrial, university, and other research laboratories involved in this field increased

very rapidly.

The present research in the field of integrated optics is mainly focussed on finding

a suitable material that can be used as a substrate for IOCs with higher functionality.

Many kinds of materials and the corresponding process techniques have been con-

sidered. Some of the promising technologies are based on lithium niobate (LiNbO3),

glass (SiO2on Si), Gallium Arsenide (GaAs), polymers, etc.

Up to now, integrated optics technology based on ferroelectric LiNbO3is being widely

investigated because of its attractive optical properties. This crystal of LiNbO3were

grown for the first time by Ballman in 1965; it is not available in nature. The crys-

tallographic structure and some fundamental physical properties of this ferroelectric

crystal were intensively studied by Abraham et al in 1966 [1–5]. The basic experiments

on acoustic wave propagation, electrooptic light modulation, optical second harmonic

generation, parametric oscillation and holographic storage were performed between

1965-1968. Meanwhile, most of the physical and chemical properties of LiNbO3have

been investigated and are understood very well. The most important crystallographic

and physical parameters are also documented in the literature [6,7].

The successful history of LiNbO3lies in the unique combination of excellent elec-

trooptic, acoustooptic, nonlinear and photorefractive properties. Importantly, low-

loss optical waveguide which is the back-bone of an integrated optical circuit (IOC),

can be easily implemented by titanium (Ti) in-diffusion or by proton-exchange in this

material. In fact, LiNbO3based integrated optic devices have been developed for op-

tical switch arrays, fiber-optic gyroscope, cable TV (CATV) signal distribution, and

long-haul telecommunications. Some of the device technologies have already been

transferred to high-volume manufacturing in the latter two huge application mar-

kets [8].

Apart from the large number of passive/active devices already developed in LiNbO3,

there is also a growing interest in rare-earth-doped optically pumped amplifiers and

lasers [9–16] during the last years. In particular, erbium-doped titanium-indiffused

lithium niobate (Ti:Er:LiNbO3) laser sources (1.53 µm< λ < 1.62 µm) are attrac-

tive [17, 18]. Besides, cw Fabry-Perot lasers of high efficiency (∼40%), acousto-

optically tunable lasers, Q-switched lasers, actively mode-locked lasers, there have

also been some attempts in developing narrow linewidth lasers [19,20]. The approach

was to integrate a grating structure in the waveguide to get single-frequency laser

emission: this concept is routinely used to develop distributed Bragg reflector (DBR)

and distributed feedback (DFB) lasers in semiconductors [21–23] and fibers [24–30].

Single-frequency lasers have major applications in the field of heterodyne detection

and in fiber-optic ultra-dense wavelength division multiplexed systems.

1.2 Motivation

The first DBR laser was reported in Ti:Er:LiNbO3using a surface relief Bragg grat-

ing [19]. Single-frequency laser emission was observed frequently during its operation.

Afterwards, an integrated optical transmitter unit consisting of such a DBR laser and

a Mach-Zehnder interferometer was also demonstrated [31]. This type of transmitter

unit is essential for fiber-optic communications. But, due to the complicated fabri-

cation technology, limited quality of the gratings and high scattering losses of these

surface relief Bragg gratings, work has not been progressed any more in this direction.

Besides their application in lasers, gratings or more general, periodic structures can

also be used for couplers, add/drop filters, switches, dispersion compensators, etc, in

integrated optical circuits [32,33]. Therefore, it is a great challenge to fabricate effi-

cient periodic structures in LiNbO3channel waveguides. As the surface relief Bragg

grating in LiNbO3waveguides mentioned above is found to have some problems, pho-

torefractive gratings generated by an illumination with a periodic light pattern on the

sample surface can be exploited. Fiber Bragg gratings are examples withe a periodic

index modulation induced in the photosensitive fiber core. They are now commercially

manufactured and used for a variety of applications, including dispersion compensa-

tion and wavelength add/drop filters.

Recently, Becker et al. [20] demonstrated an attractive integrated optical DBR laser

consisting of (i) a photorefractive Bragg grating in a Ti:Fe:LiNbO3section at one end,

(ii) an amplifying Ti:Er:LiNbO3section in the middle and (iii) a broadband dielec-

tric mirror at the other end. Although, single-frequency laser emission could not be

achieved with this type of laser, the work has opened a new direction in LiNbO3based

integrated optics. To follow this direction and to explore the new field of integrated

optical lasers with photorefractive gratings was the main goal of this thesis.

1.3 Organization of the Thesis

This work contributes some extended studies on photorefractive Bragg gratings and

their applications in developing different DBR and DFB lasers in Er-doped LiNbO3

waveguides. Single-frequency laser emission has been achieved with a DBR-cavity

comprised of two photorefractive Bragg gratings fabricated in Ti:Fe:LiNbO3waveg-

uide sections [34, 35]. By writing a photorefractive grating in a Ti:Fe:Er:LiNbO3

waveguide section, a DFB-laser/amplifier combination has been developed [36, 37].

Finally, an attractive single-frequency laser has been demonstrated with a DFB-DBR

coupled cavity design [38,39].

It was known from the previous work of Becker et al [20] that an efficient photorefrac-

tive Bragg grating can be fabricated in Ti:Fe:LiNbO3with a grating vector parallel

to the Z-axis (c-axis). To take this advantage, we choose to develop all of our de-

vices with Z-propagating waveguides on X-cut LiNbO3wafers. Since single-mode

Ti:LiNbO3waveguide fabrication is well-established and very good quality waveg-

uides can be fabricated in our group (Prof. W. Sohler, Applied Physics, University

of Paderborn, Germany), the work was mainly concentrated on the optimization of

the fabrication of photorefractive Bragg gratings and the integration of such gratings

with erbium-doped amplifier sections to develop different types of narrow linewidth

lasers. Accordingly, the entire thesis is organized into the following four main chapters.

In Chapter 2, the origin of the photorefractive effect in LiNbO3and the principle of

refractive index grating formation in Fe:LiNbO3are presented, respectively. Besides,

the coupled mode theory allows us to investigate the optical properties of a Bragg grat-

ing without gain (in a Ti:Fe:LiNbO3waveguide) and with gain (in a Ti:Fe:Er:LiNbO3

waveguide). Chapter 3 is dedicated to the fabrication and characterization of three

differently doped waveguides, i.e, Ti:Fe:LiNbO3, Ti:Er:LiNbO3, and Ti:Fe:Er:LiNbO3.

The fabrication and characterization of thermally fixed photorefractive gratings are

discussed in Chapter 4. Finally, in Chapter 5, four different types of DBR and DFB

lasers are described individually with device structure and properties.

Chapter 2

Photorefractive Gratings:

Theoretical Analysis

2.1 Introduction

Photorefractive gratings are generated inside electro-optic crystals upon the incidence

of a periodic light pattern via a “photorefractive effect”. The photorefractive effect

is an optical phenomenon for which the local index of refraction is changed by the

spatial variation of the light intensity. The spatial index variation of the crystal leads

to the distortion of the wavefront of propagating light. Therefore, the photorefractive

effect is sometimes referred as “optical damage”. In fact, this photorefractive optical

damage is a bottle-neck for some of the integrated optical device applications based

on congruently grown LiNbO3crystal [40].

However, the photorefractive effect has shown to be very useful for high density optical

data storage in LiNbO3[41,42]. Utilizing a similar concept as for the case of optical

data storage, integrated optical Bragg gratings have been fabricated in single-mode

LiNbO3waveguides [20,43]. They are proved to be useful in filtering/reflecting light

of very narrow spectral linewidth. Therefore, these integrated optical Bragg gratings

are fabricated and investigated (see Chapter 4) for developing different types of DBR

and DFB lasers in LiNbO3channel waveguides (see Chapter 5). A theoretical discus-

sion is given in this chapter for understanding the origin of the photorefractive effect

in LiNbO3, the principle of Bragg grating formation, and its response properties.

2.2 Photorefractive Effect in Fe:LiNbO3

Although, the photorefractive effect is a common property of all ferroelectric crystals,

it was observed first in LiNbO3during the 1960s [44,45]. Since that time this crys-

tal is widely investigated to learn about the origin of its photorefractive effect. The

mechanisms of this photorefraction in LiNbO3is also known for long time [46].

The origin of the photorefractive effect arises from the migration of optically generated

charge carriers, if the crystal is exposed to a spatially varying pattern of illumination

with photons having sufficient energy. The driving forces of the charge migration or

transport are considered to be (i) photovoltaic effect, (ii) drift, and (iii) diffusion. The

charge transport produces a space charge separation, which then gives rise to a strong

space-charge field. Such a field induces a refractive index change via the electro-optic

(Pockels) effect of the crystal.

It was Glass [46] in 1978, who argued first in details about the existence of a photo-

voltaic effect in bulk LiNbO3. Later on, it was verified experimentally and explained

theoretically that this photovoltaic effect plays the dominant role for the photorefrac-

tive effect in LiNbO3. Kukhtarev et al [47,48] in their two landmark papers studied

the holographic storage exploiting this photorefractive effect using nominally pure

LiNbO3crystal. They also formulated some basic equations and solved them under

different conditions. Their model allows to understand the dynamics of the photore-

fractive effect in all electrooptic materials.

The presence of iron (Fe) impurities in the ppm (<10 ppm) range in nominally pure

LiNbO3crystals plays a key role for its photorefractive properties [49]. The pho-

torefractive sensitivity can be enhanced and/or controlled by additional doping of Fe

in LiNbO3(Fe:LiNbO3). Besides Fe, other divalent transitional metals like Cu, Mn,

Cr, etc., can also create the photorefractive centers when incorporated into LiNbO3.

But, Fe:LiNbO3is found to be very attractive for its higher photorefractive sensitivity.

The photorefractive effect in Fe:LiNbO3is based on three distinguished processes:

(i) photo-excitation of electrons from a deep donor to the conduction band (Nb5+),

(ii) their transport and (iii) subsequently trapping into another photorefractive center.

Once we identify the photorefractive centers then it will be easy to concentrate on the

charge transportation, which is mainly determined by the characteristic photovoltaic

effect and the photoconductivity [50].

There are two valence states of iron, Fe2+ and Fe3+, found to be the active pho-

torefractive centers when the light intensities are not very high (I < 106W/m2) and

2.6< E < 3.1 eV. In this case, no light-induced absorption changes are observed.

For higher light intensities (I > 106W/m2) and higher photon energies (>3.1 eV)

, Nb4+ and Nb5+ in Li+sites, respectively, are produced as additional photorefrac-

tive centers. As a result, light-induced absorption changes are observed [51]. In fact,

(Nb5+)Li and (Nb4+)Li together form a bi-polaron and can be dissociated into small-

polarons in presence of strong light intensities causing the light-induced absorption

changes.

Fe2+

Fe3+

2.6 eV

(Nb )

(O )

Fe2+

Fe3+

(Nb )

(O )

3.1 eV

( a ) ( b )

Fe2+

Fe3+

2.6 eV

(Nb )

(O )

(Nb )

1.6 eV

( c )

Fig. 2.1: Photorefractive centers in Fe:LiNbO3. For the light intensity I < 106W/m2

(a) and (b). For the light intensities I > 106W/m2(c). CB: conduction band, VB:

valence band, e: electron, h: hole, (Nb4+)Li: Nb4+ on Li+sites, (Nb5+)Li: Nb5+ on

Li+sites

Based on the two cases discussed above, the probable charge (electrons/holes) genera-

tion and their transport under the illumination of light with different photon energies

are shown in Fig 2.1. Out of the three situations (a), (b), and (c) described in Fig.

2.1, (a) and (c) exhibit photorefractive effect and are supported by various reported

experimental results. Only the situation of (a) has been considered for this thesis

work because of its practical advantages.

As mentioned, the light-induced charge transport in doped LiNbO3is mainly deter-

mined by the photovoltaic effect [50]. Therefore, photo-illumination causes stationary

currents without any external electric field. The photovoltaic current density −→

jpv was

found to be linear on light intensity Iand hence bilinear in the polarization (unit)

vector −→

eof the light, as pointed out by Belincher et al. [52]:

−→

jpv

i=βijk I−→

ej−→

ek(2.1)

The quantities βijk are components of the photovoltaic tensor. This tensor has four

non-vanishing independent components in the case of LiNbO3which belongs to 3m

point group:

jpv =β31I(e2

x+e2

y)z+β33Ie2

zz+β22I[(e2

y−e2

x)y−2exeyx]+2β15I(exezx+eyezx) (2.2)

The unit vectors ex,ey, and ezdescribe the corresponding axes which are chosen in

accordance with the standard of piezoelectric crystals [53]. However, the photovoltaic

current density along the c-axis can be simplified for ordinary and extra-ordinarily

polarized light:

jpvo =β31Iand jpve =β33I(2.3)

Here oand erefer to ordinary and extraordinary polarization, respectively.

The tensor description of the photovoltaic effects has been confirmed experimen-

tally [54]. Though the largest current densities are obtained along the c- axis, the

current perpendicular to c- axis, which is about an order of magnitude smaller, is

also unambiguously identified by the dependence on the polarization angle. Only the

tensor element β15 could not be obtained by these means because the corresponding

current is modulated on account of birefringence effect. The values of β33 and β31 are

almost comparable whereas the value of β22 is about one order of magnitude less in

comparison. All the photovoltaic tensor elements are found to be linearly depend on

the concentration of Fe2+ and with the photon energy when illuminated with photon

energies between 2 eV(λ∼620 nm) - 3 eV(λ∼412 nm) [55].

A constant dc photocurrent as described by the equation (2.3) was measured along

the c-axis of the crystal when it was uniformly illuminated [50]. This was the first

experimental observation of the unidirectional charge transportation in LiNbO3. Ac-

cordingly, the open circuit photovoltage should be consistent with the following steady

state equation (for ordinarily polarized light):

j=β31I+σpEsat = 0 (2.4)

where σpmeasures the photoconductivity along the c-axis. The measured open circuit

photovoltage:

Esat =β31I/σp(2.5)

is just that required to account for the maximum index change in the same crystal.

The photoconductivity σpis given by σp=neµe, where nis the electron density, eis

the charge, and µeis the mobility of excited electrons in the conduction band. The

density ncan be derived from the rate equation and the equations for constant trap

density assuming charge conservation [56]:

dt =−rnA + (qsI +βth)D,D+A=N,A+n=Nc(2.6)

Here Aand Ddenote the concentrations of the empty (cF e3+ ) and filled (cFe2+ ) traps,

ris the recombination coefficient, qis the quantum efficiency for generating a mobile

electron upon absorption of a photon, sis the absorption cross section, βth is the

thermal generation rate, Nis the total concentration of filled and empty traps and

Ncis a constant concentration of compensation charge to maintain all over charge

neutrality. If space-charge limiting effects and thermal excitations are neglected, we

obtain in equilibrium: n= (qsID)/(rA) and σp∼(ID)/A, i.e., for Fe:LiNbO3,

σp∼cFe2+ /cFe3+ .

2.3 Refractive Index Modulation

by Two-Beam Interference

We have seen in the previous section that a photovoltage is generated under the

illumination of light with suitable photon energy. This photovoltage causes refractive

index change via the electrooptic effect. So, it is straightforward that a periodic

refractive index modulation or an index grating (period = Λ) can be introduced by a

spatially periodic illumination. Such a refractive index grating along the waveguide

axis gives a narrow-band filter response around a Bragg wavelength (λB), similar to

that of fiber Bragg gratings. The explicit expression for the Bragg wavelength can

be derived easily. In fact, the grating vector (|~

KG|= (2π)/Λ) mediates matching

between an input ( ~

Kin) and an output ( ~

Kout) wave:

Kin −~

Kout −~

KG= 0 (2.7)

For the contradirectional Bragg reflection in a waveguide, we have: |~

Kin|=|~

Kout|=

(2πneff )/λBand therefore,

λB= 2Λneff (2.8)

In LiNbO3waveguides, the Bragg response in the communication window (∼1.55

µm) can be achieved by a refractive index grating of periodicity Λ∼350 nm. Such an

intensity distribution of light along the surface of the waveguide can be made either

using a phase mask or the two-beam interference method as shown in Fig. 2.2. We

shall concentrate here only on two-beam interference method because of its practical

flexibility in writing gratings of any specified periodicity (Λ), just by changing the

angle (2θ) between the beams. The resulting period is given by:

Λ=λw

2 sin θ(2.9)

where λwis the writing wavelength of the spatially periodic illumination.

Let us consider the simple situation of two coherent beams which are forming the

interference fringes on the surface of a Ti-indiffused waveguide fabricated on a X-cut

Fe:LiNbO3crystal (see Fig. 2.2). The interference fringes are made parallel to the

Y-axis of the crystal whereas the waveguide propagation direction is parallel to the Z-

axis. The sinusoidal intensity pattern along the waveguide (Z-axis) can be expressed

as:

I(z) = I0(1 + mcos Kz) (2.10)

where the spatial frequency K= 2π/Λ and the modulation depth is m(⩽1). The

dynamic grating formation can be modelled using the basic equations derived by

Kukhtarev et al [47].

