Facultad
de
Ciencias
POLARIZACIÓN DE LÁSERES DE CAVIDAD
VERTICAL (VCSELs) SOMETIDOS A
INYECCIÓN ÓPTICA PARALELA
(Polarisation of vertical-cavity surface-
emitting lasers (VCSELs) subject to parallel
optical injection)
Trabajo de Fin de Grado
para acceder al
GRADO EN FÍSICA
Autor: Alexandra Paola Popp
Director: Angel Valle Gutiérrez
Enero - 2016
En este trabajo investigamos la polarizaci´on de la luz emitida por un l´aser de cavidad
vertical (VCSEL) sujeto a inyecci´on ´optica paralela de luz proveniente de otro laser.
En la primera parte del trabajo medimos las caracter´ısticas del VCSEL emitiendo en soli-
tario. Investigamos propiedades clave del VCSEL para medir algunos de los par´ametros
que caracterizan el funcionamiento del dispositivo. Encontramos una corriente umbral
Ith
= 1
.
618
±
0
.
014 mA con saturaci´on a corrientes cercanas de los 9 mA, una eficiencia
cu´antica interna de
η
= 0
.
1882
±
0
.
0006, encendidos de polarizaci´on y biestabilidad ´optica
interna dependiente de la corriente aplicada. Encontramos un rango de longtitudes de
orden del operaci´on entre 1540 - 1544.5 nm y mediante la medida de los picos de os-
cilaciones de relajaci´on de sistema encontramos una ganancia de
GN
= (1
.
64
±
0
.
2)
·
10
4
Hz.
En la segunda parte del trabajo inyectamos luz de un l´aser sintonizable en un VCSEL
usando un circulador ´optico de tres puertos. Medimos la polarizaci´on dominante (llamada
paralela) y la perpendicular a la anterior (llamada ortogonal). Encontramos una evoluci´on
lineal anticorrelacionada de las potencias de ambas polarizaciones dependiendo de la
potencia inyectada de acuerdo al modelo presentado en el capitulo 2. Presentamos un
mapa del r´egimen de bloqueo a la inyecci´on y encendido de polarizaci´on (IL+PS). Inves-
tigando el comportamiento cuando se aumenta y se disminuye la potencia de inyecci´on
encontramos biestabilidad en la frontera entre las regiones de bloqueo a la inyecci´on y
IL+PS. La evoluci´on de la potencia de las polarizaciones de salida al cambiar la desinton´ıa
en frecuencia se muestra como no lineal, en acuerdo con el modelo utilizado. De nuevo la
frontera anterior se puede identificar como biestable en la mapa de estabilidad. Inves-
tigando como la polarizaci´on depende de la corriente aplicada al VCSEL confirmamos
cualitativamente las predicciones te´oricas.
palabras clave: VCSEL, encendido de polarizaci´on, inyecci´on ´optica paralela
In this work we investigate the polarisation of vertical-cavity surface-emitting lasers
(VCSELs) subject to parallel optical injection from a master laser.
In the first part of the work we measure the characteristics of the free running VCSEL.
Key properties of the used VCSEL have been investigated in order to measure some
of the laser parameters that characterize the device performance. We find a threshold
current of
Ith
= 1
.
618
±
0
.
014 mA with saturation at about 9 mA, an internal quantum
efficiency of
η
= 0
.
1882
±
0
.
0006 and polarisation switching and internal optical bistability
dependent on the bias current. For all possible bias currents we find a wavelength
range of operation between 1540 - 1544.5 nm and by measuring the relaxation oscilla-
tion peaks of the system a differential gain of
GN
= (1
.
64
±
0
.
2)
·
10
4
Hz has been estimated.
In the second part of the work, we inject light from a tuneable laser via a three port
optical circulator into a VCSEL and measure the dominant polarisation (denoted parallel)
and the one perpendicular to it (denoted orthogonal). We observe an anticorrelated linear
power evolution for both polarisations depending on the input current according to the
model presented in chapter 2 and present a map of the injection locking and polarisation
switching (IL+PS) regime. Investigating the behaviour when increasing and decreasing
the injected power we find bistability in the boundary between IL+PS and complete
injection locking. The power evolution of the output polarisations when varying the
frequency detuning could be shown to be nonlinear in agreement with the used model.
Again the boundary between injection locking and IL+PS could be identified as bistable
in a stability map. Measuring the polarisation evolution dependence on the VCSEL bias
current we qualitatively confirm the theoretical predictions.
Keywords: VCSEL, polarisation switching, parallel optical injection
Contents
1 Introduction 3
2 Theoretical Background 4
2.1 SemiconductorLASER............................. 4
2.2 VCSEL ..................................... 5
2.2.1 Structure and Characteristics . . . . . . . . . . . . . . . . . . . . . 5
2.2.2 Advantages and Applications . . . . . . . . . . . . . . . . . . . . . 8
2.3 OpticalInjection ................................ 9
2.4 OpticalFibers.................................. 11
3 Characterisation of the free running Device 13
3.1 Description and Characteristics of the experimental Equipment . . . . . . 13
3.1.1 VCSEL ................................. 13
3.1.2 Analysers ................................ 14
3.1.3 Fiber optical components . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Dependency of VCSEL output Power on applied Current . . . . . . . . . 16
3.2.1 Polarisation Independent . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.2 Polarisation Dependent . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Dependency of VCSEL output Wavelength on applied Current . . . . . . 21
3.4 Spectral Analysis and Relaxation Oszillations . . . . . . . . . . . . . . . . 22
4 Method, Experimental Setup and Results 25
4.1 ExperimentalSetup .............................. 25
4.2 Dependence on the Injected Power . . . . . . . . . . . . . . . . . . . . . . 26
4.2.1 Increasing Injected Power . . . . . . . . . . . . . . . . . . . . . . . 26
4.2.2 Decreasing Injected Power . . . . . . . . . . . . . . . . . . . . . . . 32
4.3 Dependence on the Frequency Detuning . . . . . . . . . . . . . . . . . . . 32
4.4 Dependence on the VCSEL Bias Current . . . . . . . . . . . . . . . . . . . 36
5 Summary and Outlook 41
Bibliography 43
1
1 Introduction
Only very recently, in 2014, the Nobel prize in physics was awarded to Isamu Akasaki,
Hiroshi Amano and Shuji Nakamura for the invention of efficient blue light-emitting
diodes which has enabled bright and energy saving light sources. This is only one of the
many awards for semiconductor technologies but it reminds us of the importance of
semiconductor devices in our daily life. The invention of the blue LED has triggered
a transformation of lighting technology and made it possible to have energy saving,
bright and long lasting light sources. It also reminds us, that there are still challenges in
semiconductor research.
This work focuses on another, but less well known semiconductor device: the vertical-
cavity surface-emitting laser (VCSEL). Invented in 1977 [
1
] it today holds the second
largest production volume of all semiconductor lasers [
2
] but is still rather unknown
to the public. It took 17 years for the devices to become commercialized. The first
application for VCSELs back then in 2004 were optical computer mice, which still is a
large field of application today [
2
]. However, their main applications today lie in optical
signal transmission in local area networks, where data transmission rates up to tens of
Giga-Bits per second can be achieved [
2
,
3
]. In this sector, mainly 850, 1300 and 1550 nm
devices are used.
In this work our objective is to investigate the polarisation of the light emitted by a long
wavelength VCSELs subject to parallel optical injection from a master laser. The work
is divided into four parts. We give theoretical background about semiconductor lasers
and VCSELs in particular as well as optical injection and the expected output evolutions
are considered. Furthermore a brief introduction on optical fibers is presented. In the
second part our experimental equipment is presented and a characterisation of the used
VCSEL is conducted. Methods, setup details and results are shown in the third part of
the work. We discuss the dependence of the polarisation-resolved output power of the
optical injection setup on the injected power, the frequency detuning and the bias current
and also consider optical bistability. In the last chapter a summary and an outlook on
the generality of our findings is given.
3
2 Theoretical Background
In this chapter, a theoretical introduction to relevant concepts and theoretical models
is given. First the general semiconductor laser is introduced before going into detail on
vertical-cavity surface-emitting lasers (VCSELs). Basic concepts of optical injection and
optical fibers are presented.
2.1 Semiconductor LASER
There are three possibilities for light-matter interaction. Spontaneous emission, stimu-
lated emission and absorption. The key process for semiconductor lasers, like for all lasers,
is stimulated emission. Stimulated emission is an interaction between a photon
hν
and
an electron in the upper level of a system. When the photon passes the excited electron it
can cause downconversion. This downconversion leads to the emission of a clone photon
of our initial one. These two photons can now interact with more excited electrons,
leading to amplification of the initial radiation. This amplification can however only take
place if the photons encounter a sufficient amount of excited electrons. Therefore a pump
source is used to ensure population inversion. [4]
Characteristic for a semiconductor is its band gap between valence band (
E < Ev
) and
conduction band (
E > Ec
). In a semiconductor laser, the two states of the system
involved in laser operation are energy levels from the conduction band and the valence
band, respectively. Interaction can only occur for hν > Eg.
Figure 2.1:
Possible light matter interactions for a semiconductor. a) absorption, b)
emission c) stimulated emission [5]
4
The active medium of semiconductor lasers is usually heterostructured layers with a
pn
junction with current in the forward direction.When the current is large enough,
there is a sufficient number of electrons in the conduction band to provide light am-
plification. Due to the high electron density in semiconductors a very high gain can
be achieved and already small cavity distances on the order of
∼
1 mm are possible
[
4
]. Cavity mirrors for semiconductor lasers are the crystal surfaces itself, which can
be enhanced using additional Bragg mirrors directly grown on both sides of the active
material. For a GaAs semiconductor with an emission at
λ
= 850 nm and an refractive
index of
n
= 3
.
5 reflectivities on the order of 30% can be achieved. The gain from the
pn
junction is however sufficient to produce laser radiation even for a loss of 70% per turn. [
4
]
We can distinguish two types of semiconductor lasers, depending on the direction of the
active medium in relation to the emitted light beam. For edge emitting devices the active
medium is parallel to the light beam while for vertical emitters the active medium is
orthogonal to the light beam. A comparison between edge emitters and VCSELs can be
found in figure 2.4.
2.2 VCSEL
Vertical-cavity surface-emitting lasers are vertical semiconductor emitters which means
that their active medium is orthogonal to the emitted laser radiation. They were invented
by Kenichi Iga in 1977 [
1
] and currently hold the second largest production volume
among all types of semiconductor lasers while recently being subject to intensive research
[
2
]. VCSEL wavelengths of 414 - 2400 nm have been achieved [
2
]. In this work we will
focus on so called long wavelength VCSELS emitting at around 1500 nm. These are
of particular interest because the glass material of optical fibers has a significantly low
absorption at this wavelength and it is thus popular within optical telecommunications.