+ +

+++

+ +

+++

+ +

+++

+ +

+++

+ +

+++

+ +

+++

+ +

+++

( d )

( c )

( b )

( a )

Effective Index

( n )

eff

Electric Field

( E )

Charge

( )ρ

Light Intensity

( I )

2θ

Interference Beams

π/2

Fig. 2.2: Periodic refractive index modulation along the waveguide parallel to the

Z-axis of the crystal by the surface illumination two-beam interference pattern; (a)

sinusoidal spatial light intensity distribution, (b) resulting sinusoidal space-charge

distribution, (c) sinusoidal spatial electric field and (d) sinusoidal refractive index

modulation

According to the spatially periodic illumination, we can write down the zdependance

of the evolved photoconductivity σpand of the free electron density n, respectively:

σp(z) = σp0(1 + mcos Kz) (2.11)

n(z) = n0(1 + mcos Kz) (2.12)

where σp0and n0have constant values. If we define the space charge field generated

by the photovoltaic effect as Esc(z, t), then the current density along the Z-axis obeys

the following relation:

je(z, t) = eDe

∂n(z)

∂z + (σp+σd)Esc(z, t) (2.13)

Here, De= (µekBT)/e is the diffusion constant and σdthe dark conductivity. The

time dependence of Esc(z, t) is derived using the continuity and Poisson’s equations,

considering small diffusion length i.e rdK−1[55]:

Esc(z, t) = kBTm0Ksin Kz

e(1 + m0cos Kz)1−exp −[σp(z) + σd]t

0 (2.14)

where m0=m/(1 + σd/σp0), the static dielectric constant, kBthe Boltzman’s

constant, Tthe temperature. For a special case when σdσp0,m1 and t→ ∞,

equation (2.14) becomes:

Esc(z, t) = kBT

emK sin Kz (2.15)

As a consequence of the periodic space charge field, the refractive index change

for the ordinarily polarized light beams due to the Pockel’s effect is:

∆no(z, t) = −1

2n3

effor13Esc(z, t) (2.16)

Here, neffo is the ordinary effective refractive index of the waveguide and r13 the cor-

responding electrooptic coefficient. It is clear from equations (2.10) and (2.16) that

the refractive index pattern is phase shifted by π/2 with respect to the light intensity

distribution as shown in Fig. 2.2.

Sometimes, the light induced refractive index changes may be characterized by the sat-

uration value, ∆ns, of the refractive index change and the sensitivity S=d(∆n)/(d(It)|t=0

at the beginning of illumination. These quantities are approximated by the following

expressions [57]:

∆nso =1

effor13mβ31I

σp

(2.17)

and

S=1

effor13mβ31

0

(2.18)

2.4 Thermal Fixing and Developing

At room temperature a periodic illumination (along the waveguide) with light of a

wavelength within the absorption band of Fe2+ ions (λp= 470 nm) modulates the

concentration of Fe2+ (Fe3+) ions. This is possible by the transportation of excited free

electrons from the brighter regions to the darker ones mainly due to the photovoltaic

effect, which dominates along the optical-axis. In this way an index grating is induced

by the periodic electronic charge distribution via the electrooptic effect. However, this

type of index grating is volatile; it decays with time when the periodic illumination is

removed. Therefore, holographic writing is normally done at elevated temperatures

(∼180 oC) to get a higher proton mobility leading to an ionic compensation of the

original electronic space charge distribution. (H+ions are usually induced in LiNbO3

during crystal growth. However, its concentration can be enhanced by wet annealing

of the crystal in a reducing ambient.) After fast cooling to room temperature, a uni-

form illumination helps to redistribute the electrons homogeneously. Consequently,

an ionic grating remains inducing a phase-shifted replica of the index grating of the

original electronic space charge. This type of refractive index grating is called a“fixed

grating”. This thermal fixing technique was invented by Amodei et al in 1971 [41]

and the role of H+was confirmed by Vormann et al in 1981 [58]. In Fig. 2.3, the

mechanisms of thermal fixing are shown schematically.

Now, we will analyze mathematically the thermal fixing mechanisms at the fixing

temperature Tfunder the periodic illumination as defined in Equn. (2.10) [59]. In

this case we have to consider both types of charge transportation i.e., electrons and

protons. The rate equations for the donors D(here Fe2+), the acceptors A(here

Fe3+), the free electrons nand the protons Hfrom equation (2.5):

−∂D

∂t =∂A

∂t = (βth +qsI)D−rnA (2.19)

∂n

∂t = (βth +qsI)D−rnA +1

∂je

∂z (2.20)

−∂H

∂t =∂jh

∂z (2.21)

In the above equations the current densities jeand jhare given by:

je=eµenE +Dee∂n

∂z −β31ID (2.22)

jh=eµhnE −Dhe∂H

∂z (2.23)

where Deand Dhare the diffusion constants electrons and protons, respectively.

The steady distributions of donors, acceptors and protons can be written under the

condition of m << 1 in Equn. (2.10):

D=D0+Mscos (Kz +φ) (2.24)

Fe2+ Fe2+

Fe3+

e-e-

Eel Eel

Fe2+ Fe2+

Fe3+

e-e-

Eel Eel

H-

EHEH

Fe2+

Fe3+

e-e-

Eel Eel

EHEH

Fe3+

( a )

( b ) ( c )

Fig. 2.3: Mechanisms of the photorefractive grating formation; (a) electronic grating

at room temperature, (b) electronic and H+grating at fixing temperature (say, ∼

180 oC) and (c) development of fixed H+grating. Eel and Eion are the electric fields

generated by electronic and H+grating, respectively.

A=A0−Mscos (Kz +φ) (2.25)

H=H0−hscos (Kz +φ) (2.26)

where D0,A0and H0are the initial concentrations of donor, acceptor and proton,

respectively. Using three equations (2.24), (2.25) and (2.26) in the material equations

for steady state (i.e., ∂je/∂z = 0 and ∂jh/∂z = 0), the expressions for Msand hsare

determined and they are related by:

hs=Ms

1+(kBT/e2)(K2/H0)(2.27)

To develop the proton grating formed during the fixing process, the surface of the

waveguide must be illuminated homogeneously at or near room temperature. The

final charge (proton) density amplitude after development is deduced as [59]:

ρd=hse

1+[e2/(βkBTK2)] (2.28)

with β= 1/A0+1/D0. Thus the amount of proton grating that is developed as charge

grating depends on the donor and acceptor concentrations i.e., on βand the grating

spacing Λ= (2π)/K. Accordingly, the amplitude of the sinusoidal refractive index

modulation along z-coordinate is:

∆no=1

2n3

effor13hse

K{1 + e2/(βkBTK2)}(2.29)

It is to be noted that the refractive index modulation suffers a slow compensation due

to the electronic dark conductivity (σd) in the absence of uniform illumination. How-

ever, continuous uniform illumination of lower intensity light (I∼100 mW/cm2and

λ∼470 nm) can keep refreshing the proton grating for permanent device applications.

2.5 Grating Response:

Coupled Mode Theory Analysis

Once the refractive index modulation is done along the surface of Ti-indiffused chan-

nel waveguide (see Fig. 2.4), coupled mode theory can be used to model the interac-

tions between the grating structure and the guided modes [60]. From the theory, we

learned that periodic refractive index perturbation causes the energy transfer among

the modes. In particular, in a single-mode waveguide with a refractive index mod-

ulation discussed in the previous sections, the energy transfer happens between the

forward- and backward propagating waves of identical polarization (TE TE or TM

TM). In this case, energy can not be transferred between the modes of orthogonal

polarizations (TE 6TM), although, a single-mode waveguide is capable of guiding

both the polarizations (TE and TM). So, it is sufficient to limit the discussion to one

polarization (say, TE-polarization) for analyzing the grating properties.

The electric field of the forward- and backward propagating waves, ~a(x, y, z, t) and

b(x, y, z, t), respectively, can be represented by:

~a(x, y, z, t) = A(z)φa(x, y)ei(ωt−βaz)~ey(2.30)

b(x, y, z, t) = B(z)φb(x, y)ei(ωt+βbz)~ey(2.31)

Here, A(z) and B(z) are the z-dependent amplitudes of the forward- and backward

propagating waves, respectively. φa(x, y) = φb(x, y) represent the field amplitude

distribution in the x-y plane and they can be derived from the intensity distribution

Waveguide

Photorefractive grating

c - axis

z = 0 z = L

Fig. 2.4: Schematic structure of a Ti-indiffused optical waveguide with a photorefrac-

tive grating of length Lon the surface of a X-cut LiNbO3crystal; the waveguide and

the grating vector ~

Kare parallel to the Z-axis (c-axis).

which is approximately Hermite-Gaussian along the x-axis and Gaussian along the

y-axis according to the configuration sketched in Fig. 2.4 [61–65]. The magnitudes of

the propagation constants are the same for the forward- and backward propagating

waves, i.e., |βa|=|βb|=β= (2πneffo)/λ. Two counter propagating modes described

by equations (2.30) and (2.31) are coupled via two differential equations [60]:

dz =−iκBe−i∆βz (2.32)

dz =iκAei∆βz (2.33)

where the coupling coefficient κis approximated by:

κ=π∆no

λ(2.34)

and

∆β = 2β−2π

Λ(2.35)

The solutions for A(z) and B(z) with the boundary condition B(L) = 0 are given

by [60]:

A(z) = A(0)sκcosh{sκ(L−z)}−i∆β

2sinh{sκ(L−z)}

sκcosh(sκL)−i∆β

2sinh(sκL)e−i∆β

2z(2.36)

B(z) = A(0)−iκ sinh{sκ(L−z)}

sκcosh(sκL)−i∆β

2sinh(sκL)ei∆β

2z(2.37)

Wavelength [nm]

1549.6 1550.41550.0 1550.21549.8

Reflectivity

0.0

1.0

0.6

0.2

0.4

0.8

κ.L = 2.2

κ.L = 1.2

κ.L = 0.7

0.0 10.04.0 6.02.0 8.0

z [mm]

Forward wave

Backward wave

( a ) ( b )

Intensity [a.u.]

0.0

1.0

0.6

0.2

0.4

0.8

Fig. 2.5: Calculated grating response using coupled mode theory. (a) The reflectivity

spectrum as a function of wavelength with κL as parameters and Λ= 350 nm. (b)

The intensity evolutions of the forward- and backward propagating waves inside the

grating section when ∆β = 0. κ: 1.2 cm−1,L: 1 cm.

with s2

κ=κ2−(∆β/2)2. It is to be pointed out here that the above two equations

are valid only in the waveguide region where the refractive index grating exists, i.e.,

0⩽z⩽L. Hence, the expression of reflectivity is given by:

R=

B(0)

A(0)

=κ2sinh2(sκL)

κcosh2(sκL) + ∆β

22sinh2(sκL)(2.38)

From the above equation, it is evident that the reflectivity becomes maximum if

∆β = 0 which is the condition of Bragg reflection and the corresponding Bragg

wavelength λBcan be deduced from the equation (2.35):

λB= 2Λneffo (2.39)

The calculated reflectivity spectrum and intensity evolutions are plotted in Fig. 2.5.

The results correspond to the effective refractive index neffo = 2.21, a grating period

Λ= 350 nm and κL as parameters. The reflectivity spectrum shows that there are

some sidelobes around the actual Bragg response. The spectral spreading centered to

the Bragg response is given by:

δλBragg =2λBraggΛ

πsπ

L2

+κ2(2.40)

In fact, by choosing appropriate values of the grating length Land the z-dependent

functions Λ=Λ(z) and κ=κ(z), one can modify the Bragg response spectrum ac-

cording to the requirements [66].

Up to now we have discussed the properties of the passive gratings fabricated in

Ti:Fe:LiNbO3waveguides, i.e., without gain. We will see later on, these gratings have

been used to develop the integrated optical DBR-lasers. But, the photorefractive

gratings could be fabricated also in Ti:Fe:Er:LiNbO3waveguides. Presence of erbium

atoms in the grating section is helpful to achieve distributed feedback gain. There-

fore, DFB laser oscillation can also be demonstrated if sufficient gain and distributed

feedback provided. In this case, the frequency dependent reflectivity of light Rcan

be derived also using coupled mode theory [32]:

R(g, ν) = 

iκ sinh(γL)

iγ cosh(γL)−{δ+i(g−α)}sinh(γL)

(2.41)

where, γ=pκ2+{(g−α)−iδ}2,δ= [2πneffo(ν−νB)] /c,νthe linear frequency,

νBthe frequency corresponding to the Bragg condition, αthe scattering loss coeffi-

cient, and gthe gain coefficient. From equation (1.39), we note that the oscillation

frequencies of a DFB-laser are determined by the condition:

iγ cosh(γL)−{δ+i(g−α)}sinh(γL)→0 (2.42)

For an example, the reflection contours of a DFB-structure of length L= 1.8 cm

0.5

2.5

100

-10 -5 0 5 10

ν − ν0[GHz]

Gain [dB/cm]

gth

Fig. 2.6: Contours of constant reflectivity of a DFB laser structure, as a function

of gain and frequency deviation from the Bragg condition. DFB-structure evaluated

from coupled mode theory. For a length L= 1.8 cm and uniform coupling strength

κ= 0.85 cm−1, the threshold gain gth ≈4 dB/cm and ∆ν ≈8 GHz for the two lowest

order DFB-modes. Waveguide loss is assumed to be 0.2 dB/cm.

and uniform coupling coefficient κ= 0.85 cm−1, have been plotted in the plane of

{g, (ν−νB)}in Fig. 2.6. The threshold gain (gth) and the frequency separation (∆ν)

of the two lowest order DFB-modes are estimated to be ∼4 dB/cm and ∼8 GHz,

respectively.

2.6 Conclusions

In this chapter, the origin of the photorefractive effect, the principle of the Bragg

grating formation, and their response properties (reflection and transmission) in both

passive Ti:Fe:LiNbO3and laser-active Ti:Fe:Er:LiNbO3waveguides have been dis-

cussed theoretically.

The origin of the photorefractive effect in LiNbO3has been analyzed by considering

only the Fe-impurities in the crystal. The principle of photorefractive Bragg grating

formation in the waveguides by surface illumination with two beam interference pat-

tern (holographic exposure) has been described.

As the photorefractive effect is a reversible phenomenon, i.e., the periodic (electron)

space-charge field created during the illumination decays after the withdrawal of the

illumination. This seems to be an issue for some practical applications. However,

a spatially Λ/2 -shifted periodic (proton) space-charge field can be generated simul-

taneously by a thermal fixing method for permanent use of the grating structure.

Therefore, the mechanisms of the thermal fixing process have also been described.

Finally, the coupled mode theory is outlined to analyze the grating properties. The

reflection characteristics of a photorefractive Bragg grating in a passive Ti:Fe:LiNbO3

waveguide have been obtained numerically. From the theoretical characteristics it is

predictable that a photorefractive grating of length 1 cm could provide a peak reflec-

tivity of >90% and spectral bandwidth of <80 pm if sufficient dose of a holographic

exposure is given.

The reflection characteristics of a photorefractive grating in a laser-active Ti:Fe:Er:-

LiNbO3waveguide have also been investigated numerically. The results predict that

an integrated optical DFB laser in Ti:Fe:Er:LiNbO3can be developed if sufficient gain

is provided (∼4 dB/cm).

Chapter 3

Doped Waveguides: Fabrication

and Characterization

3.1 Introduction

In the previous chapter, we have seen from numerical simulations that distributed

Bragg gratings can be realized in Fe-doped LiNbO3waveguides. Such a gratings in

a passive Ti:Fe:LiNbO3waveguide section can be used either as narrowband wave-

length filters or reflectors for integrated optical circuits. The presence of Er3+ in a

Ti:Er:LiNbO3(or in a Ti:Fe:Er:LiNbO3) waveguide can provide the optical gain in

the emission band of 1.53 µm< λ < 1.62 µm [67–69].

Therefore, monolithic integration of a photorefractive Bragg grating in Fe-doped

waveguide section and a laser-active Er-doped waveguide section has been investi-

gated under the scope of this thesis work. Five different types of samples have been

prepared, investigated (see Fig. 3.1), and later on they are used to develop different

types of DBR and DFB lasers (see Chapter 4 and Chapter 5). In this chapter, we will

concentrate on the sample preparation by diffusion doping of Er and Fe, waveguide

fabrication by indiffusion of photolithographically defined Ti-stripes and finally, the

necessary characterizations.

3.2 Fabrication

Optical grade X-cut LiNbO3crystals of 1 mm thickness have been used for the fab-

rication of different types of doped waveguides. The waveguides have to be aligned

parallel to the Z-axis to exploit the highest photovoltaic coefficients (β31 or β33); that

facilitates the fabrication of the photorefractive gratings with grating vectors along

the same axis (Z).