2.2.1 Structure and Characteristics
There are three common possibilities to fabricate long wavelength VCSELs, using ei-
ther GaInAs/InP, AlGaInAl/AlGaInAs or GaAs systems [
1
]. A schematic scheme of a
VCSEL is presented in figure 2.2. The VCSEL is mounted on a metallic contact (1).
The bottom mirror (2) is usually an
n
-doped DBR with a reflectivity on the order of
99
.
5%, while the top mirror (6) is a
p
-doped DBR. Doped mirrors are used in order
to reduce ohmic losses and achieve a higher conductivity [
6
]. The mirror reflectivity
needs to be higher than in the case of edge emitters, due the vertical structure with
a very short cavity length. They usually consist of alternating GaAs and AlAs layers
[
6
]. The VCSEL is electrically pumped by a current in forward direction of the
pn
junction by a current source. As an active medium, a quantum well is used. The vertical
structure and high reflectivity mirrors allow to build structures even smaller than for
edge emitters. Cavity length is on the order of 1
µ
m [
6
] while complete devices can be
as small as few
µ
m in all directions [
5
]. VCSELs can be multimode or single mode devices.
5
Figure 2.2:
Schematic scheme of a VCSEL. 1 metallic contact 2 bottom mirror 3 oxidised
layer 4 active medium 5 cavity 6 top mirror 7 laser emission [5]
The standard rate equation model for a linearly polarised single-mode semiconductor
laser can be used to derive the temporal evolution of the light emitted by these devices
[7]:
dP
dt =GN(N−Nt)P−P
τP
+Rsp(N) (2.1)
dN
dt =I
e−R(N)−GN(N−Nt)P
where
P
is the number of photons in the cavity,
N
is the number of carriers in the active
region,
GN
is the differential gain,
Nt
is the number of carriers at transparency,
τP
is the
photon lifetime,
Rsp
(
N
) is the spontaneous emission rate coupled to the laser mode,
I
is
the bias current,
e
the electron charge and
R
(
N
) the carrier recombination rate. Fur-
ther specifications regarding the functions
Rsp
(
N
) and
R
(
N
) can be found in reference [
7
].
From equations 2.1 the relaxation oscillation frequency
νR
and the damping rate Γ
R
of
the relaxation oscillations can be derived [7]. They are given by
νR=rGN
e(I−Ith) (2.2)
ΓR=1
21
τn
+GNτp
e(I−Ith)
where
τn
is the differential carrier lifetime at the lasing threshold. Relaxation oscillations
are oscillations that arise from the periodic interaction between the population inverted
6
level of the laser and the electric field inside the cavity [
6
]. They appear when the system
departs from its steady state due for instance to a change in the bias current driving
the laser and get damped over the operation time. A scheme of the change in current,
population and output power is presented in figure 2.3.
Figure 2.3:
Damped relaxation oscillations caused by a change in current (a) in the
population, (b) the number of photons and (c) the power [8]
The optical power emitted by a laser is directly proportional to the number of photons
emitted. Following from equations 2.1 in which we assume steady state, hence
dN
dt
=
dP
dt
= 0
an expression of the optical power can be derived as:
P=η·hν
e(I−Ith) (2.3)
where
P
is the power emitted by the VCSEL,
η
is the internal differential quantum
efficiency,
h
is the Planck constant,
ν
is the frequency the VCSEL is emitting at,
I
is the
bias current corresponding to the output
P
and
Ith
is the threshold current [
8
]. Following
this equation, the internal differential quantum efficiency of a device is the ratio of the
number of photons in the light beam to the carriers above threshold. When the output
power
P
and applied current
I
to a VCSEL are measured while the frequency
ν
and the
threshold current Ith are known, ηcan be estimated.
7
2.2.2 Advantages and Applications
Todays the main application for VCSELs lie in near and midrange optical communications.
They are becoming key devices for LAN [
1
] especially for metropolitan areas and wide
area networks [
3
]. State of the art 2013, transmission rates of up to 25 GBits
/
s were
predicted [2]. However in 2014 already rates of 46 Gbits/s have been reported [9].
Features of vertical emitters are low power consumption together with a high speed
modulation and low driving current. The narrow circular beam can be used for direct
fiber coupling [
3
] or applications where only simple beam shaping optics are desirable.
Devices are also characterised by high reliability and accurately predictable lifetimes on
the order of 10 million hours at room temperature [2].
Diverse applications for VCSELs arise from the possibility of having single-mode emis-
sion with one linearly polarised quasi-Gaussian transverse mode as well as continuous
wavelength tuning available just by changing cavity dimensions [2].
The advantages of VCSELs compared to the other two most common semiconductor
devices, edge emitters and LEDs, are listed in table 2.1. Schemes of the three devices in
comparison are presented in figure 2.4.
Figure 2.4: Edge emitting device (left), VCSEL (center), LED (right) [2]
VCSEL vs. edge emitter VCSEL vs. LED
+ low threshold current + high modulation bandwidth
+ circular beam profile output + circular beam profile output
+ high power conversion efficency + high power conversion efficency
+ wafer-level testing + small operating current
+ simple mounting and packaging + high output power
+ possibility of 2d arrays + narrow spectrum
Table 2.1: VCSEL advantages against LEDs and edge emitters [2]
8
2.3 Optical Injection
Due to their high gain, low facet reflectivity and amplitude-phase coupling through
the linewidth enhancement parameter
α
, semiconductor lasers are sensitive to optical
injection from another laser [
10
]. Under certain conditions we can achieve optical injection
locking (OIL) from this procedure. OIL signifies that the slave laser oscillation frequency
equals that of the master laser. Also a constant phase difference between the electric
fields of master and slave laser is obtained. It has been intentionally developed to control
and stabilise laser oscillations, today the applications include intensity, frequency and
partition noise reduction, microwave signal generation or the production of chaotic signals
for secure communications and random number generation [
10
]. OIL can be achieved by
injecting a single-mode signal from a master laser with a frequency difference between
the signals of the two lasers on the order of GHz. This frequency difference is called
detuning.
OIL locking for VCSELs has been subject to studies for some time, however only recently
the attention has shifted to also considering polarised optical injection [
11
]. Our VCSEL
has two linear polarisation modes, of which one is dominant in the free running operation.
We call them parallel (
X
) and orthogonal (
Y
). The directions of
X
and
Y
electric fields
are orthogonal and lie in the active region plane. We consider parallel optical injection
as injecting linearly polarised light from the master laser with a polarisation parallel
to the dominant linear polarisation of the VCSEL and orthogonal optical injection as
injection with light orthogonally polarised to the dominant VCSEL polarisation direction.
A schematic example of optical injection with corresponding terminology is given in
figure 2.5.
Figure 2.5:
Scheme for optical injection.
X
dominant polarisation, injection (red) and
detuning with respect to
X
. Parallel optical injection: polarisation of injected
light parallel to
X
, orthogonal optical injection: polarisation of injected light
orthogonal to X
9
Most experimental work so far has been dealing with orthogonal optical injection, only
recently parallel optical injection in 1550 nm VCSELs has been studied and stability maps
have been presented [
11
,
12
]. Predominantly the phenomena of injection locking has been
studied so far. Other phenomena such as polarisation switching (PS) or periodic dynamics
and a period-doubling route to chaos are however also possible depending on the injection
conditions. Polarisation switching is a phenomena, where under certain conditions the
dominant polarisation can change. In a VCSEL with two linear polarisation directions,
where initially
X
is the dominant and
Y
is suppressed, after PS,
Y
is dominant and
X
is
suppressed. This is illustrated in figure 2.6.
(a) Parallel polarisation dominant, orthogonal sup-
pressed
(b) Orthogonal polarisation dominant, parallel sup-
pressed
Figure 2.6:
Schematic plot of polarisation switching. (a)
X
dominant,
Y
suppressed after
PS (b) Ydominant, Xsuppressed
An extension of the model 2.1 to a VCSEL with two linear polarisation modes under
parallel optical injection is given in [
13
]. A variety of dynamical states is found in [
13
].
A new state in which the
X
polarisation is locked to the injection and the
Y
polarisation
of the VCSEL is excited is predicted in [
13
]. We call it IL+PS state. A similar state has
also been predicted very recently by using a similar model of edge-emitter semiconductor
lasers subject to optical injection [
14
]. This work also includes analytical expressions in
order to analyse the stability of this solutions. Figure 3 of reference [
14
] gives the regions
in the plane detuning vs injected power in which this solution is stable and hence can be
observed. In order to calculate the theoretically expected behaviour, we use the approach
from reference [
14
] and expressions (10), (11) and (12) of reference [
13
], which describe
the evolution of
X
and
Y
in dependency of the power injected into the slave laser
Pinj
and the frequency detuning denoted by νi:
10
Px=κ
2γa2
·Pinj
1 + πνi
γa+α2(2.4)
Py=µ
1−γa
κ
− Px(2.5)
φx= arctan πνi
γa
+α(2.6)
where
κ
is the field decay rate,
γa
the linear dichronism,
α
the linewidth enhancement
factor and
µ
the normalised bias current [
15
].
Px
is the normalised output power of the
parallel polarisation,
Py
of the orthogonal.
νi
is the frequency detuning,
Pinj
the power
injected into the VCSEL and
φx
the phase difference of the electrical fields between the
VCSEL and the master laser.
2.4 Optical Fibers
An optical fiber consists of a core, a cladding and a polymer jacket, as shown in figure
2.7a. The refractive index of the respective layer decreases from inside to outside. Usually
optical fibers are made from a core of doped silica (glass) and a cladding of pure silica.
(a) Schematic drawing of an optical fiber [16] (b) Propagation of light in an optical fiber [16]
Figure 2.7: Setup and rey propagation of fibers
Signal transmission in optical fibers is based on total internal reflection. A scheme of
the propagation is shown in figure 2.7b. We have a core with an refractive index
n1
, a
11
cladding with refractive index
n2
and a critical angle
φc
. The incoming light ray with an
angle
φ>φc
undergoes total internal reflection at point B, then at point C and like this
at all following core to cladding interfaces. Like this it continues to the end. Total internal
reflection is characterised by the fact that the
R
=
reflected power/incident power
= 1
[16]. When using Snell’s law
n1sin (φin) = n2sin (φtrans) (2.7)
sin (φin) = n2
n1
sin (φtrans)
we can derive the critical angle for sin (φtrans) = 1, hence
φin =φc= arcsin n2
n1.(2.8)
When using fibers in experiments, we have to consider two possible types of connectors
distinguished by their ferrule polishing, angled physical contact (APC) and physical
contact (PC). Connection schemes are shown in figure 2.8. APC connectors have an 8
◦
cutoff in their ferrules in order to make a tighter connection and to decrease the reflected
power at the connector [
17
]. It is not possible to directly connect PC to APC without
inducing extra losses.