For developing our four different types of DBR and DFB lasers (see Chapter 5),

Ti-indiffused waveguide Er:LiNbO3Fe:LiNbO3Fe:Er:LiNbO3

Sample Er-diffusion Fe-diffusion Ti-diffusion

Pb874xz

Pb106xz

Pb107xz

Pb145xz, Pb150xz

43 mm 27 mm

50 mm 15 mm15 mm

30 mm 20 mm

50 mm 15 mm

Thickness: 15 nm

T : 1120 °C

t : 120 h

diff.

Thickness: 19 nm

T : 1130 °C

t : 120 h

diff.

Thickness: 19 nm

T : 1130 °C

t : 120 h

diff.

Thickness: 20 nm

T : 1130 °C

t : 140 h

diff.

Thickness: 37 nm

T : 1060 °C

t : 72 h

diff.

Thickness: 32 nm

T : 1060 °C

t : 72 h

diff.

Thickness: 41 nm

T : 1060 °C

t : 72 h

diff.

Thickness: 33 nm

T : 1060 °C

t : 72 h

diff.

Thickness: 97 nm

Width: 8 m

T : 1060 °C

t : 7.5 h

diff.

Thickness: 100 nm

Width: 7 m

T : 1060 °C

t : 7.5 h

diff.

Thickness: 100 nm

Width: 7 m

T : 1060 °C

t : 7.5 h

diff.

Thickness: 100 nm

Width: 7 m

T : 1060 °C

t : 7.5 h

diff.

Pb66xz

30 mm

16.5 mm 16.5 mm Thickness: 40 nm

T : 1060 °C

t : 72 h

diff.

Thickness: 97 nm

Width: 7 m

T : 1060 °C

t : 7.5 h

diff.

No erbium

Fig. 3.1: Five different types of representative samples with their doping parameters.

a combination of any two types out of the three differently doped single-mode waveg-

uides, i.e. Ti:Er:LiNbO3, Ti:Fe:LiNbO3, and Ti:Fe:Er:LiNbO3have been used. It will

be evident afterwards that the Er is indiffused to create the laser-active medium, Fe

to create photorefractive centers, and Ti to create guiding channels. That means,

selective dopings of Er, Fe, and Ti (photolithographically defined) are prerequisites.

The easiest and most suitable way for selective doping of Er is thermal indiffusion [70].

Fe is also chosen for thermal indiffusion for its selective doping. For waveguide fabri-

cation in LiNbO3, two standard techniques are generally established; they are the pro-

ton exchange method and the method of Ti-indiffusion. Proton exchanged waveguides

have a lower photorefractive sensitivity (because the electrooptic effect is reduced),

higher scattering losses and can support only one polarization (extraordinary) of light.

They are often used in nonlinear optical devices to take advantage of the lower pho-

torefractive damage due to the second harmonics in the visible region. But, due

Fe - deposition: 30 - 40 nm

Er - deposition: 15 - 20 nm

Er - diffusion

T = 1130 C, t ~ 130 hrs

Fe - diffusion: T = 1060 C, t = 72 hrs

Ti - deposition: ~100 nm

7 m-wide Ti-stripe definition by photolithographyµ

Ti - diffusion: T = 1060 C, t = 7.5 hrs

X-cut LiNbO3

Ti:Er:LiNbO3

X-cut LiNbO3X-cut LiNbO3

Annealing: T = 500 C, t = 5 hrs

Ti:Fe:Er:LiNbO3

Ti:Fe:LiNbO3

Fig. 3.2: Flow chart for the fabrication of the three different types of waveguides used

for the laser development with fabrication parameters.

to higher scattering losses and guiding in only extraordinarily polarized light, these

waveguides are disadvantageous for other integrated optic applications. Additionally,

the proton-exchanged Er-doped LiNbO3waveguides are not suitable for lasers because

there is an extreme reduction of the radiative lifetime of the 4I13/2→4I15/2transi-

tion of Er3+. In comparison, Ti-indiffused waveguides have lower scattering losses

(<0.2 dB/cm), unchanged electrooptic properties, reasonably high radiative life-time

of Er3+ (∼2.6 ms for 4I13/2→4I15/2), and can support both polarizations of light.

Therefore, Ti-indiffused waveguides are preferably used for this work.

All the dopants, Er, Fe, Ti are incorporated one after another by thermal indiffu-

sion well below the Curie temperature of LiNbO3(Tc∼1140 oC) in the pre-defined

locations of the sample surface. The diffusion depth and concentration profile of the

individual dopants can be estimated from the diffusion theory of solids [71]. The

theoretical depth concentration profile relevant to the parameters used for a specific

dopant is given by:

c(x, t, D, d) = ρNAd

m√πDte−x

2√Dt 2

(3.1)

where ρis the density of the deposited film, dthickness, mthe molecular mass, NA

the Avogadro number and Dthe diffusion coefficient.

The above equation is valid for a diffusion time ttd, where tdis the time by

which the deposited film just exhausted and entered into the surface layer of the crys-

tal during thermal indiffusion. As the diffusivity of Er is lowest, we have to indiffuse

Er first, followed by Fe and Ti. In the following, the fabrication steps of differently

doped waveguides are discussed in some more details (see Fig. 3.2).

3.2.1 Er-Diffusion Doping

To achieve a pre-defined Er-concentration profile, the knowledge of diffusion coeffi-

cients for the relevant temperatures is needed. Therefore, thin films of metallic Er

were indiffused into the surface of X-cut LiNbO3crystals at different temperatures and

for different durations [70]. The depth profiles of the Er-concentration were obtained

either by secondary ion mass spectroscopy (SIMS) or by secondary neutral mass spec-

troscopy (SNMS) (see Fig. 3.3a). From these profiles the diffusion coefficients were

determined and plotted versus the reciprocal diffusion temperature 1/T (Arrhenius

plot, see Fig. 3.3b). From this plot an activation energy of 2.44 eV and a diffusion

constant of 12 ×10−5cm2/s were evaluated. All these results predict that the surface

concentration of Er can be as high as 2.2×1020 cm−3(limit of solid solubility), if the

diffusion is carried out at 1130 oC.

The optimum diffusion parameters for developing our different types of DBR and

DFB lasers have been deduced from the above results. Planar metallic film of Er of

a: T = 1060°C (SIMS)

b: T = 1100°C (SIMS)

c: T = 1130°C (SNMS)

diff

From SNMS mesurements

From SIMS mesurements

( a ) ( b )

Temperature (°C)

2.5

2.0

1.5

1.0

0.5

0.00 1 2 3 4 5 6

Depth [ m]µ

C [x10 cm ]

20 -3

10-12

10-13

10-14

10-15

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4

1130 1100 1060 1010 960 920

1/T [x10 K ]

-4 -1

Temperature [°C]

Diffusion Coefficient [cm /s]

Fig. 3.3: (a) Erbium doping profiles by thermal indiffusion in X-cut LiNbO3crystals,

and (b) Arrhenius plot of the diffusion coefficients of erbium perpendicular to the

c-axis (along the X-axis) [70].

thickness ∼20 nm is indiffused at 1130 oC during ∼140 h (depending on the corre-

sponding thickness). This yields a nearly Gaussian concentration profile of 1/e depth

of ∼4.5µm. The corresponding surface concentration of Er is ∼2.0×1020 cm−3.

These results generate a good overlap of the Er-concentration profile with the Ti-

indiffused waveguide to be fabricated later.

The standard deposition and diffusion processes developed earlier in our laboratory

have been utilized. Metallic Er is e-beam evaporated at a rate of 0.1 nm/s and a pres-

sure of 1.5×10−7mbar. After the deposition, thermal diffusion is carried out inside

a quartz tube with flowing argon (1 litre/min), keeping the sample inside a plat-

inum box. During the cooling down process, oxygen gas flows (1 litre/min) through

the tube to compensate the oxygen deficiency underneath the sample surface which

occurs during diffusion process.

3.2.2 Fe-Diffusion Doping

The Fe diffusion parameters were also measured in a similar experimental investigation

as has been done for Er. The diffusion coefficient of Fe is determined by the indiffu-

sion of metallic Fe layers into X-cut LiNbO3. Two different Fe:LiNbO3samples were

prepared (with the collaboration of the group of Prof. E. Kr¨

atzig, University of Os-

nabr¨

uck, Germany), with different diffusion parameters (sample1 (XFe1): Fe-thickness

- 171 nm, diff. temp. - 1060 oC, diff. time - 3 h; sample2 (XFe2): Fe-thickness - 30

nm, diff. temp. - 1060 oC, diff. time - 3 h;). For the sample1 the vacuum deposited

metallic Fe-layer of a thickness of 171 nm represents a dopant source, which could

not be exhausted during the relatively short diffusion time of 3h. Therefore, an erfc-

concentration profile is expected from diffusion theory. On the contrary, in case of

sample2, the metallic Fe-layer of 30 nm thickness was completely indiffused into the

crystal surface layer. Hence, a nearly Gaussian concentration profile was expected.

Meas.

Fit erfc curve

Meas.

Fit Gaussian curve

0510 15 20 25 30

0.0

0.5

1.0

1.5

2.0

0.00

0.05

0.10

0.15

0.20

0.25

Depth [ m]µDepth [ m]µ

Concentration [at%]

( a ) ( b )

Fig. 3.4: The depth profiles of Fe atoms of the samples XFe1(a) and XF e2(b)

The Fe concentration profiles (depth) of both samples were measured using SNMS

(measurements were performed in collaboration with the group of Prof. M¨

uller,

Soest); they are presented in Fig. 3.4 together with calculated results using the

diffusion coefficient as fitting parameter. As expected an erfc-profile and a Gaussian

distribution were obtained. From the comparison of the calculated and fitted results,

a diffusion coefficient at 1060 oC of 3.85 ×10−11 cm2/s was obtained.

Based on the above investigations, we have determined our optimum Fe-diffusion

parameters suitable for both LiNbO3and Er:LiNbO3samples (assuming same diffu-

sion coefficients in both cases). Usually, a vacuum-deposited planar metallic Fe film

of thickness ∼35 nm has been indiffused at 1060 oC during ∼75 h (depending on the

thickness). The resultant Fe-concentration has a Gaussian profile. The corresponding

diffusion depth (1/e) and surface concentration are calculated to be ∼40 µm and

∼6×1019 cm−3, respectively.

We have setup a special e-beam evaporation system and a diffusion furnace dedicated

for preparing only the Fe-doped samples. First, the metallic Fe-layer is deposited on

the sample surface at a rate of ∼0.5 nm/s and at a pressure of ∼2.5×10−6mbar.

Afterwards, the indiffusion is carried out in the furnace in flowing argon (1 litre/min),

keeping the sample inside a platinum box. During the cooling down, oxygen gas flows

(1 litre/min) through the tube to compensate the oxygen deficiency underneath the

sample surface which occurs during the diffusion process.

3.2.3 Fabrication of Ti-Indiffused Waveguides

Fabrication of a Ti-indiffused LiNbO3waveguide is a well established technique for

a long time in our laboratory. The same Ti-indiffusion technology has been used

for fabricating waveguides in Er:LiNbO3, Fe:LiNbO3, and Fe:Er:LiNbO3. Same Ti

indiffusion parameters can be used for all the three cases for single-mode waveguide

fabrication.

First, a 100-nm-thick planar film of metallic Ti is vacuum deposited on the sam-

ple surface using an e-beam evaporation system at the rate of ∼1 nm/s and at a

pressure of ∼2.6×10−7mbar. Afterwards, about 1-µm-thick positive photoresist

was spin-coated uniformly over the Ti-film. The sample is then baked (pre-baking)

at 90 oC for 30 min. After masking (parallel stripes of 7-µm-width along Z-axis), a

photolithographic exposure is given for 18 sec (UV-light λ= 312 nm). Post-baking

is done at 120 oC for the duration of 45 min and then the sample is developed with

a commercial developer (OPD5280) for 60 sec. The unwanted Ti-layer is etched by

using EDTA (Ethylene Di-amino Tetra-acetic Acid) for the duration of 12 min at 30

oC. In this way, 7 µm wide Ti-stripes parallel to the Z-axis are prepared. The residual

photoresist on top of the Ti-stripe is removed with acetone followed by rinsing with

deionized water. Finally, the thermal diffusion process is carried out at 1060 oC for

7.5 h, inside a furnace in argon flow (1 litre/min), keeping the sample in a platinum

box. During cooling down of the furnace, oxygen gas flows as usual (1 litre/min) to

compensate the oxygen deficiency underneath the sample surface which occurs during

the indiffusion process.

3.2.4 Annealing

The photorefractive sensitivity of the sample is controlled by the subsequent anneal-

ing treatment in a proper ambient. This treatment helps to control the concentra-

tions of Fe2+ (cFe2+ ) and Fe3+ (cF e3+ ). It is found from the theory that the ratio of

(cFe2+ )/(cFe3+ ) should be 0.1 or above to be able to fabricate a photorefractive Bragg

grating efficiently [72].

We also observed in our experiments that annealing in a reducing atmosphere en-

hances the photorefractive sensitivity, because it increases cFe2+ . Therefore, an op-

timized annealing treatment of the sample is done in a reducing atmosphere (Ar, 1

litre/min) at 500 oC for the duration of ∼3−6 h. Furthermore, the flowing argon

is bubbled through water at 80 oC to increase the concentration of H+in the sample,

which is needed for the creation of a fixed grating [73].

The above annealing process does not influence the waveguide losses. This is con-

firmed experimentally by measuring the waveguide losses (see next section) before

and after the annealing process.

3.3 Characterization

After the diffusion doping steps and the annealing process described in the previ-

ous section the optical properties such as waveguide losses, mode size, wavelength

dependent absorption and gain, and the amplified spontaneous emission (ASE) are

characterized.

3.3.1 Waveguide Loss and Mode-Size

The waveguide loss is measured by analyzing the low-finesse Fabry-Perot resonances as

shown in Fig 3.5. The polished end faces of a passive waveguide i.e, either Ti:LiNbO3

or Ti:Fe:LiNbO3forms a low-finesse Fabry-Perot cavity. The cavity is tuned by in-

creasing the temperature of the sample as a function of time. A highly coherent

single-frequency laser light at λ∼1550 nm ( either from single-mode He-Ne laser

or from an external cavity laser) is launched into the waveguide and the output is

detected using an InGAs photodiode. The time-dependent output from the detector

is recorded by a computer and the waveguide losses (mainly scattering loss) are easily

evaluated from the data [74]. Typical waveguide losses of a Ti:Fe:LiNbO3waveguide

are about 0.15 dB/cm (nearly polarization independent).



He-Ne Laser

(632 nm)

Single-mode Laser

(~1550 nm)



Heater

Ti:Fe:LiNbO waveguide

Polarizer

Partial mirror

Mirror

Lens (10X)

Detector

Shutter

Multimeter

010 20 30 40 50 60 70

0.0

0.3

0.6

0.9

1.2

Time (s)

Intensity (a.u.)

Fig. 3.5: Schematic diagram of the loss measurement setup utilizing the low-finesse

Fabry-Perot contrast method.

He-Ne Laser

(632 nm)

EDFA ASE source

(~1550 nm)



Sample

Polarizer

Partial mirror

Mirror

Lens (10X)

IR Camera

Shutter

5 nm BPF Lens (100X)

Vedio

Fig. 3.6: Schematic diagram of the setup to measure the mode intensity profiles. BPF:

band pass filter, IR: infrared, EDFA: erbium doped fiber amplifier, ASE: amplified

spontaneous emission

The scattering loss of a Ti:Er:LiNbO3or Ti:Fe:Er:LiNbO3waveguide is estimated

by subtracting the total losses (measured by the above mentioned method) and the

absorption due to Er3+ (measurement to be discussed latter).

The mode-size of guided light is determined by measuring the near-field intensity

distribution at the output end of the waveguide. In this case light from an incoherent

amplified spontaneous emission (ASE) of an erbium doped fiber amplifier (EDFA) is

filtered by a band pass filter (BPF) and launched into the waveguide. The purpose of

using an incoherent light source is to avoid unwanted interferences. The output near-

field pattern of the guided mode is magnified (100X) and imaged on to an infrared

(IR) camera. The measured intensity profile confirms its single-mode properties. The

typical polarization independent (nearly) mode-size (1/e full width) was measured

to be ∼7.5µm (along X-axis, Gaussian profile) ×4.5µm (along Y-axis, Hermite-

Gaussian profile) which is close to the mode-size of a standard single-mode fiber used

in the communication systems (see Fig. 3.6).