Figure 2.8: Connection scheme for APC and PC connectors
12
3 Characterisation of the free running
Device
In this chapter components of the setup used for the following measurement are presented
along with a characterisation of the used single mode VCSEL. All measurements are
performed at a temperature of T= 25.00 ±0.05 ◦C.
3.1 Description and Characteristics of the experimental
Equipment
In this section, setup elements and analysers used for this work are presented. At first
the used VCSEL and its controllers are introduced, then our analysers are described and
in the end of this section all components connected with the fiber optics in our setup will
be presented.
3.1.1 VCSEL
We employ a commercial singlemode VCSEL (RayCan) with an emission range of ap-
proximately 1540 - 1545 nm. Detailed analysis of the specifications of the laser is given
in the later part of this chapter. A scheme of our VCSEL is presented in figure 3.1.
Figure 3.1:
Schematic structure of our VCSEL: 1 top contact 2 top mirror 3 InP spacer
4 current confienment 5 active medium 6 bottom contact 7 bottom mirror 8
InP substrate 9 emitted light [6]
13
It is fabricated on a InP substrate with an active region of height 0
.
5
λ
, where
λ
is
the wavelength of the light inside the device, and consists of multiple quantum wells.
The active medium is placed in between two n-InP plates, which are used to decrease
electric resistance. Top and bottom mirrors are made from layers of InAlAs/InAlGaAs. [
6
]
The VCSEL current is controlled by a Thorlabs LDC202B laser diode controller. The
controller allows input precision of 0.001 mA in a range from 0 to 20 mA. It handles
the Thorlabs TCLDM9 laser diode mount which typically operates in a temperature
range from 5 - 70
◦
C. The temperature control of the mount is operated by the Thorlabs
TED 200 temperature controller that allows an input precision of 0.01
◦
C and permanent
temperature surveying. Operating temperature ranges from 0 - 40
◦
C. When monitoring
the active temperature due to external influences, a real ∆
T
= 0
.
05
◦
C is however more
reasonable.
3.1.2 Analysers
High resolution optical spectrum analyser (BOSA)
The Aragon Photonics BOSA 210 is used for optical spectral analysis. It uses stimulated
Brillouin scattering spectroscopy for optical spectrum analysis. The Brillouin response
of a tuneable laser with a continuously changing wavelength over a desired spectral
range is measured to obtain the desired spectrum in high resolution [
18
]. A maximum
resolution of 10MHz at an 80 dB dynamical range can be obtained. The tuneable laser
allows high sweep speeds in order to obtain nearly instantaneous measurement results.
Due to internal heating of the tuneable laser, the device should undergo a run and stop
procedure before each measurement when measuring absolute wavelength values to avoid
shifting of the spectra.
Optical Spectrum Analyser (OSA)
For higher amplitude resolution optical spectrum analysis the Anritsu MS9710B diffraction-
grating spectrum analyser is used. The OSA operates within a wavelength range of 600
- 1750
,
nm with a precision of ∆
λ
=
±
0
.
05 nm (∆
ν
=
±
6
.
3 GHz). Minimum resolution
is 0.07 nm. It can resolve amplitudes in a range of -90 - +10 dBm with an accuracy of
∆
P
= 0
.
4 dB (videobandwidth 10 Hz for 10 times sweep averaging) [
6
]. It therefore has a
higher amplitude but lower wavelength resolution than the BOSA.
Photodetector (PD)
A photodetector produces an output voltage pulse proportional to an optical input signal
that can be processed by analysers. We use the Thorlabs PDA8GS, which is a InGaAs
PIN photodiode coupled with a transimpedance amplifier. Our device has a bandwidth
of 9 GHz and a peak response of 0.95 A/W at 1550 nm.
14
Microwave Spectrum Analyzer (MSA)
The Microwave Spectrum Analyzer Anritsu MS2719B is used to monitor the microwave
emission spectra of our VCSEL. Input are electrical impulses from a photodetector. It
measures the intensity of certain frequencies in a range from 9 kHz to 20 GHz. It provides
an output of signal strength in dBm.
Fiber-optic power meter (PM)
We use multiple Thorlabs PM20 fiber-optic power meter to record output powers of
our lasers. The device has a InGaAs sensor. The measurable optical power ranges from
-60 dBm to 20 dBm, the covered wavelength range is 400 - 1700 nm. Measurements can
be conducted in dBm or W, with a measurement uncertainty of ∆
P
=
±
0
.
25 dB. Signal
input is via direct fiber connection.
Attenuator
We use the OZ Optics Digital Variable Attenuator DA-100. It allows direct input of the
desired attenuation in dB through a keypad. The attenuator works by block type, which
means that a blocking device is inserted into a beam of collimated light from the source
fiber. The angle of the blocking device is depending on the desired attenuation [
19
]. The
device allows attenuation from 0 - 60 dB.
Tuneable Laser
The external cavity semiconductor tuneable laser Anritsu Tunics Plus is used in our
experiments. It can be tuned in a wavelength range from 1500 - 1625 nm with a minimum
resolution of 1 pm and a maximum output power of 8 mW. The device consists of a diode
laser, a dihedral reflector and a diffraction grating. Its tuneability is achieved by rotating
the reflector around a center of rotation, so that the ratio of cavity length to wavelength
is kept constant. [6]
3.1.3 Fiber optical components
Fiber Polarisation controller (FPC)
We use the Fiber U-Bench polarisation controller Thorlabs FBR05. It consists of three
waveplates which are placed between two fiber collimators. The two outer waveplates
correspond to
λ/
4, while the inner plate corresponds to
λ/
2. The desired polarisation can
be selected by rotating the waveplates against each other. Due to their mode of operation
fiber U-Bench polarisation controllers are more stable than looped fiber controllers.