3.3.2 Absorption and Gain

All optical transitions of Er3+ ions in an Er:LiNbO3crystal were experimentally ob-

served long time ago (see Fig. 3.7) [75]. The most interesting transitions occur

between the ground state (4I15/2) and the first excited manifold (4I13/2); the absorp-

Energy [ X 1000 cm ]

-1

4F7/2

4I15/2

4I13/2

4I11/2

4I9/2

4F9/2

4S3/2

2H11/2

1.53 - 1.64 mµ

1.48 mµ

0.66 mµ

0.55 mµ

1.48 mµ

1.64 mµ

0.5

7.0

Energy [ X 1000 cm ]

-1

6.5

1.48 mµ

1.53 mµ

1.64 mµ

4I15/2

4I13/2

( a ) ( b )

4F5/2

4F3/2

4F9/2

4G11/2

1.64 mµ

0.39 mµ

Fig. 3.7: (a) Erbium energy level diagram after Gabrielyan [75] with possible transi-

tions if it is excited by λ= 1.48 µm and (b) enlarged part of the diagram with the

lower laser level 4I15/2and the upper laser level 4I13/2. The energy scale is given in

reciprocal wavelengths (cm−1) as usual for spectroscopy.

tion/emission band (1.42 µm< λ < 1.64 µm) is well-matched to the communication

wavelengths (centered at ∼1.55 µm). The fluorescence lifetime of the 4I13/2-level

was measured to be ∼2.6 ms [76]. Due to the strong crystal field the (4I15/2) and

(4I13/2) levels are splitted into manifolds with 8 and 7 closely spaced energy lev-

els, respectively. At room temperatures these energy levels are occupied according

to the Boltzman’s distribution law. With a proper pumping a population inversion

can be created between the levels (4I15/2) and (4I13/2) to exhibit a quasi two-level

laser systems. However, if there is a population inversion between the levels (4I15/2)

and (4I13/2), there are possibilities of excited state absorptions (see upwards pointing

dashed arrows in Fig. 3.7). As a result, fluorescence can also be observed in the wave-

length ranges ∼660 nm, ∼550 nm, and ∼390 nm (see downwards pointing dashed

arrows in Fig. 3.7).

The wavelength dependent absorption and emission cross-sections were measured



Sample

Monochromator

Pump ( = 1480 nm)λp

Pol. Cntrl.

WDM

PBS

( = 1420-1620 nm)λs

LED driver

(mod. current source) Lock-in-amplifier

Stepper motor

Signal light

Detector

LED

WDM

Residual pump ( = 1480 nm)λp

Fig. 3.8: Schematic diagram of the absorption/gain measurement setup. PBS: polar-

ization beam splitter, Pol. Cntrl.: polarization controller, LED: light emitting diode,

WDM: wavelength division multiplexer.

with α-polarized light (E,B⊥c-axis and kkc-axis) in a bulk Er-doped LiNbO3

crystal [77]. The absorption cross-sections at λ < 1.53 µm are clearly higher than

the emission cross-section, whereas for λ > 1.53 µm the situation is reversed. At λ∼

1.53 µm, both the absorption and emission cross-sections are almost equal. Therefore,

it is worth to mention here that optical gain can be easily achieved in the region of

1.53 µm< λ < 1.62 µm if an Er-doped waveguide is pumped at λ= 1.48 µm, where

the absorption cross-section is relatively high. Absorption and gain of our Er-doped

waveguides (either Ti:Er:LiNbO3or Ti:Fe:Er:LiNbO3) have been investigated using

the experimental setup schematically shown in Fig. 3.8.

The absorption was evaluated from the measured transmission of the waveguide. A

low-power near-infrared light emitting diode (LED) has been used as a broadband

light source. The input signal light was electronically modulated and the output from

the waveguide was detected by a Lock-in-technique. Both the TE and TM polariza-

tion of lights showed similar characteristics due to Z-propagation (α- polarization)

of the guided mode. Fig. 3.9a shows the absorption characteristics of a 5 cm long

Ti:Er:LiNbO3waveguide for TE polarization (sample: Pb106xz). At λ∼1480 nm

(used as pump for our laser operations), the absorption is -7 dB.

For gain measurements the pump light (λp= 1480 nm) is coupled to the waveg-

uide by using a wavelength division multiplexer (WDM) (see Fig. 3.8). Sufficient

pump light creates a population inversion inside the waveguide and hence any sig-

nal light (1.53 µm<λ<1.62 µm) can be amplified. The gain characteristics were

measured in the same 5 cm long Ti:Er:LiNbO3waveguide (sample:Pb106xz). At 85

mW of coupled pump power, a peak gain of about 7 dB at 1531 nm (and ∼3 dB

at 1561 nm) wavelength was achieved (see Fig. 3.9b); both, pump and signal were

TE-polarized. There were only small differences in the gain characteristics for other

combinations of the polarization of pump and signal.

Ti:Er:LiNbO3

( a ) ( b )

Fig. 3.9: (a) Absorption spectrum of a Ti:Er:LiNbO3waveguide and (b) gain spectrum

for 85 mW coupled pump power (λp= 1480 nm); waveguide length: 5 cm, pump:

TE, signal: TE.

3.3.3 Amplified Spontaneous Emission (ASE)

ASE of a an EDFA is well-known and usually used as a broadband (incoherent)

light source (1.53 µm<λ<1.64 µm). Similar to an EDFA, ASE is possible in

Ti:Er:LiNbO3or in Ti:Fe:Er:LiNbO3waveguides if sufficient pump power is provided.

Therefore, measuring the ASE spectra we can also perform a qualitative characteri-

zation of Er-doped waveguides.

The measured ASE spectrum for TE polarization is shown in Fig. 3.10 along with the

schematic experimental setup. ASE spectra were obtained from a 5 cm long Er-doped

waveguide (sample: Pb107xz), which was codoped with Fe in a 2 cm long section.

It is evident that the ASE spectrum of an Er-doped waveguide with a Fe-codoped

section has a similar shape as the gain spectrum obtained from a waveguide only

Er-doped (see Fig. 3.9b). This also indicates that Fe-doping does not influence the

Er-emission spectrum and the optical gain. In the next chapter we will see that the

photorefractive grating fabricated in the Fe-doped section could also be characterized

by measuring the ASE spectrum of the waveguide in transmission through the grat-

ing. When the pump light (λp= 1480 nm) is launched to the waveguide amplifiers

(Ti:Er:LiNbO3or Ti:Fe:Er:LiNbO3), green fluorescence (λ∼550 nm) becomes visible

along the waveguide surface. Very weak red fluorescence (λ∼660 nm) also becomes

visible with higher pump power levels.

ASE [dBm]

Wavelength [nm]

1520 1530 1540 1550 1560 1570

-66

-63

-60

-57

-54

-51

ASE

( a )

Fe:Er:LiNbO3

Er:LiNbO3

20 mm

50 mm

Waveguide

WDM

Pump

( b )

Pump power: 130 mW

Fig. 3.10: (a) Experimental setup for the ASE measurement and (b) ASE spectrum

for 130 mW coupled pump power; pump and ASE are TE-pol.

3.4 Conclusions

Fabrication and characterization of single-mode (at λ∼1.55 µm), laser-active and/or

photorefractive, Ti-indiffused LiNbO3waveguides have been described in this chap-

ter. Three different types of doped waveguides, i.e. Ti:Er:LiNbO3(only laser-active),

Ti:Fe:LiNbO3(only photorefractive), and Ti:Fe:Er:LiNbO3(laser-active and photore-

fractive) have been investigated. Diffusion doping of Er and Fe, waveguide fabrication

by Ti indiffusion, and the necessary annealing treatment have been discussed in de-

tails.

Ti:LiNbO3and Ti:Fe:LiNbO3waveguides have been characterized in terms of waveg-

uide loss and mode-size, whereas, Ti:Er:LiNbO3and Ti:Fe:Er:LiNbO3waveguides are

also characterized by the measurement of optical absorption and gain, and finally by

ASE. The results prove that the waveguides are good enough for the development of

integrated optical DBR- and DFB-lasers only if a photorefractive Bragg gratings can

be realized in the Fe-doped waveguide sections. The next chapter is dedicated for the

fabrication and characterization of the thermally fixed photorefractive gratings.

Chapter 4

Photorefractive Gratings:

Fabrication and Characterization

4.1 Introduction

Fabrication and characterization of thermally fixed photorefractive Bragg gratings

(λB∼1.55 µm) in Fe-doped LiNbO3waveguides are discussed in this chapter. In

fact, the successful development of our different types of integrated optical DBR and

DFB lasers using Er-doped LiNbO3waveguides has been possible only after the re-

alization of thermally fixed photorefractive Bragg gratings. For the development of

DBR lasers, gratings have been fabricated in the passive Ti:Fe:LiNbO3section(s),

whereas for DFB lasers they have been fabricated in the laser-active Ti:Fe:Er:LiNbO3

waveguide.

Thermally fixed photorefractive Bragg gratings were already fabricated holograph-

ically in the past (but only in Ti:Fe:LiNbO3waveguides) [20, 43]. The properties of

these Bragg gratings were also found to be very attractive (L = 1 cm, R >50%,

FWHM ∼100 pm). However, because of the lack of parameter optimizations, it took

a long holographic exposure time (>2 h) for grating fabrication. Therefore, a very

higher degree of stability is needed for the experimental setup as well as the for the

surrounding atmosphere.

Under the scope of this work a compact holographic setup has been developed and

the fabrication parameters have been optimized. As a result it needs only a few min-

utes of holographic exposure for fabrication of an efficient grating. E.g, a 18-mm-long

grating (R >95%, FWHM ∼60 pm) could be fabricated with a holographic exposure

of only 5 min!

4.2 Fabrication

Thermally fixed photorefractive Bragg gratings were fabricated in Fe-doped waveg-

uide sections with the grating vectors parallel to the waveguide axis (Z-axis). The

fabrication technology has been developed on the basis of the theoretical discussion

given in Chapter 2. The compact experimental setup (see Fig. 4.1) has allowed to per-

form the grating definition (holographically), online characterization, thermal fixing,

and development of the fixed grating in step by step.

Fig. 4.1: The experimental setup developed for grating fabrication. A: argon laser

(λ= 488 nm, P = 1 W), B: optics for wavefront shaping, C: sample held by a

goniometric stage, D: EDFA, E: optical spectrum analyzer, F: temperature controller

of the sample, G: cooling air gun.

4.2.1 Grating Definition

The gratings were fabricated by the illumination of an interference pattern of light

along the waveguide axis. Therefore, the reflections from the back surface of the

sample could cause of a reduction of the contrast of the interference pattern. We

prevented these reflections by depositing an antireflection (AR) coating (alternating

layers of SiO2and TiO2) on the back surface of the sample. In addition, an AR

coating (λ∼1.55 µm for 90 oincidence angle) at the end-faces of the waveguides also

helped to characterize the gratings more precisely by mode transmission and reflection

experiments.

An argon laser (λ= 488 nm, P = 1 W) has been used in the holographic setup

for grating definition (see Fig. 4.1). There are three main sections of the whole

setup: (i) optics for proper wavefront shaping, (ii) the holographic setup, and (iii) the

equipment for online grating characterization.

Wavefront Shaping:

The interference fringe pattern required for grating fabrication has been generated

L = 0 1 8 30 31 51

cm scale

0.5cm

2.0cm

SF1

L2 L3

SF2 G

SF1

SF2

( a )

( b )

Ar laser

Fig. 4.2: Schematic structure for 20 mm ×5mm wavefront shaping from an argon laser

beam of 1/e diameter ∼1.3 mm: (a) along vertical direction and (b) along horizontal

direction. L1: focussing lens (f1= 1 cm), L2: collimating cylindrical lens (f2= 8 cm),

L3: collimating spherical lens (f3= 30 cm), SF1: pinhole spatial filter (φ= 10 µm),

SF2: spatial filter (20 mm ×5 mm), G: position of the goniometric stage on which

the Lloyd setup is to be placed.

by folding the laser wavefront in a Lloyd-type interferometer. Therefore, generation

of a good quality wavefront is crucial for a good fringe pattern. Uniformity and high

degree of contrast of the interference pattern along the waveguide surface has to be

ensured. Moreover, the intensity itself should be as high as possible to reduce the

exposure time for grating fabrication. The shorter the exposure time the better is the

stability of the interference pattern with respect to the environmental perturbations

(vibration, convection, etc.).

Keeping all the above in mind a cylindrical wavefront of the argon laser beam has

been generated as shown in Fig. 4.2. The fundamental TEM00 mode of the argon

laser (1/e2beam-waist ∼1.3 mm) polarized along the vertical direction was focussed

by a lens (L1) of focal length f1= 1 cm. The focussed beam is spatially filtered by

a pinhole (SF1) of diameter 10 µm. The beam is then collimated along the vertical

direction by a cylindrical lens, L2 (f2= 8 cm). Afterwards, the beam passes through

a rectangular aperture (SF2) of size 20 mm ×10 mm. Behind the exit of SF2, it is

collimated along the horizontal direction and focussed along the vertical direction by

the lens L3 (f3= 30 cm). Finally, passing another 20 cm from L3, it reaches the center

of the Lloyd setup placed on a goniometric stage (G). In this way, it was possible to

achieve a rectangular beam (dimension: ∼20 mm ×5 mm, average light intensity:

∼500 mW/cm2) in the vertical plane at the center of the Lloyd setup.

Holographic Setup:

A schematic diagram of the Lloyd setup along with a zoomed photograph of the holo-

OSA

ASE (EDFA)

φGoniometer

Mirror (488 nm)

AR (488 nm)

AR (~1550 nm)

Sample

Ar Laser

(488 nm, 500 mW/cm2

Interference

Sample

Mirror

Heating element

( a ) ( b )

Fig. 4.3: Lloyd setup used for photorefractive grating fabrication: (a) photograph

of the Lloyd-type arrangement taken from the experimental setup and (b) schematic

diagram showing interference fringe generation along the waveguide. AR: antireflec-

tion coatings, OSA: optical spectrum analyzer, ASE (EDFA): amplified spontaneous

emission from an erbium doped fiber amplifier, φ: glancing angle of wavefront on the

surface of the sample.

graphic setup is shown in Fig. 4.3. In a special copper holder (designed by Dr. H.

Suche, Dept. Applied Physics, University of Paderborn, Germany), a square mirror

(2.5 cm ×2.5 cm, Thickness: 1.0 cm) and the sample (Length: 5-9 cm, Width: 1.2

cm, Thickness: 1 mm) are placed in such a way that the waveguides are perpendicular

to the reflecting surface of the mirror. The mirror has an effective reflecting area of

2.4 cm ×2.4 cm with surface flatness ∼λ/20 and reflectivity 99% at λ= 488 nm.

Nearly half of the incoming wavefront is reflected from the mirror and superimposed

on the other half to produce the periodic interference pattern along the waveguide

axis. The required periodicity of the interference pattern is achieved by adjusting the

glancing angle φ. For the adjustments of this angle we use a goniometric stage (see

also the Setup Calibration and Thermal Fixing part of this section).

The sample could be uniformly heated up to 250 oC with an electronic control (pro-

portional integral derivative) loop arrangement, although for thermal fixing process it

needs only 180 oC. A heating wire made of Ni-Cr passing through a number of ceramic

tubes has been used as the heating element. The ceramic tubes are carefully inserted

inside the copper holder so that the sample could be heated uniformly. To achieve a

good thermal conduction from copper holder to sample the holder was black-painted

(camera-black). This camera-black also helps to avoid stray light during the holo-

graphic exposures. The holder is mounted on the goniometric stage by means of three

needle-edged metallic supports for thermal isolation.

Online Characterization of the Electronic Grating:

At room temperatures, when the holographic exposure starts, the refractive index

grating starts forming. The growth of gratings can be monitored online by measuring

the transmission at the output of the waveguides after launching incoherent broad-

band light into the input. In this case, ASE from an EDFA is used. The ASE source

has about 35 mW power distributed in the emission band of 1.52 µm< λ < 1.62 µm.

An optical spectrum analyzer (OSA) of spectral resolution ∼10 pm is used for the

transmission measurements.

E.g. the growth and decay dynamics of two photorefractive gratings of 15 mm length,

each written in Ti:Fe:LiNbO3and Ti:Fe:Er:LiNbO3waveguides, respectively, fabri-

cated on the same substrate (Pb107xz) separated by ∼1.5 mm, are shown in Fig.

4.4a. The reflectivity shown in Fig. 4.4a is deduced from the transmission character-

istics shown in Fig. 4.4b. The efficiencies of both the gratings saturate in less than 5

min of holographic exposure.

When the holographic exposure is switched off, initially, both gratings decay very

fast for few minutes. During this stage, the grating in Ti:Fe:LiNbO3decays faster

than the grating in Ti:Fe:Er:LiNbO3. However, after a few minutes, both gratings

decay with decay constants of almost equal magnitudes.

In transmission characteristics, the polarization dependent Bragg responses and their

slightly different efficiencies in both types of waveguides are observed. Although, in X-

cut and Z-propagating LiNbO3waveguides, both TM- and TE-modes are α-polarized

010 20 30

500 1500 2500

Writing exposure on

Writing exposure off

Time [min]

Reflectivity [%]

1555.0 1555.5 1556.0 1556.5 1557.0

Wavelength [nm]

Ti:Fe:Er:LiNbO3

Ti:Fe:LiNbO3

Ti:Fe:Er:LiNbO3

0.4

0.6

0.8

0.4

0.6

0.8

1.0

Transmission [a.u.]