Fiber Optical Circulator
We use a non-polarisation maintaining fiber optical circulator from Newport with a center
wavelength of 1550 nm. Our circulator has three ports. A schematic plot is presented in
15
figure 3.2. When light enters port 1 it can only exit through port 2. When it enters port
2 it can only exit port 3 and when it enters port 3, it will suffer a large amount of losses
in ports 1 and 2. Fiber optical circulators are non-reciprocal, which means that changes
induced in the light by traveling in one direction are not reversed when traveling in the
other [6].
Figure 3.2: Schematic scheme of a 3 port optical circulator [6]
Polarisation Beamsplitter
We use the Newport F-PBC-15-SM-FA polarisation beam combiner/splitter. The device
can be used to combine light from two fibers into one single fiber or split the signal of one
fiber into its parallel and orthogonal polarisation components. The device has a center
operation wavelength of 1550 nm. The ratio of parallel to orthogonal polarisation loss is
2.25 dB.
Optical Fiber 50/50 Coupler
We use the Newport F-CPL-F12155 optical fiber 50/50 coupler. The device has a center
operation wavelength of 1550 nm, return loss of 55 dB and a maximum insertion loss of
3.4 dB.
3.2 Dependency of VCSEL output Power on applied Current
In order to characterise the device, at first a measurement of the output power depending
on the driving current of the VCSEL is conducted. Two different situations are monitored,
first the VCSEL is directly connected to a power meter (PM) and the total output power
independent of the polarisation is measured. In a second step the VCSEL output is first
sent into a polarisation controller (PC) and from there into a bench fiber with a rotating
linear polariser before entering the PM.
16
3.2.1 Polarisation Independent
The results of the polarisation independent measurement can be seen in figure 3.3.
I [mA]
0246810
Power [µW]
0
100
200
300
400
500
600
700
800
900
(a) Full Measurement
I [mA]
6 6.2 6.4 6.6 6.8 7
Power [µW]
600
610
620
630
640
650
660
670
680
690
700
(b) Detail
Figure 3.3:
Measurement of the total output power over a range of different bias currents
As expected very small output is present underneath the threshold current. Through
a linear fit the threshold could be determined as
Ith
= 1
.
618
±
0
.
014 mA, which is in
agreement with previous measurements for this device [
20
]. After the threshold the
output power increases linear until about 6.4 mA. From figure 3.3b (Detail) it can be seen
that a drop in the total power of about 20
µ
W appears at this point. This drop arises
when switching from a dominant polarisation (denoted as parallel) to a polarisation with
smaller gain (denoted as orthogonal) is occurring. We choose in the optical spectrum that
parallel (orthogonal) polarisation is corresponding to the longer (shorter) wavelength.
After the switch, operation is again linear before reaching saturation at about 9 mA.
From this measurement, the internal quantum efficiency for the transformation of electric
to optical power can be determined using equation 2.3. We compute
η
= 0
.
1882
±
0
.
0006
by a fit of
P
over (
I−Ith
). This value is in agreement with previous measurements for
this device [20].
3.2.2 Polarisation Dependent
Now, the VCSEL output is first sent through a polarisation controller (PC) before passing
a bench fiber and the PM. We choose
I
= 5 mA for emission in parallel direction. The
linear polariser in the bench fiber is set to 0 degrees perpendicular to the optical tabel
and the polarisation is adjusted to a minimum. All measurements now correspond to a
state where only the orthogonal polarisation is present. For measurements of the parallel
polarisation, the polariser is set to 90 degrees perpendicular to the optical tabel. Mea-
surements of the two polarisations for one current are taken successively. Results can be
17
obtained from figure 3.4, where
I
is given in a linear scale, while for
Pa
a logarithmic scale
is chosen. Spectra corresponding to figure 3.4 taken with the BOSA are given in figure 3.6.
I [mA]
2 4 6 8 10
Power [µW]
100
101
102
103Parallel Polarization
Orthogonal Polarization
Figure 3.4:
Polarisation dependent measurement of the output power over a range of
different driving currents
Right after the threshold current, the orthogonal polarisation is dominant for a short
range followed by a period where both polarisations are active over a range of about 1 mA.
Then the orthogonal polarisation switches off and the parallel becomes the dominant
one over a range of about 3 mA. In theory the inferior polarisation is supposed to stay
constant while the dominant polarisation increases. Due to the logarithmic scale of our
graphical representation we discover, that there is a slight trend of increase in the inferior
polarisation. This behaviour occurs, due to imperfect polarisation alignment between
the direction of the linear polariser and the direction of the linear polarisation of the
VCSEL. Before and after each measurement the polarisation is switched from one state
(either 0
◦
or 90
◦
) to the other. This manual alignment is however not in a way that
zero intensity in the inferior polarisation can be achieved. Hence, while the power in the
dominant polarisation increases this polarisation contaminates the inferior. With increase
of the dominant polarisation we see an increase of this contamination through out the
measurement. Also baseline jumps can be explained by the fact that new polarisation
alignment is done for each measurement, due to this the alignment may vary slightly
between measurements. Close to 6 mA the dominant polarisation switches from the
parallel to the orthogonal polarisation. This result is in agreement with the result from
section 3.2.1 where we studied an effect in the total power due to a switch where the
inferior polarisation becomes the dominant one. The parallel polarisation is switched
back to the dominant position at about 8 mA and stays dominant until saturation is
reached.
18
During all polarisation switchings we observe several currents where both polarisations
are of equal value corresponding to the value of the previously dominant polarisation,
independent of the kind of switching. Consistently this should go along with peaks in
figure 3.3, which is not the case. If we look at the optical spectrum at some of the
values where this behaviour occurs, we observe jumps between two stable states. This
phenomenon is qualitatively presented in figure 3.5 where two different polarisation states
for the same bias current
I
= 6
.
4 mA are shown. Both spectra were taken with the same
parameters. Figure 3.5a was recorded right after setting the parameters. After waiting
for a short time the polarisation state changed due to noise resulting in figure 3.5b. The
slight decrease in wavelength from figure 3.5a to b is most probably due to the heating
of the internal tuneable laser of the BOSA.
Wavelength [nm]
1541.8 1542 1542.2 1542.4 1542.6 1542.8
Signal [dBm]
-70
-60
-50
-40
-30
-20
-10
0
(a) Orthogonal polarisation dominant, parallel sup-
pressed
Wavelength [nm]
1541.8 1542 1542.2 1542.4 1542.6 1542.8
Signal [dBm]
-70
-60
-50
-40
-30
-20
-10
0
(b) Parallel polarisation dominant, orthogonal not
visible
Figure 3.5: Spectra for I= 6.4 mA illustrating internal bistability of the VCSEL
The rate equations for the VCSEL predict internal optical bistability of our system in
some regions [
21
]. If we go close to the boundaries of these regions, we do not only see
stable polarisations but often instantaneous jumping between two polarisation states.
Our only explanation for the behaviour in figure 3.4 lies in the way the PM measures at
these points. As we see in our optical spectrum, jumps occur in a time scale of seconds.
Readings in our power meter correspond to averages in much shorter scales. These
readings change between a large and a small value. In figure 3.4 we have represented
the large value. This is the reason why figure 3.4 is inconsistent with figure 3.3 in the
bistable regions. A power average of low and large values in the bistable regions should
be done to achieve consistency in future work.
19
Wavelength [nm]
1539.6 1539.8 1540 1540.2 1540.4 1540.6
Signal [dBm]
-70
-60
-50
-40
-30
-20
-10
0
(a) I= 1.8 mA
Wavelength [nm]
1539.8 1540 1540.2 1540.4 1540.6 1540.8
Signal [dBm]
-70
-60
-50
-40
-30
-20
-10
0
(b) I= 2.3 mA
Wavelength [nm]
1541.2 1541.4 1541.6 1541.8 1542
Signal [dBm]
-70
-60
-50
-40
-30
-20
-10
0
(c) I= 4.5 mA
Wavelength [nm]
1542.6 1542.8 1543 1543.2 1543.4
Signal [dBm]
-70
-60
-50
-40
-30
-20
-10
0
(d) I= 7.3 mA
Wavelength [nm]
1544 1544.2 1544.4 1544.6 1544.8
Signal [dBm]
-70
-60
-50
-40
-30
-20
-10
0
(e) I= 9.0 mA
Figure 3.6:
Spectra corresponding to the total power over a range of different driving
currents
20
3.3 Dependency of VCSEL output Wavelength on applied
Current
Taking into account the previous results, an analysis of the output wavelength for a range
of currents is conducted. Therefore the VCSEL is directly connected to the BOSA where
the center wavelength of the spectra is measured for each current. When more than one
peak is present in the spectrum, the one with the highest intensity is chosen. Results can
be obtained from figure 3.7.
I [mA]
0246810
Wavelength [nm]
1540
1540.5
1541
1541.5
1542
1542.5
1543
1543.5
1544
1544.5
Figure 3.7:
Measurement of the wavelength with maximum intensity over a range of
different driving currents
Results show three different regions, now denoted as
λ1
,
λ2
and
λ3
. The first region
λ1
corresponds to the region before the first switching between
Ith
and about 3 mA, where
the orthogonal polarisation is dominant. A linear increase is visible. Then a polarisation
switch to the parallel polarisation takes place. This is consistent with our previous results.
The wavelength of the parallel polarisation is greater than the one of the orthogonal and
we measure a sudden jump in wavelength to a higher value. Again the increase is linear
until 6 mA where another jump, this time to a lower wavelength, and hence a switch
back to the orthogonal is visible. Increases in all three ranges can be considered linear.
R2and slope values are given in table 3.1.
m±∆m R2
λ10.391 ±0.002 0.997
λ20.528 ±0.009 0.998
λ30.668 ±0.007 0.999
Table 3.1: Slope and R2values for output current ragnes λi
From previous results [
20
], we thought that the slopes of the two polarisations should
stay constant over the complete range of currents. Results from table 3.1 however show
21
that this is not the case. We see a constant increase of the slope from low to high
current values. This discrepancy probably arises from the measurement procedure. In
previous experiments, this measurement was conducted with the OSA, which offers a
better amplitude resolution, hence both polarisation peaks have been visible throughout
the whole range of currents. Slope fits previously were only conducted over the total
range of currents. The measurement presented here was taken with the BOSA, therefore
we trade a higher wavelength resolution for a lower amplitude resolution. Due to this it
was not possible to monitor both polarisations throughout the complete range of currents,
hence only the dominant one is plotted and hence three fits were done. These fits show
that over the whole current range a single linear relation between
λ
and
I
does not hold.