( a ) ( b )

Fig. 4.4: Online characterization of the photorefractive gratings written in

Ti:Fe:LiNbO3and Ti:Fe:Er:LiNbO3at room temperature (Pb107xz): (a) growth and

decay dynamics of the grating responses for the TE-mode, (b) grating transmission

for TE- and TM-polarized light, respectively.

E, ~

B⊥c-axis and ~

kkc-axis), the different boundary conditions of the guiding layer

result in slightly different Bragg responses. However, the polarization independent

linewidth of the Bragg response is measured to be ∼60 pm, the same for both waveg-

uides.

The measured results confirms that both the Ti:Fe:LiNbO3and Ti:Fe:Er:LiNbO3

waveguides have almost equal photorefractive sensitivity. That means, incorporation

of erbium does not change significantly the photorefractive sensitivity of the crystal.

Setup Calibration:

The Bragg wavelength λBis defined as a function of glancing angle, φB:

λB=neff (λB)·λw

cos φB

(4.1)

Therefore, one can calculate the value of λBat a specific glancing angle φBonly, if

the effective refractive index, neff , of the guided mode is known. But the calculated

Bragg wavelength using neff = 2.21, estimated by standard methods (effective in-

dex or variational method) using the Ti-indiffusion parameters, slightly differs with

our experimental results. This is because the refractive index change due to Fe (Er-

incorporation does not change the refractive index) incorporation could not be in-

cluded in the calculations because of the lack of experimental results.

However, we obtained the (φB−λB) calibration curve as shown in Fig. 4.5 for the

setup. The shift of ∆λB≈5 nm of the Bragg response from the theoretical results is

due to the error in effective refractive index and the mechanical errors in the Lloyd

setup configuration.

42 44 46 48

1450

1475

1500

1525

1550

1575

1600

Ti:Fe:Er:LiNbO (exp.)

Ti:Fe:LiNbO (exp.)

Ti:LiNbO (theo.)

ΦΒ[degree]

λΒ[nm]

Calibration

43 45 47

Fig. 4.5: The Bragg wavelength (λB) as a function of glancing angle (φB) for waveg-

uides with different dopants.

4.2.2 Thermal Fixing and Development of Ionic Gratings

The refractive index gratings written at room temperatures are volatile; they can not

be used for permanent applications. Therefore, the ionic (H+) gratings have been fab-

ricated using the thermal fixing method. For thermal fixing, the holographic exposure

is done at an elevated sample temperature (150-200 oC), so that thermally activated

protons can move to compensate the electronic grating. We found the best results

when the temperature of the sample holder was kept at 180 oC.

Two types of sample holders were built up: the first type can heat the whole sample

whereas the second type can heat the specific sample area alone where the grating is

to be fabricated. The steady state surface temperature profile (measured by touching

the sample with a flat-surface platinum resistance thermometer) along the length of

the sample for both cases are shown in Fig. 4.6. Using the second type (see Fig.

4.6b), we were able to fabricate two different fixed gratings at two different positions

in the same waveguide to develop the single-frequency laser to be discussed in the

next chapter.

In general, ⩽10 min of holographic exposure is used for thermal fixing. When the

exposure stops, the sample is cooled down very fast to room temperature to freeze the

proton distribution. Cooling the sample takes less than 4 min using a fan cooler. Dur-

ing thermal fixing, it is not possible to monitor online the grating response because the

electronic gratings formed by the holographic exposure are completely compensated

by the H+gratings. For fixing a grating at a specific Bragg wavelength one has to

correct the room temperature calibration curve (φB−λB) shown in Fig. 4.5 for ther-

mal fixing temperatures. For a defined glancing angle φB, a shift of ∆λB≈-0.5 nm

is observed in Bragg wavelength λB, compared to the room temperature environment.

100

120

140

160

180

200

-10 010 20 30 40 50 60 70

Distance [mm]

Mirror Sample

Holder

Temperature [°C]

Mirror Sample

Holder

( b )

-10 010 20 30 40 50 60 70

Distance [mm]

( a )

100

120

140

160

180

200

Temperature [°C]

Fig. 4.6: Surface temperature profile along the sample length when the sample holder

kept at 180 oC temperature: (a) heating the whole sample (b) heating limited to a

defined section of the sample.

At the end of the thermal fixing procedure, the index grating is developed by a homo-

geneous illumination with blue light either using the expanded beam of an argon laser

(λ= 488 nm) or an array of GaN LEDs (λpeak = 470 nm). E.g., the developing of a

fixed grating of a length of 13 mm in a Ti:Fe:LiNbO3waveguide (Pb66xz), fabricated

by a holographic exposure of 10 min is given in Fig. 4.7a. In this case, it was de-

veloped by the illumination from LEDs (I≈25 mW/cm2at the sample surface). In

Fig. 4.7b, the corresponding grating transmission characteristics for TM-polarization

is shown; it has been measured after the development exposure of 1 h. The reflectivity

at the Bragg wavelength λB≈1552.5 nm is 70%.

It is clear from the developing dynamics that the developing speed of the fixed grating

decays exponentially with an intensity dependent time constant. However, use of very

high intensity light for fast development should be avoided because unwanted uniform

refractive index change throughout the illuminated area may appear as an “optical

damage” of the guided mode.

4.3 Properties of Fixed Gratings

Some important properties of thermally fixed photorefractive gratings studied experi-

mentally are discussed in this section. As it was possible to fabricate fixed gratings in

015 30 45 60 75 90 105 120

100

1551 1552 1553 1554

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Time [min] Wavelength [nm]

Reflectivity [%]

( a ) ( b )

Transmission

70 pm

Fig. 4.7: Thermally fixed photorefractive grating in a Ti:Fe:LiNbO3waveguide (sam-

ple: Pb66xz): (a) development of peak reflectivity vs. time by homogeneous illu-

mination with an array of GaN LEDs and (b) transmission characteristics for the

TM-polarized light after the development exposure of 1 h.

both Ti:Fe:LiNbO3and Ti:Fe:Er:LiNbO3waveguides, it is interesting to see what are

the differences of their properties. In general, the gratings in both types of waveguides

show almost similar photorefractive sensitivity. But, in presence of green fluorescence

(when Er3+ ions are excited by pump laser light at λp= 1.48 µm) in Ti:Fe:Er:LiNbO3

waveguides, the grating dynamics is influenced significantly.

Dark Decay:

After the fabrication a thermally fixed photorefractive grating needs a homogeneous

illumination of blue light to exhibit the fixed ionic (H+) grating. As mentioned earlier

while thermal fixing process, the ionic grating is formed as a result to compensate

the electronic grating generated by the holographic exposure. During development

exposure, the electrons are redistributed and subsequently the H+grating builds up.

However, withdrawal of uniform developing exposure can reverse electron motion due

to the dark conductivity and starts compensating the so called fixed H+grating. This

compensation causes a decay in reflectivity/efficiency with time as shown in Fig. 4.8.

The similar behavior of the decay of the grating in both types of waveguide confirms

again that erbium has no influence on the photorefractive sensitivity.

Refreshing:

Due to the dark conductivity of electrons, a fixed ionic grating decays with time as

we have seen in our previous experiments. However, the ionic grating can be re-

freshed with uniform illumination of light of appropriate wavelength and intensity.

By controlling this refreshing light intensity level one can achieve any desired reflec-

tivity/efficiency (below the saturation efficiency) of a fixed grating. This argument

is clearly demonstrated by an experimentally observed dynamical behavior of a ther-

17 51

Time [hrs]

340

Reflectivity [%]

Ti:Fe:Er:LiNbO3

Ti:Fe:LiNbO3

Exponential decay fit

1560 1561 1562 1563 1564

0.6

0.8

1.0

1.2

Normal. Transmission

Wavelength [nm]

Ti:Fe:Er:LiNbO

TE-polarization

( b )( a )

Fig. 4.8: (a) Electronic compensation of two thermally fixed ionic gratings of 10 mm

length each in the dark, in Ti:Fe:LiNbO3and Ti:Fe:Er:LiNbO3waveguides, respec-

tively, fabricated on the same substrate (Pb107xz) with the same holographic exposure

of 4 min. (b) The transmission characteristics of one of the fixed gratings (just after

developing) for TE-polarization.

0510 15 20 25 30 35

100

Time [hrs]

( a ) ( b ) ( c )

1557.1 1557.3 1557.5

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Wavelength [nm]

I = 250mW/cm (Ar laser)

I = 50mW/cm (LEDs)

Normal. Transmission

Reflectivity [%]

( d )

Fig. 4.9: Dynamical behavior of a thermally fixed photorefractive grating fabricated

by a holographic exposure of 5 min in a Ti:Fe:Er:LiNbO3waveguide (Pb150xz): (a)

development by a uniform Ar laser beam (I = 250 mW/cm2,λ= 488 nm), (b) the

fixed grating reflectivity decays in absence of developing exposure, (c) refreshment by

an array of 8 GaN LEDs (I ≈50 mW/cm2,λpeak = 470 nm), and (d) the grating

transmission characteristics of the TE-mode for both types of illumination.

mally fixed photorefractive grating fabricated in a Ti:Fe:Er:LiNbO3waveguide (see

Fig. 4.9).

Amplified Grating Response in Ti:Fe:Er:LiNbO3:

The presence of Er3+ in a Ti:Fe:Er:LiNbO3waveguide can provide an amplified grat-

ing response in the wavelength region, 1.53 µm< λ < 1.64 µm, when it is excited

by diode laser light of 1.48 µm (or 0.98 µm) wavelength (see also Fig. 3.10). The

internal ASE itself is used to characterize the grating response both in transmission

and reflection.

ASE

1530 1550 1570

1.0

0.0

0.5

Wavelength [nm]

Intensity [a.u.]

Grating

response

( a )

( b ) ( c )

Fe:Er:LiNbO3

Er:LiNbO3

18mm

50mm

Waveguide

Grating WDM

WDM

PumpExcess Pump

Grating

response

1.0

0.0

0.5

Wavelength [nm]

Intensity [a.u.]

1530 1550 1570

Fig. 4.10: Amplified grating response in a Ti:Fe:Er:LiNbO3waveguide (sample:

Pb107xz) for TE-polarized light measured with OSA resolution of 0.1 nm: (a)

schematic structure of the experimental setup, (b) grating response along with ASE

(measured at the right output) and (c) grating transmission response along with ASE

(measured at the left output). WDM: wavelength division (de-)multiplex, Pump: 100

mW power at 1.48 µm wavelength.

The experimental setup shown in Fig. 4.10a was used for studying a fixed grating us-

ing internal ASE. In fact, for our study, a 18-mm-long grating (λB∼1562 nm and R

>80 %) was thermally fixed in a Ti:Fe:Er:LiNbO3waveguide, which is combined with

another 32-mm-long Ti:Er:LiNbO3waveguide section. The pump light (λp= 1480

nm, P = 100 mW) was launched to the waveguide from the grating side and the ASE

spectra from both sides were separated by two wavelength division (de-)multiplexers

(WDMs). As expected, the ASE spectrum travelling to the right, reveals approx-

imately the transmission characteristics of the grating (Fig. 4.10b). On the other

hand, from the amplifier side, the ASE spectrum travelling to the left reveals the

reflected part of the right-travelling ASE (Fig. 4.10c).

Grating Stabilization by Green Fluorescence:

Along with the ASE, there is a green up-conversion fluorescence (λ= 550 nm,

(4S3/2→4I15/2)) in Ti:Fe:Er:LiNbO3waveguides in presence of pump light at λp

= 1.48 µm ( or 0.98 µm). Our interest was to utilize this green fluorescence for the

compensation of the decay of a fixed grating as an alternative to the refreshing expo-

sure with a separate source. The experimental observation is very promising as shown

in Fig. 4.11.

01000 2000 3000

100

Time [min]

Dark decay

100 mW Pump

( a )

Reflectivity [%]

01000 2000 3000

Time [min]

( b )

Dark decay

100 mW Pump

Fig. 4.11: Stabilization of the reflectivity of thermally fixed photorefractive gratings

fabricated in a Ti:Fe:Er:LiNbO3waveguide (Pb107xz) by pumping with 1.48 µm light

(100 mW); reflection versus time: (a) initial grating reflectivity ∼95% and (b) initial

grating reflectivity ∼35%. The results are taken for TE-polarized light.

For the study we used the same experimental arrangement as shown in Fig. 4.10a.

The gratings of initial reflectivities of ∼95% and ∼35%, respectively, are stabilizing

at reflectivities of ∼70% and ∼16%, respectively, when they are pumped with 100

mW. The cause of the initial rapid decay is not known yet. However, one can specu-

late with the erbium fluorescence at λ∼388 nm (4G11/2→4I15/2) which can generate

holes in the valence band of LiNbO3(see also Chapter 2, Fig. 2.1b and Chapter 3,

Fig. 3.7) and with the fluorescence at λ∼660 nm (4F9/2→4I15/2) which can produce

small polarons (see also Chapter 2, Fig. 2.1c and Chapter 3, Fig. 3.7).

In other experiments, we have also observed that a fixed grating response could decay

to almost zero efficiency, if the pump laser is switched on and off, respectively, for a

few times. Afterwards, it needs another refreshing exposure by external blue illumina-

tion to refresh the H+grating to its initial strength. Although, the presence of green

fluorescence can reduce the grating decay significantly, the refreshment of a decayed

grating by the up-conversion fluorescence is not that much promising as hoped. Only

up to 10% of the grating efficiency could be refreshed by the green fluorescence.

Temperature Tuning:

Changing the temperature of the sample produces two main effects influencing the

1556.8 1557.0 1557.2 1557.4 1557.6

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Wavelength [nm]

20 C

30 C

25 C

35 C

Transmission [a.u.]

Fig. 4.12: Temperature tuning of a thermally fixed grating in a Ti:Fe:Er:LiNbO3

waveguide (sample: Pb150xz). The observed tuning slope is ≈5 pm/oC.

Bragg grating filter. The effective refractive index, neff , increases by increasing the

temperature according to the Sellmeier’s equation [6] and the grating period, Λ, in-

creases as a consequence of the thermal expansion. So, the change of the Bragg

response is expressed as [78]:

∆λB

λB

=∆neff

neff

+∆Λ

Λ(4.2)

where ∆Λ

Λ=α33∆T and ∆neff

neff

=β0∆T (4.3)

Here, α33 ≈5.6×10−6K−1and β0≈5.9×10−6K−1are the appropriate coefficients

for linear thermal expansion along the c-axis and ordinary refractive index change,

respectively. The corresponding theoretical temperature tuning ∆λB/∆T ≈6 pmK−1.

The temperature tuning slope observed in our experiment is ≈5 pmK−1(see Fig. 4.12)

which is close to the theoretical predictions.

Electrooptic Tuning:

The Bragg response can also be tuned by exploiting the electrooptic effect of LiNbO3.

1561.00 1561.50 1562.00

0.5

0.6

0.7

0.8

0.9

1.0

Wavelength [nm]

Transmission [a.u.]

TM - polarization

120 V

0 V

TE - polarization

( a )

0.5

0.6

0.7

0.8

0.9

1.0

Transmission [a.u.]

1561.00 1561.50 1562.00

Wavelength [nm]

( b )

120 V

0 V

Fig. 4.13: Electrooptic tuning of a thermally fixed grating in a Ti:Fe:Er:LiNbO3waveg-

uide (sample: Pb145xz) for both TM- (a) and TE-polarizations (b). The observed

tuning slope is ≈0.75 pm/V. The transmission spectrum was observed with 50 pm

resolution of the OSA.

When an external electric field (~

E) is applied across the grating by fabricating two

electrodes on both sides of the waveguide, there is a change of the index of refraction

given by:

∆neff =−1

2n3

eff rEΓ (4.4)

where the electrooptic coefficient r=r22 for TE-polarization and r=−r22 for TM-

polarization, Γis the overlap integral of guided optical mode and applied electric field

distribution.

To observe the electrooptic tuning of a grating, two parallel gold electrodes sepa-

rated by 15 µm were fabricated on both sides of the Ti:Fe:Er:LiNbO3waveguide

(Pb145xz). Afterwards, a thermally fixed grating (L = 15 mm, R = 30%, FWHM =

50 pm) was fabricated with a holographic exposure of 5 min. The Bragg responses

of the grating for both TM- and TE-polarizations were measured for 120 V and 0

V, applied to the electrodes (see Fig. 4.13). As expected from the equation (4.4),

the Bragg wavelengths for TM- and TE-polarizations are tuned in opposite directions

and the average tuning slope is found to be about ±0.75 pm/V. Using this opposite

tuning slope, a polarization independent grating response could also be obtained.

4.4 Conclusions

Fabrication and characterization of thermally fixed photorefractive Bragg gratings in

both passive Ti:Fe:LiNbO3and laser-active Ti:Fe:Er:LiNbO3waveguides have been

performed. A compact holographic setup (Lloyd configuration) was developed for

grating fabrication. With this setup, up to 18-mm-long gratings (R >95% and

FWHM <60 pm) have been fabricated with a very short holographic exposure (⩽10

min). Although the results are quite reproducible, sometimes the air turbulence due

to thermal convection induces some problems during the thermal fixing process. It

could be avoided completely if the whole setup is placed in a vacuum chamber. Exper-

imental results of the grating development, decay in the dark, refreshing, stabilization

of the grating response, thermal tuning and electrooptic tuning are presented. All

these properties have been determined by measuring the transmission characteristics.

To use a phase mask is an alternative method of writing photorefractive Bragg grat-

ings, which requires no sensitive holographic set up. The Bragg response is defined

by the periodicity of the phase mask. Therefore, to write gratings of different periods

several phase masks are needed, which is not only inconvenient but also expensive.

For that reason we used the holographic method only.

Chapter 5

Lasers with Photorefractive

Gratings

5.1 Introduction

The excellent properties of the photorefractive gratings and their integrability with

gain sections as discussed in the previous chapter stimulated our development of inte-

grated, Er-doped, optically pumped lasers in LiNbO3[17,18]. Besides cw Fabry-Perot

lasers of high efficiency (∼40%) and output power (∼60 mW), Q-switched lasers (∼4

ns long pulses of up to 2 kW peak power with ∼1 kHz repetition rate) and actively

mode-locked lasers (∼4 ps pulses of 10 GHz repetition rate; ∼6 mW average power)

another variety of attractive narrow-linewidth, fixed frequency and fully integrable

lasers can now be developed taking advantage of photorefractive gratings as narrow-

band reflectors.

Photorefractive Bragg gratings can favorably replace the surface relief gratings of

DBR-lasers developed earlier [19,31]. Moreover, DBR-lasers with two gratings, DFB-

lasers and DFB-DBR coupled cavity lasers have been developed. In the following

sections these new devices are discussed; device description, operation and typical

results are presented.

5.2 Basic Theory of Ti:Er:LiNbO3Waveguide Lasers

The general theory of Ti:Er:LiNbO3waveguide lasers was already developed [79,80].

The basic structure of these lasers is shown in Fig. 5.1. A Ti-indiffused optical

strip waveguide is embedded in (locally) Er-diffusion doped LiNbO3. Optical gain

(λs∼1.5µm) is achieved by the optical excitation of Er3+ ions by coupling external

radiation (say, λp= 1480 nm) directly into the waveguide (longitudinal pumping).

The wavelength dependent feedback elements are the two mirrors R1and R2, respec-

tively, forming in this way a longitudinal resonator.

Ti:Er:LiNbO3

Mirror, R ( )

1λMirror, R ( )

2λ

P-, k

s, out

p, ex

P+, k

s, out

z = 0 z = L

Fig. 5.1: Schematic diagram of an erbium-doped integrated optical waveguide laser

with amplifying length of L.Pp,exk:k-polarized (k=π, σ) external pump power,

Ps,out

±,k: signal output power in forward (+) and backward (-) directions.

We restrict our theoretical discussion to the 1.48 µm pump-band as preferred ab-

sorption band in LiNbO3with negligible excited state absorption, and hence negligi-

ble photorefractive damage. Furthermore, monomode waveguides for both pump and

signal, both having a good overlap with the erbium diffusion profile - a quasi-two-

level-model can be used to model the optical amplification in the wavelength range

λs∼1.5µm [81]. The energy splitting of the 4I15/2ground state (level-1) and the first

excited state 4I13/2(level-2) (see Fig. 3.7) due to the Stark-effect is taken into account

with the wavelength dependent absorption and emission cross sections, σ12 and σ21,

respectively. In addition, A21 = 1/τ describes the spontaneous transition from the

excited state to the ground state; τis the fluorescence lifetime. If in the presence of

pump and signal light, N1(x, y, z, t) and N2(x, y, z, t) are the population densities of

Er3+ ions of the ground- and excited-state, respectively, they can be deduced from

the steady state rate equation:

N1=w21 +A21

w12 +w21 +A21

No(5.1)

N2=w12

w12 +w21 +A21

No(5.2)

Here, the Er3+-concentration No(x, y) = N1(x, y, z, t)+N2(x, y, z, t) is independent of

the coordinate zand time t. The rate of stimulated absorption (emission) is defined

by w12 (w21):

wmn =X

j=p,s 1

hc X

k=π,σ Z0

∞

λjσk

mn,jik

j(x, y, z, λj)dλj!(5.3)

where his the Planck’s constant, cis the vacuum velocity of light, jstands either for

pump (p) or for signal (s) light. ik

j(x, y, z, λj) are the spectral density profiles. It can be

expressed in terms of transverse mode intensity profiles, jk

0(x, y, λj) (normalized over

cross-section of the waveguide) and zdependent evolutions in forward and backward

directions, (j±,k(z):

j(x, y, z, λj) = P0,k

jjk

0(x, y, λj)(j+,k(z) + j−,k(z))fk

j(λj) (5.4)

The term fk

s(λs) takes the possible longitudinal mode spectrum into account. The

amplitudes of the different modes (with a mode spacing ∆λs=λs,i+1 −λs,i =

λ2

s,i/(2neff (λs,i)L) between two neighboring modes) are proportional to the gain spec-

trum, which is represented by ˜

s(λs) = ˜

δ(λs−λs,i) (5.5)

The functions fk

jare normalized according to R∞

0fk

j(λj)dλj= 1.

The evolution of the pump and signal intensity amplitudes (j±,k(z, t)) along the

propagation direction zcan be deduced from the equation of continuity for a gain

medium [81]:

dj±,k(z)

dz =±γk

j(z, λj)j±,k(z) (5.6)

with

γk

j(z, λj) = −˜αk

j+Z Z(σk

21,jN2−σk

12,jN1)jk

0dxdy (5.7)

The term ˜αk

jdescribes the waveguide scattering losses, σk

21,jN2losses by absorption,

and σk

12,jN1winnings by stimulated emission. The integration has to be carried out

over the waveguide cross section taking into account the overlap of the normalized

transversal intensity distributions jk

0(x, y, λj) with the space dependent population

densities N1and N2, which are themselves proportional to the erbium concentration

profile No(x, y).

For a given coupled pump power Pk

p,coup, the signal (pump) power P0,k

s(P0,k

c) and

its z-dependent intensity amplitude, s±,k(z)(p±,k(z)) described in equation (5.4), can

be calculated after solving the equations (5.6) with the proper boundary conditions of

the resonator [79,80]. The forward and backward signal output power can be written

as:

P+,k

s,out = (1 −Rs

2)s+,k(L)P0,k

s=1−Rs

pRs

1Rs

P0,k

s(5.8)

P−,k

s,out = (1 −Rs

1)s−,k(0)P0,k

s=1−Rs

P0,k

s(5.9)

A Fabry-Perot type Ti:Er:LiNbO3waveguide laser is easily fabricated by depositing

14 alternating layers of SiO2and TiO2(thickness of each layer is λp/4) on to the

polished end faces. Usually, the reflectivity spectrum of such a dielectric mirror has a

broad wavelength response centering at λp. Therefore, the laser oscillation takes place

with a number of longitudinal modes (spaced by ∆λ =λ2/(2neff L)). (However, single

longitudinal mode of oscillation is obvious for an ideal case: homogeneously broadened

medium without hole-burning effects). For a wavelength selective laser oscillation, for

example in a DBR laser, at least one of the cavity mirror is replaced by a Bragg

grating (either surface relief or photorefractive). In this case, the reflectivity (Rs(λ))

as a function of wavelength can be calculated by coupled mode theory (see section 2.5)

and can be used in equations (5.8) and (5.9). Again, if the grating itself is fabricated

in the gain medium, a wavelength selective laser oscillation (DFB laser) is possible

even in the absence of additional feedback mirrors. The principle of a DFB laser can

be completely understood by analyzing coupled mode theory (see Fig. 2.6) [32, 82].

However, if a waveguide laser is made by combining a DFB-structure, amplifier and/or

a dielectric mirror, etc., the laser emission can be understood by the superpositions

of different effective Bloch waves or the method of multiple reflections [83,84].

5.3 DBR-Laser with One Grating

The first DBR-laser with one photorefractive grating was already developed in our

group by Christian Becker during his Diploma (Master) thesis work [77]. This laser

was reinvestigated during the present thesis work. It is found to be equally efficient

even 2 year after its fabrication. No observable degradation of the efficiency of the

fixed photorefractive grating is observed. For the consistence and completeness of

this thesis, the description and the performance of this laser are presented here once

again.

Fe:LiNbO3

Ti- indiffused waveguide

Er:LiNbO3

Fixed photorefractive grating

DBR Laser

70 mm

10 mm

0.11 nm

0.5

0.6

0.7

0.8

0.9

1.0

Normal. Trans.

1530 1531 1532 1533 1534

Wavelength [nm]

( a ) ( b )

Fig. 5.2: (a) Schematic structure of the DBR-laser with one photorefractive grat-

ing and (b) normalized transmission characteristics of the grating in TE-polarization

(sample: Pb874xz).

Device Description:

A schematic diagram of the DBR-laser fabricated with one thermally fixed photore-

fractive grating is presented in Fig. 5.2a. The laser was fabricated in a 70 mm

long X-cut LiNbO3substrate that had been Er-doped over 43 mm by indiffusion and

the remaining surface was Fe-diffusion doped (sample: Pb874xz). A 8 µm wide, 97

nm thick photolithographically defined Ti-stripe parallel to the c-axis was indiffused,

forming the optical channel guide. The sample was then annealed at 500 oC during

3 hrs in flowing Ar (0.5 litre/min) to enhance the necessary photorefractive sensitivity.

The laser resonator consists of a broadband dielectric high reflector on the polished

waveguide end face of the Er-doped section and of a narrowband grating reflector in

the Fe-doped section. In addition, the polished end face of the waveguide near the

grating was antireflection coated for fiber butt coupling. A 10 mm long photorefrac-

tive Bragg grating (Λ∼346 nm) was thermally fixed (at 170 oC) in the Fe-doped

waveguide section with a holographic exposure of 2 hrs. The reflectivity of the fixed

ν − ν [ ]

oGHz

Grating reflectivity

-10 -5 0510

0.1

0.2

0.3

0.4

0.1

0.2

0.3

0.4

Cavity transmission [a.u.]

Fig. 5.3: Calculated grating response and transmission of a passive DBR-cavity (equiv-

alent to the DBR-laser comprised of one grating, Fig. 5.2a) as a function of frequency

deviation from the Bragg frequency of the grating.

grating was measured to be >40% at λ= 1531.7 nm (see Fig 5.2b). The spec-

tral linewidth of the grating was 0.11 nm (∼14 GHz) measured with an OSA of 0.1

nm resolution bandwidth. The calculated grating reflectivity response and the passive

longitudinal cavity resonances are shown in Fig. 5.3. It is evident from this figure that

more than one longitudinal laser mode can oscillate simultaneously in a DBR-laser

with one grating.

Operation and Properties:

To operate the laser a fiber-pigtailed diode laser (λp= 1480 nm) was used for pump-

ing. The pump radiation was coupled to the DBR laser through the photorefractive

grating and double-pass pumping could be achieved because of the broadband dielec-

tric mirror on the other side. (Whereas in case of a DBR-laser with a surface relief

Bragg grating the pump radiation could not be coupled through the grating because

of substrate mode excitation in the grating section [19]).

A fiber-optic wavelength division de-multiplexer (WDM) was used to launch the pump

power and to extract the laser output (see Fig. 5.4a). An in-line fiber-optic isolator

was also used in the signal branch to avoid the back-reflections from other optical

components used to characterize the laser. Laser emission could be achieved in both

TE and TM polarization. The actual polarization was determined by the location of

the actual eigen-modes with respect to the peak reflectivity of the Bragg reflector.

By thermal drift, alternating TE and TM emission could be observed. However, TE

polarization for both pump and emission yielded the maximum output power, as the

smaller TE modes resulted in a better overlap with the Er concentration profile. To

Pump

Laser

WDM

Isolator

020 40 60 80 100 120

Pump power [mW]

Output power [mW]

1.5 GHz

Exp result

=1531.7 nm

TE-pol.

Modelling

DBR Laser

( a ) ( b )

Fig. 5.4: (a) Operation scheme of the DBR-laser with one photorefractive grating.

(b) The power characteristics. Inset: Scanning Fabry-Perot spectrum with three

longitudinal modes of laser oscillation, Pump: TE, Laser: TE.

04812 16 20 24 28

Time [hrs]

0.0

0.4

0.6

0.8

1.2

Output power [mW]

( b ) ( c )

Pump power: 100 mW, TE

( a )

Fig. 5.5: The performance of the packaged DBR-laser with one photorefractive grat-

ing as a function of operating time obtained 2 years after its fabrication (sample:

Pb874xz) (a) grating is illuminated by an array of blue LEDs; the output power be-

comes maximum as the grating is refreshed to maximum reflectivity, (b) laser output

power remains constant as long as the grating is illuminated and (c) the laser output

starts decaying after the illumination is switched off. Pump: TE, Laser: TE.

suppress the TM emission completely a stripe of silver paste was deposited across

the waveguide close to the high reflector operating as a TE-pass polarizer. From the

power characteristics of the laser shown in Fig. 5.4b it is evident that lasing sets in

at about 40 mW of launched pump power. The maximum output power of 5 mW

was measured for a pump power level of 110 mW. The emission wavelength of the

laser was at 1531.7 nm clearly determined by the grating response shown in Fig. 5.2b.

After the laser characterization, a single-mode standard telecommunication fiber was

glued to the antireflection coated waveguide end face (pigtailing); finally, the sample

was packaged in a temperature stabilized aluminum box. After packaging of the sam-

ple, the laser was characterized once again. In comparison with the results presented

in Fig 5.4b, the maximum output power was slightly reduced due to non-ideal fiber

pigtailing.

During laser operation because of the electronic compensation, the fixed ionic grat-

ing response dies out and the laser performance degrades with time. Therefore, each

time before laser operation the grating requires a refreshing exposure (as described in

Chapter 4). The grating response could be even kept constant during laser operation

by continuously illuminating with light from an array of blue LEDs. The performance

of the packaged DBR-laser as a function of time was characterized two years after its

fabrication and the corresponding results are given in Fig. 5.5.

5.4 DBR Laser with Two Gratings

The DBR-laser with one grating was not capable to run on a single longitudinal mode

as we have seen in the last section. True single frequency emission could be achieved

by replacing the broadband dielectric mirror of the DBR-laser by another narrow-

linewidth photorefractive grating [34,35]. The laser is now fully integrable, i.e., it can

be placed anywhere (aligned parallel to the Z-axis) on a substrate of an integrated

photonic circuit.

Device Description:

The structure of the DBR-laser with two photorefractive gratings is shown in Fig.

5.6a. It was also fabricated in the surface of a X-cut LiNbO3crystal (sample: Pb106xz)

with a 80 mm long Z-propagating single-mode waveguide. The middle section of 50

mm length was Er-doped and the two remaining sections on both sides of 15 mm

length were Fe-doped. In these sections two thermally fixed photorefractive gratings

R1and R2were fabricated, respectively.

Both gratings have the same period (Λ∼352 nm) and were fixed at 180 oC, but

had to be fabricated one after another because only one grating can be fabricated

at a time using our holographic setup. The grating R1was fabricated first with a

holographic exposure of 8 min. Afterwards, R2was fabricated with a holographic ex-

posure of 6 min. During the fixing process of R2at 180 oC, the sample was placed in a

specially designed oven so that the temperature of the other grating section (R1) was

maintained around room temperatures. This was necessary because a fixed “ionic”

grating can be erased easily at elevated temperatures (>80 oC).

The transmission characteristics of the individual gratings are shown in Fig. 5.6b

with nearly identical Bragg wavelengths near λB= 1561.1 nm. The reflectivity and

linewidth of grating (R1) are 90% and 200 pm (24 GHz), respectively, whereas the

corresponding figures of the grating (R2), which serves as output coupler, are 60% and

60 pm (7 GHz), respectively. These properties were observed when the gratings were

homogeneously illuminated with light of an Ar laser (λ= 488 nm, I = 100 mW/cm2);

the transmission characteristics was monitored by an OSA of resolution bandwidth of

10 pm. When the light was switched off, the grating efficiencies decayed with time in

about 120 min (20 min) for R1(R2) to half of its maximum response due to electronic

compensation by the dark conductivity. However, it took only 20 min to refresh the

gratings; they continued to keep their maximum efficiencies as long as they were illu-

minated as usual (see Fig. 5.6c). These gratings could be kept refreshed for a long

duration by an array of blue LEDs without any additional photorefractive damage.

The calculated longitudinal modes of the DBR-cavity comprised of both gratings

R1and R2are shown in Fig. 5.7 along with the calculated grating response equiv-

alent to R2. It is evident from the result that the longitudinal mode nearer to the

1560.6 1561.0 1561.4

Wavelength [nm]

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Transmission [a.u.]

200 pm

60 pm

0 20 40 90 170 250

Time [min]

100

Reflectivity [%]

Uniform illumination

(488 nm, 100 mW / cm2

Illumination stopped

Er:LiNbO3Fe:LiNbO3

Fe:LiNbO3

Ti- indiffused waveguide

Fixed photorefractive

grating (R )

Fixed photorefractive

grating (R )

80 mm

15 mm15 mm

( a )

( b ) ( c )

Fig. 5.6: (a) Schematic structure of the DBR-laser with two fixed photorefractive

gratings (sample: Pb106xz), (b) transmission characteristics of the gratings in TE-

polarization and (c) development of the gratings by uniform illumination and decay

after stopping the illumination.

ν − ν [ ]

oGHz

Grating ( ) reflectivityR1

-10 -5 0510

0.2

0.6

0.8

0.2

0.6

0.8

Cavity transmission [a.u.]

Fig. 5.7: Calculated grating response (R2) and transmission of a passive DBR-cavity

(equivalent to the DBR-laser comprised of two gratings (R1,R2), Fig. 5.6a) as a

function of frequency deviation from the Bragg frequency of the grating.

Bragg response has reasonably high degree of resonance compare to its neighboring

two modes. Therefore, a single-frequency laser operation is likely.

Operation and Properties:

The DBR-laser was pumped using a fiber-pigtailed diode laser with an emission

spectrum centered at ∼1480 nm wavelength, the optimum pump wavelength for α-

polarization in the Ti:Er:LiNbO3waveguide. The pump light was fed into the laser

resonator through the output coupler grating R2via the common branch of a WDM

(see Fig. 5.8a). The laser output was extracted through the second branch of the

WDM and guided through an inline fiber-optic isolator to protect the DBR-laser from

optical feedback. During operation the two photorefractive gratings of the laser cavity

were continuously illuminated by a uniform low intensity of Ar laser light (λ= 488

nm, I = 100 mW/cm2).

The power characteristics of the laser is shown in Fig. 5.8b. Lasing sets in at about

70 mW of incident pump power measured at the output of the common branch of the

WDM; the emission wavelength was 1561.1 nm. The laser was always running in TE-

polarization independent on the pump polarization (TE/TM). This might be due to a

slightly lower waveguide loss for the TE-mode compared to TM-mode. With 120 mW

of incident pump power (Pp) an output power (Pout) of 1.1 mW was achieved, mea-

sured behind the isolator; the corresponding slope efficiency (dPp/dPout) is about 2 %.

Using a high resolution OSA we could clearly identify that the DBR- laser runs in

a single longitudinal mode of the cavity in TE- polarization (see Fig. 5.9a). It was

running half an hour without any observable wavelength fluctuations. The observed

Pump

(1480nm)

Laser

(1561.1nm)

Isolator

WDM

DBR Laser

Pump power [mW]

0 40 80 120

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Output power [mW]

Pump : TE-pol

Laser : TE-pol

( a ) ( b )

R ( 90 % )

1R ( 60 % )

Fig. 5.8: (a) Operation scheme of the DBR-laser with two photorefractive gratings

(b) The power characteristics as output power versus coupled pump power.

1560.9 1561.0 1561.1 1561.2 1561.3

Wavelength [nm]

0.0

0.2

0.4

0.6

0.8

1.0

Output [mW]

6 pm (~740 MHz)

1561.0 1561.1 1561.2

Wavelength [nm]

0.00

0.05

0.10

0.15

0.20

0.25

Output [mW]

25 C

o30 C

35 C

( a ) ( b )

Fig. 5.9: (a) Spectral characteristics (TE) of the DBR-laser. (b) Tuning characteristics

of the DBR-laser; the high reflector grating R2was kept at room temperature, while

the output coupler grating R1was temperature tuned.

linewidth of ∼0.75 GHz is clearly limited by the resolution of the OSA. A much bet-

ter resolution (scanning Fabry-Perot or delayed self-heterodyne technique) is required

to resolve the true laser linewidth of estimated <10 kHz as observed with a surface

etched device [17].

As the linewidth of the high reflector grating is broader (200 pm) than that of the

output coupler grating (60 pm), thermal tuning of the lasing wavelength was possi-

ble via the temperature of the output coupler alone (see Fig. 4.8b). We achieved a

mode-hop free tuning range of about 80 pm (∼10 GHz) with a slope of 8 pm/K (∼

1 GHz/K). A wider tuning range can be obtained by an additional temperature shift

of the high reflector grating.

5.5 DFB Laser/Amplifier

By writing the holographic grating in a Ti:Fe:Er:LiNbO3waveguide section even a

fully integrable DFB-laser can be realized [36,37]. In this work basically we have in-

vestigated an integrated optical DFB-laser/amplifier combination has been developed.

1531.1 1531.3 1531.5 1531.7

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Wavelength [nm]

Grating Trans. [a.u.]

Fe:Er:LiNbO3

Er:LiNbO3

Photorefractive grating

Ti- indiffused waveguide

DFB Laser

50 mm

20 mm

( a ) ( b )

Amplifier

75 pm (~8.5 GHz)

Fig. 5.10: (a) Schematic structure of the DFB-laser/amplifier with a fixed photore-

fractive grating (sample: Pb107xz), (b) transmission characteristics of the grating in

TE-polarization.

Device Description:

The laser was fabricated in the surface of a 50 mm long, 12 mm wide and 1 mm thick

optical grade X-cut LiNbO3crystal (sample: Pb107xz) with the optical- (Z-) axis

aligned parallel to the direction of the optical waveguide (see Fig. 5.10a). The whole

surface of the sample is Er-doped whereas a section of 20 mm width was Fe-doped as

well. Therefore, a single-mode (1470 nm < λ < 1580 nm) waveguide parallel to the

Z-axis has a 30 mm long Er-doped section and a 20 mm long Er/Fe codoped section.

Both polished end faces were antireflection- (AR-) coated for λ∼1550 nm.

From DFB-laser modelling we learned that both, the optical gain and the feedback

in the amplifying grating structure should be as high as possible to get an acceptable

laser threshold. We therefore decided to write the active DFB-grating (Λ∼346 nm)

for 1531 nm wavelength, where the optical gain in the Er-doped waveguide can even

exceed 1.5 dB/cm sufficient pump power provided. Using our standard holographic

setup, an exposure time of only 2 min was sufficient to get a grating peak reflectivity

exceeding 80%. The spectral linewidth measured in transmission was ∼75 pm (∼8.5

GHz) (see Fig. 5.10b). As a reflectivity ∼90% was necessary to achieve lasing, fixed

(ionic) photorefractive gratings could not be used; their maximum reflectivity did not

exceed 80%.

g = 3 dB/cm

2 dB/cm

1 dB/cm

0 dB/cm

ν−ν [

οGHz]

g = 3 dB/cm

2 dB/cm

1 dB/cm

0 dB/cm

-10 -5 0 +5 +10

ν−ν [

οGHz]

-10 -5 0 +5 +10

Reflection

Transmission

( a ) ( b )

Fig. 5.11: (a) Calculated reflection and (b) transmission of a 20 mm long DFB-laser

structure at different gain levels: the passive grating reflectivity is taken as 95%.

The reflection and transmission spectra for the 2 cm long DFB-laser structure with

different gain levels have been calculated using coupled mode theory (see Fig. 5.11).

It is evident from both spectra that two peaks just outside the stop band of Bragg

grating start arising as the gain level approaches to a certain threshold. These peaks

finally appears as the two lowest order DFB-laser modes (theoretically infinite reflec-

tion) just above the threshold gain.

In contrast to the DFB-laser discussed above, if a DFB-laser structure is integrated

with an amplifier section as shown in Fig. 5.10a, the result is somewhat different. In

this case there are also have two symmetric peaks in both reflection and transmission

spectra but they appear within the stop band of the grating response [84]. There-

for, in this case the threshold gain is reduced reasonably as the two lasing-modes are

within the Bragg response of the grating.

Operation and Properties:

The pump light (λp= 1480 nm) of two laser diodes was coupled from the right- and

from the left-hand side into the waveguide structure (see Fig. 5.12a) during holo-

graphic exposure for grating definition. Fiber-optic wavelength- (de-) multiplexers

allowed extracting the laser emission, which sets in at a launched pump power level of

about 175 mW. The maximum of the output power emitted to the right was ∼95 µW

at about 240 mW total launched pump power. At the same pump power level 1.12

mW was emitted to the left, thanks to the optical gain of more than 10 dB in the 30

mm long Er-doped waveguide amplifier on the left of the DFB-structure. Fig. 5.12b

gives the power characteristics of the laser. The emission wavelength of the laser was

∼1531.4 nm, clearly determined by the grating characteristics. The two distinguished

DFB-laser/amplifier modes in the emission spectrum could already be resolved with

an optical spectrum analyzer of 10 pm resolution; their wavelength separation is ∼27

pm.

1531.1 1531.3 1531.5 1531.7

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Wavelength [nm]

Normal. output power

~3.9GHz

Normal. grating transmission

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Pump

Laser

WDM

Laser

Pump

DFB Laser

( a )

( c )

140 160 180 200 220 240

emission to the left

(> 10dB amplification)

emission to the right

Pump power [mW]

1.2

0.8

0.4

0.0

Output power [mW]

1.0

0.6

0.2

( b )

Amplifier

Fig. 5.12: (a) Operation scheme of the DFB-laser/amplifier, (b) laser output vs.

launched pump power and (c) laser emission spectrum consists of two peaks. Inset:

two lasing modes are better resolved by a scanning Fabry-Perot spectrum analyzer of

15 GHz free spectral range.

The emission spectrum is shown in Fig. 5.12c together with the grating response.

It is evident that the emission lines arise symmetrically on both sides of the peak

reflectivity in accordance with theory. The separation of the two emission frequencies

was even better resolved with a scanning Fabry-Perot spectrum analyzer; a figure

of 3.9 GHz was measured. Besides emission of both modes in TE-polarization, also

emission in TM-polarization was sometimes observed. The cause of the polarization

flipping is not yet known.

5.6 DFB-DBR Coupled Cavity Laser

With a little modification of the DFB-laser/amplifier described above an attractive

DFB-DBR coupled cavity laser was developed [38, 39]. Single-frequency emission

could also be achieved with this laser configuration. It has a low threshold pump

power level and a higher slope efficiency.

Fe:Er:LiNbO3

Er:LiNbO3

Ti- indiffused waveguide Fixed photorefractive grating

DFB -DBR Cavity

65 mm

15 mm

( a )

1557.0 1557.2 1557.4

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Wavelength [nm]

TE-pol.

Transmission

( b )

70 pm

Fig. 5.13: (a) Schematic diagram of the DFB-DBR coupled cavity laser (sample:

Pb150xz). (b) The transmission characteristics of the fixed grating fabricated in

Ti:Fe:Er:LiNbO3waveguide section and refreshed by Ar laser light (λ= 488 nm, I =

250 mW/cm2).

Device Description:

As usual the laser was fabricated in the surface of a 65 mm long, 12 mm wide and

1 mm thick optical grade X-cut LiNbO3 crystal (sample: Pb150xz). A 7 µm wide

Ti-indiffused waveguide aligned parallel to the Z-(optical-) axis, has a 50 mm long

Er-doped section and 15-mm-long Er/Fe codoped section (see Fig. 5.13a). The pol-

ished end face on the Fe-doped side was AR- (antireflection-) coated whereas the other

polished end face was HR- (high reflection) coated.

Finally, a 14 mm long photorefractive Bragg grating was written in the Fe-doped

waveguide section using our standard holographic setup using an argon-ion laser (λ

= 488 nm, P = 1 W). It was fixed at 180 oC by a holographic exposure of 4 min, fol-

lowed by a rapid cooling of the sample down to room temperature to get a fixed ionic

(protonic) grating of 352 nm periodicity. It was developed by a uniform illumination

with blue light either from an Ar laser or an array of blue LEDs.

The transmission characteristics of the grating was measured with an OSA of 10

pm resolution by monitoring the transmitted amplified spontaneous emission of an

DBR-cavity resonance I DBR-cavity resonance II

ν−ν [

οGHz]

( a ) ( b )

-6 -4 -2 0 +2 +4 +6

104

2.104

3.104

4.104

5.104

100

200

300

-6 -4 -2 0 +2 +4 +6

0.1

0.2

0.3

0.4

0.1

0.2

0.3

0.4

ν−ν [

οGHz]

Cavity gain :

1 dB/cm

Cavity gain :

1 dB/cm

Gain :

0 dB/cm Gain :

0 dB/cm

0.1

0.2

0.3

0.4

0.1

0.2

0.3

0.4

Signal trans.[a.u.]

Signal trans.[a.u.] Grating reflectivity

Cavity trans. [a.u.]

Fig. 5.14: Theoretical demonstration of the two extreme situations of the DFB-DBR

coupled mode of laser oscillations (a) Two DBR-cavity modes are symmetrical to

the two lowest order “lasing-modes” of the DFB-laser/amplifier combination; their

frequencies do not coincide. (b) One DBR-cavity mode is exactly resonant to one

of the two lowest order “lasing-modes” of the DFB-laser/amplifier combination; their

frequencies do coincide.

EDFA through the grating. Up to 90% peak reflectivity (deduced from the transmis-

sion spectrum) could be achieved if the Ar laser (λ= 488 nm, I = 250 mW/cm2,

20 min exposure time) was used to develop the ionic grating. After the development

the grating slowly decays due to the electronic dark conductivity. It can be refreshed

again up to 75% peak reflectivity by an array of 8 blue LEDs within 30 min. The

spectral half-width of the polarization independent grating response is 70 pm (∼8.5

GHz). However, the laser is operated with the grating of reflectivity ∼40%. More-

over, during laser operation it could be observed that the grating becomes almost

stabilized as function of time at about 30% reflectivity without any additional blue

illumination from outside. This favorable self-stabilization is probably due to the

green up-conversion light produced in the Er-doped grating itself (details are given in

Chapter 4).

For a theoretical investigation we assumed that the device consists of two laser-active

cavities: the 14 mm long grating section alone is a DFB-laser cavity; the high reflector

(HR) together with the grating forms a DBR-cavity with a 50 mm long waveguide

section. Therefore, the two lowest order “lasing-modes” of the DFB-laser/amplifier

combination can easily resonant with the DBR-cavity modes. Using coupled mode

theory, the above hybrid cavity is analyzed. Fig. 5.14 shows the two extreme laser

oscillation situations corresponding to two DBR-cavity resonances. Single-frequency

laser oscillation is expected if one of the DBR-cavity modes coincides with one of the

two lowest order “lasing-modes” of the DFB-laser/amplifier combination (as shown in

Fig. 5.14b).

Operation and Properties:

For laser operation the pump light (λ= 1480 nm) is fed into the laser resonator

through the grating via the common branch of a fibre-optic WDM. The laser output

is extracted through the second branch of the WDM and isolated to protect the laser

from optical feedback (see Fig 5.15a). In our experiment we observed at low pump

power levels laser operation is determined essentially by the DBR-cavity. Single-

frequency emission at 1557.2 nm wavelength with a linewidth <185 MHz could be

observed by a Fabry-Perot spectrum analyzer. The exact frequency of the laser emis-

sion is determined by the frequency of that DBR-cavity mode (∆νDBR ∼1.4 GHz)

closest to the reflectivity maximum of the grating. The threshold of this mode is

achieved at about 100 mW incident pump power corresponding to ∼80 mW launched

power. However, slightly above the threshold pump power the laser tends to oscillate

in more than one DBR-mode.

Pump

Laser

WDM

Isolator

DFB -DBR Cavity

80 90 100 110 120 130

Pump power [mW]

Output [mW]

Pump : TE

Signal : TE

( a ) ( b )

Fig. 5.15: (a) Operation scheme of the DFB-DBR coupled cavity laser and (b) Laser

output versus launched pump power: laser emission at ∼1557.2 nm.

At higher pump power level (>90 mW) a DFB-DBR coupled mode of laser oscil-

lation sets in. In this regime, a maximum output power of 8 mW is obtained at

130 mW pump power. This corresponds to a slope efficiency of about 22% (see Fig.

5.15b). In contrast to the DBR-mode of operation, now simultaneous emission at two

frequencies can be observed frequently, separated by ∼3.8 GHz (see Fig 5.16a). Both,

the threshold pump power and the observed frequency spacing of the two lasing modes,

are smaller than the theoretical results of a pure DFB-laser, clearly indicating the in-

fluence of the integrated amplifier section and the cavity formed by the high-reflector

dielectric mirror. The coupled-mode of laser operation is determined by the amplified

3.8 GHz

( a ) ( b )

T1T2

Fig. 5.16: Scanning Fabry-Perot spectra of the DFB-DBR coupled cavity laser ob-

tained at two different temperatures; (a) two modes at temperature T1and (b) single-

frequency laser emission at temperature T2. T1- T2∼1oC. (See also Fig. 5.14 for

an explanation).

spontaneous emission at the two distinguished frequencies of the DFB-laser/amplifier

combination in the wings of the reflectivity spectrum of the 14 mm long amplifying

grating. They determine the laser oscillation frequencies in the longer DBR cavity,

if two DBR-modes are resonant or (symmetrically) close to resonance with the two

DFB-laser/amplifier modes. However, the DBR-cavity modes can shift as function of

temperature (∆νDBR/∆T ∼700 MHz/oC), electric field (∆νDBR/∆V ∼92 MHz/V)

etc., leading to a resonance of one frequency with one DBR-cavity mode only at ap-

propriate temperatures. As a result single-frequency emission can be achieved (see

Fig. 5.16b).

Dynamics of the Laser Output Power:

The DFB-DBR coupled cavity laser is characterized in terms of the output power as

a function of time with different operating conditions (see Fig. 5.17). In the first ex-

periment the pump laser and the grating refreshing LEDs were switched on together.

After a few minutes, the laser emission started and reached maximum output power

within 20 min. An almost constant output power was recorded for 3 hrs as the refresh-

ing light switched on. The almost same output power was recorded for another 4 hrs.

even after switching off the grating refreshing light. At the end, after complete 7 hrs

of laser operation the grating reflectivity was measured to be 30%. During the whole

experiment polarization flippings were observed from time to time but not frequently.

For the second experiment, the grating was initially refreshed to a peak reflectivities

of 70% and 40%, respectively. Then the laser was pumped (130 mW, TE-polarized)

Time [hrs]

Output [mW]

LEDs on LEDs off

1 3 5 7 9 11

Time [hrs]

0 1 2 3 4 5 6 7 8

Initial reflectivity 70%

Initial reflectivity 40%

1 3 5 7 9 11

Time [hrs]

Initial reflectivity 70%

TE - pass polarizer

LEDs off LEDs on

( a ) ( b ) ( c )

Fig. 5.17: Different dynamical behavior of the pumped DFB-DBR coupled cavity

laser; (a) first few hours grating was kept refreshed by the illumination of an array of

LEDs and then no illumination, (b) laser started running with refreshing illumination

of the grating but with a initial refreshment of the grating, and (c) TE-passed polarized

laser started running with a initially refreshed grating. Pump power: 130 mW, TE-

polarized

without any grating refreshment exposure and the output was recorded for more than

10 h. It was found that for 70% (initial) grating reflectivity, the laser output contin-

ued to decrease during the first few minutes and later on almost stabilized. But for

the 40% (initial) grating reflectivity, a nearly stabilized output power was recorded as

function of time. The step-like jumps observed in the laser output power were due to

polarization flippings. At the end of laser operation with 70% and 40% initial grating

reflectivity, the grating reflectivities were measured again; they had reached ∼30%.

Finally, for the third experiment a TE-pass polarizer (Ag paste) was deposited close to

the high reflector. The laser output was recorded as a function of time using 130 mW

of TE-polarized pump power and grating refreshment LEDs were switched on. In this

case, although TE-polarized laser output was always maintained, flipping between

the two “DFB-lasing-modes” of 3.8 GHz separation could be observed with regular

interval of time. After 11 hours of laser operation the grating reflectivity once again

was measured to be about 30%.

In conclusion, after the above three experiments one can assume that the green flu-

orescence (due to up-conversion of the excited Er3+ ions) nearly stabilize the fixed

grating response, which usually experiences a decay due to a residual conductivity.

The polarization flipping could be suppressed completely by integrating a TE-pass po-

larizer at the proper position. Flipping between the “lasing-modes” can be suppressed

with a better temperature control and/or electrooptic control.

Wavelength Tuning:

The emission wavelength of a DFB-DBR coupled cavity laser can be tuned by tuning

1530 1540 1550 1560 1570 1580

0.0

0.4

0.8

1.2

1.6

Wavelength [nm]

Laser emission [a.u.]

TE - pol.

Fig. 5.18: Wavelength tuning of DFB-DBR coupled cavity laser with different grating

periodicity (sample: Pb150xz); (a) laser emission in TE-polarization. Pump power:

130 mW, TE-polarized, grating reflectivities were >80%

the Bragg wavelength of the grating response. This is possible either by tuning the

grating periodicity Λand/or by tuning the effective refractive index neff of the guided

mode. At room temperature the photorefractive Bragg gratings could be written for

different wavelengths by simply tuning the angle (2θ) between the writing beams.

In this way we could tune the emission wavelength in the wide range from 1.53 µm

< λ < 1.64 µm. Some results are given in Fig 5.18.

Electro-optically tunable DFB-DBR coupled cavity laser emission was also observed

as an external electric field can change the effective refractive index of a guided mode.

We have investigated a 64 mm long Er-doped waveguide laser structure as shown in

Fig 5.19a (sample: Pb145xz) . A 10 mm long photorefractive grating was thermally

fixed (λB= 1561.5 nm and R = 30 %) within the 14 mm long Er,Fe-codoped waveg-

uide section. Two gold stripes separated by 15 µm were deposited parallel to the

waveguide. A dc voltage could be applied to the gold electrodes for electro-optic tun-

ing. A tuning slope of about 0.5 pm/V (∼64 MHz/V) was obtained (see Fig. 5.19b).

Obviously, for the electro-optic tuning we could not utilize the highest electro-optic

coefficient r33 (30.8 ×10−12 m/V) because of our X-cut and Z-propagating waveguide

configuration. Instead, we utilized the r22 coefficient (3.4 ×10−12 m/V), which is

almost one order of magnitude smaller than r33. Although the electro-optic wave-

length tuning range was not very large, stable single-frequency laser emission could

be observed for several hours. Moreover, for further improvements the electro-optic

tuning might be utilized for a fast feedback-controlled wavelength stabilization.

Pump

Laser

WDM

Isolator

( a )

Er:LiNbO3Fe:Er:LiNbO3

Waveguide

Electrodes

Fixed photorefractive grating

(R = 30 %)

64 mm

14 mm

1561.5 1561.6 1561.7

0.0

0.4

0.8

1.2

Wavelength [nm]

0 V 45 V 88 V

Power [a.u.]

( b )

Fig. 5.19: Electro-optic wavelength tuning of a DFB-DBR coupled cavity laser (sam-

ple: Pb145xz): (a) schematic structure and (b) TE-polarized laser emission spec-

tra corresponding to three different applied voltages. Pump power: 130 mW, TE-

polarized.

Finally, temperature tuning of the emission wavelength of a DFB-DBR coupled cavity

laser was also investigated. A change of the temperature of the whole device causes

three different effects: (i) thermal expansion of the whole device (cavity) length, (ii)

change of the refractive indices, and (iii) change of the grating periodicity due to ther-

mal stretching (see also equation 4.2). Therefore, during temperature tuning switching

between the two “DFB-lasing-modes” was frequently observed. However, most of the

time single-frequency laser emission is favored: either right to the Bragg wavelength

or left, as observed by an optical spectrum analyzer. With a careful observation

of a particular “DFB-lasing-mode”, the thermal tuning experiment was performed.

The observed tuning slope was ∼5 pm/oC when the whole device temperature was

tuned from 15 to 70 oC. The device was not heated beyond 70 oC because the fixed

photorefractive grating starts erasing slowly at temperatures >80 oC.

5.7 Conclusions

Different types of integrated optical narrow linewidth DBR- and DFB-lasers (1530

nm <λ<1575 nm) are demonstrated with Ti-indiffused Er-doped LiNbO3channel

waveguides using thermally fixed photorefractive gratings. The general fabrication

procedures of the three main building blocks of these devices e.g., gain section, single-

mode waveguide, and thermally fixed photorefractive gratings are described along

with their experimental characterization. The performance of the different laser con-

figurations, i.e, DBR-laser with one grating, DBR-laser with two cavity gratings,

DFB-laser/amplifier combination, and finally the DFB-DBR coupled cavity laser is

presented in detail.

Single-frequency laser operation was obtained from the DBR-laser with two cavity

gratings as well as from the DFB-DBR coupled cavity laser. Therefore, these lasers

have applications in the field of interferometric sensing, e.g, the acousto-optic hetero-

dyne interferometer [85] and in fiber-optic ultra-dense wavelength division multiplexed

systems.

The stability of the emission wavelength and the output power of a laser are highly

governed by the grating stability. An attractive way to stabilized the grating response

is to utilize the green fluorescence in the Er-doped waveguides. Some results have also

been obtained in this work. However, further investigations are required for its better

utilizations.

Chapter 6

Summary and Conclusions

In this work different types of integrated optical DBR and DFB lasers (1530 nm < λ <

1575 nm) have been demonstrated in LiNbO3, using thermally fixed photorefractive

Bragg gratings. They are fabricated on the surface of 1-mm-thick X-cut LiNbO3

crystals with Ti-indiffused Z-propagating waveguides. Prior to a waveguide fabrica-

tion, the surface of the crystal is prepared with a laser-active section by Er-diffusion

doping and a photorefractively sensitized section by Fe-diffusion doping. The pho-

torefractive Bragg gratings could only be fabricated in the Fe-doped sections. There-

fore, a combination of two types out of three differently doped single-mode waveg-

uides, i.e, Ti:Er:LiNbO3(laser-active), Ti:Fe:LiNbO3(photorefractive-sensitive), and

Ti:Fe:Er:LiNbO3(laser-active and photorefractive-sensitive) have been used for de-

veloping our different configurations of DBR and DFB lasers.

The origin of photorefractive effect, the principle of grating formation, and their

thermal fixing mechanisms in Fe:LiNbO3have been discussed with theoretical illus-

trations. The coupled mode theory allows us to analyze the properties (transmis-

sion, reflections, FWHM, etc) of a photorefractive grating with gain (fabricated in

Ti:Fe:LiNbO3) or without gain (fabricated in Ti:Fe:Er:LiNbO3). Theoretical calcula-

tions predict that a grating fabricated within the gain region (∼4 dB/cm) could be

operated as a DFB laser.

All the three types of waveguides, Ti:Er:LiNbO3, Ti:Fe:LiNbO3, and Ti:Fe:Er:LiNbO3

have been investigated individually or in a combination of two. They were character-

ized in terms of losses, size of the guided mode(s), optical gain, and photorefractive

sensitivity. Analyzing these results, the optimized fabrication parameters have been

determined.

A compact holographic setup was developed with an argon laser (λ= 488 nm, P

= 1 W) for the holographic recording of photorefractive gratings. Using this setup

refractive index gratings of L = 18 mm, λB∼1.55 µm, R >95%, and FWHM <60

pm, could be fabricated with a holographic exposure of <5 min. Such a refractive

index grating formed at room temperatures is volatile due to electronic conduction

in the dark . Therefore, the holographic exposure is done at an elevated sample tem-

perature (180 oC). At this temperature mobile H+ions form another grating that

compensate the periodic spacecharge. Upon cooling of the sample, a permanent ionic

grating is developed by a homogeneous illumination with blue light (from an array of

blue LEDs).

Finally, a family of narrow linewidth integrated optical DBR, DFB, and DFB/DBR-

coupled cavity lasers with Er-doped LiNbO3single-mode waveguide has been devel-

oped. They have one or two photorefractive gratings in Fe-doped waveguide sections.

Antireflection (AR) and high-reflection (HR) coatings were deposited on the polished

end faces accordingly where they are necessary. For laser operation, the pump light

(λ= 1480 nm) is fed into the laser resonator through the grating via the common

branch of a fibre-optic wavelength-division demultiplexer (WDM). The laser output

is extracted through the second branch of the WDM and isolated to protect the laser

from optical feedback.

Two types of DBR-lasers have been developed. The first type has a cavity consisting

of one Bragg-grating in a Ti:Fe:LiNbO3waveguide, a gain section with Ti:Er:LiNbO3

waveguide, and a multi-layer dielectric mirror deposited on one polished end face.

Although, this laser was running with three longitudinal modes (in TE-polarization)

but it stimilates for further investigations to achieve a single-frequency laser. Later

on a second DBR-cavity comprised of two gratings in Ti:Fe:LiNbO3on both sides

of the Er-doped waveguide has been developed. Single-frequency operation could be

achieved in this case at various wavelengths in the Er-band (1530 nm <λ<1575

nm) with up to 1.12 mW output power. Emission wavelength of this laser could also

be tuned with temperature with a slope of about 8 pm/K.

For the first time, a DFB-laser with two lowest-order modes (λ∼1531 nm) has

been demonstrated with a photorefractive grating in a Ti:Fe:Er:LiNbO3waveguide;

it is combined with an integrated optical amplifier on the same substrate. The laser

emission could be extracted from both sides: about 0.1 mW at the grating side and

1.1 mW at the amplifier side.

Moreover, an attractive DFB/DBR-coupled cavity laser has been developed and inves-

tigated. Its cavity consists of a photorefractive Bragg grating in the Ti:Fe:Er:LiNbO3

waveguide section close to one end face of the sample, a Ti:Er:LiNbO3gain section

and a broadband dielectric multi-layer mirror of high reflectivity on the other end

face. The laser runs with single-frequency emission and a maximum output power

of 8 mW. The emission wavelength of this type of laser is temperature tuned with a

slope of 5 pm/K and electro-optically tuned with a slope of ±0.75 pm/V.

In conclusion, using photorefractive Bragg gratings, four different types of lasers with

Er-doped LiNbO3waveguides have been investigated. Single-frequency laser oper-

ation is obtained from the DBR-laser with two cavity gratings as well as from the

DFB/DBR coupled cavity laser. The linewidth of such a single-frequency laser can

be as narrow as ∼10 kHz [18], i.e, it has a very large coherence length (∼3×104

m). Therefore, these lasers have applications in the field of interferometric instru-

mentation and in fiber-optic ultra-dense wavelength division multiplexed systems. A

prospective immediate future work in this field could be the integration of one of the

above mentioned single-frequency laser in an integrated optical heterodyne interfer-

ometer in LiNbO3, which has also been developed in our group [85].

In spite of the above mentioned potentials, there are some difficulties to integrate these

lasers with other optical components: the lasers are fabricated with Z-propagating

waveguides in X-cut substrates. This is because efficient photorefractive Bragg grat-

ings can only be fabricated in Z-propagating waveguides on a X- or Y-cut substrate.

But the devices based on electro-optic/ acousto-optic effects (for tuning, modulation,

switching, etc.), usually have waveguides aligned either parallel to the Y- or to X-axis.

However, we are optimistic as there are some efforts to fabricate photorefractive Bragg

gratings even in waveguides fabricated in Z-cut substrates [86].

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Acknowledgement

First of all I would like to express my gratefulness to Prof. Wolfgang Sohler who had

kindly accepted me as one of his Ph.D. student nearly four years ago. I must admit

that I was fortunate to get an opportunity for my Ph.D. study in an internationally

recognized “Integrated Optics Group” headed by a personality like him. During my

stay here in Paderborn, I have been benefitted enormously by his excellent guidance

not only in academic research but also in everyday-life. After all, Prof. Sohler con-

tributed this thesis work by many helpful discussions and advice.

This work has been carried out under one of the research project of the Integrated

Optics Group, “Integrated Optics in LiNbO3: New Devices, Circuits, and Applica-

tions” sponsored by Deutsche Forschungsgemeinschaft (DFG). I am thankful to DFG

and the people those who are involved directly or indirectly in this project.

For pursuing my thesis work, I got enormous technological help from Raimund Ricken,

Katja Rochhausen, and Viktor Quiring. Without their meaningful cooperations in dif-

ferent sample preparations, this work could not be finished in time. Moreover, I have

been acquainted with lots of technological idea from them.

I am specially grateful to Dr. Hubertus Suche, from whom I got help in many fronts.

Besides academic discussions, he helped me to build an e-beam evaporation system

for iron deposition: an old e-gun was installed inside an old vacuum chamber lying

in the junk room, but the system is working as good as new one. The copper holder

used in the Lloyd setup was also designed by Dr. Suche. Finally, I am thankful to

him for his careful corrections and suggestions for preparing this thesis.

In course of my work, I also got seniors like Klaus Sch¨

afer, Rudolf Wessel, Agus

Rubyanto, Ulrich Rust and Harald Hermann. They helped me a lot in terms of teach-

ing me integrated optics, introducing different experimental equipments and giving

me valuable friendships. Particularly, I can’t express in words the help I got from

Klaus, Rudi, and Rubi for my initial settlement in Paderborn. Thanks also goes to

my other friends, like Selim Reza, Yeung-Lak Lee, Yoo Hong Min, Ansgar Hellwig,

Marc H¨

ubner, Jie Hun Lee, Suhas Bhandare, and Indira Choudhuri from whom I was

benefitted in many ways in everyday life. My special thanks goes to our secretary

Mrs. Irmgard Zimmermann who not only assisted me in all the official works but also

helped me for my smooth settlement in Paderborn. Whenever I used to get in trouble,

either in the office or in my everyday-life, she always extends her helping hands as

the troubleshooter!

Finally, I should admit that I got the most valuable cooperation from my family:

my wife Susama, and our sweet twins - Satadru and Bipasa. I must confess that I was

extremely cruel to leave them alone from 8-00 am to 10-00 pm. Yes, that is almost

everyday! I hope they have already got some taste - What is a Ph.D!

Bijoy Krishna Das

March 2003