3.4 Spectral Analysis and Relaxation Oszillations
To complete the characterisation of our device, the spectrum was analysed using the
MSA in order to measure the relaxation oscillation frequency. Spectra for three different
currents are presented in figure 3.8a, while the results following equation 2.2 are shown in
figure 3.8b. Computed relaxation oscillation frequencies for different currents are given
in table 3.2.
ν [GHz]
012345
Intensity [dBm]
-90
-85
-80
-75
-70
-65
-60
-55
I = 1.8 mA
I = 3.3 mA
I = 6.0 mA
(a) Radiofrequency spectrum of the free running
VCSEL for different currents
I - Ith [mA]
0 0.5 1 1.5 2 2.5 3
νR 2 [GHz2]
0
1
2
3
4
5
6
7
8
(b) Squared relaxation oscillation frequencies at dif-
ferent currents subtracted by threshold current
Figure 3.8: Radiofrequency spectra and obtained relaxation oscillation frequencies
The peak within each of the spectra in figure 3.8a corresponds to the relaxation oscillation
frequency at the corresponding current. With increasing current the oscillation peaks shift
further away from the initial signal. The spikes in the signal, most prominently visible
for
I
= 1
.
8 mA correspond to feedback from the cavity formed with the VCSEL mirrors
and the tip of the fiber pigailed to the VCSEL. The fiber has a length of approximately
1 m. The corresponding frequency allowed for this cavity is
c0/
2
nL
, where
c0
is the speed
22
of light in vacuum and nis the refractive index of the fiber (∼1.5). Hence
νreflection =c0
2nL =3·108m
s
2·1.5·1 m ∼100MHz (3.1)
This could be avoided by closing off remaining air in the connection between the output
fiber of the VCSEL and our detector with special gel. We chose not to do so in order
to avoid detector contamination. The 100 MHz peaks are reduced by
FFT
low pass fil-
ters with a cut-off frequency of 0.001 GHz. The smoothed data is then used for peak fitting.
In figure 3.8a a dip in all spectra is visible for
ν∼
1
.
8 GHz. This dip is an intrinsic
malfunction of the RSA. It presents no problem for our analysis as long as it does not
directly correspond to the location of the relaxation peak. Thus, measurements for
2
.
7 mA and 3
.
0 mA are not presented. A dependency of
ν2
R
= (2
.
6
±
0
.
3)
·
(
I−Ith
)+0
.
2
with
R2
= 0
.
971 is found. Our data is not as good as in previous measurements [
7
],
because we chose not to measure with the reflection reduced method. Thus it is harder to
determine the true peak of the spectra due the reflection contamination which is visible
in figure 3.8a. In order to calculate the differential gain
GN
from our dataset we use eq.
2.2. Using the slope from figure 3.8a computed as (2.6±0.3), we arrive at
GN= (1.64 ±0.2) ·104Hz.(3.2)
Compared with previous results [
8
,
20
] this value for
GN
seem reasonable. Our computed
error is however slightly larger than in previous cases. This high errors most probably
arrive from the previously mentioned difficulties in the peak fitting process. Due to these
difficulties also only very few points are observed which could also be a contribution
to the higher error. In order to check the results, in figure 3.9 an optical spectrum at
I= 3.05 mA is presented with a span of 8 GHz.
Frequency [GHz]
-4 -3 -2 -1 0 1 2 3 4
Signal [dBm]
-80
-70
-60
-50
-40
-30
-20
-10
0
Figure 3.9:
Optical spectrum at
I
= 3
.
05 mA, span of 8 GHz. Center frequency shifted
to 0 GHz.
23
Relaxation oscillation peaks appear as satellite peaks and should be located at
νR∼
2.0 GHz, which is in agreement with our computed data which predicts νR= 1.5 GHz.
I[mA] 1.8 2.1 2.4 3.3 3.6 3.9 4.2 4.5
νR[GHz] 0.62 1.15 1.39 2.39 2.41 2.49 2.67 2.54
Table 3.2: Computed relaxation oscillation frequencies after data smoothing
24
4 Method, Experimental Setup and Results
In this chapter we analyse the polarisation switching states of our VCSEL in an ex-
perimental way. Stability maps obtained by variation of injection power at a constant
detuning and variation of the detuning at a constant injection power are presented.
Variation of the bias current is also subject to our investigations.
4.1 Experimental Setup
We use an all-fiber setup shown in figure 4.1 to achieve parallel optical injection. Light
from a tuneable master laser is injected into a 1550 nm VCSEL. The laser light is passed
through a variable attenuator to adjust the injected power before the polarisation is
selected with a polarisation controller. An APC/PC connection fiber is inserted in
between the attenuator and the polarisation controller. We adjust polarisation in a way
that injection is achieved in the same polarisation direction as the dominant VCSEL
polarisation. Another PC/APC connector is installed after the controllers. Injection
is realised by a three port optical circulator. The power injected into the VCSEL is
measured with a 50/50 coupler directing half the injected power to a power meter. After
port 3 of the optical circulator another polarisation controller is placed to select the
parallel VCSEL polarisation as dominant. PC/APC connectors are placed before the
signal passes through a polarising beamsplitter where the different polarisations are
separated. Data acquisition is performed with either a power meter for each polarisation
direction or our high resolution optical spectra analyser (BOSA).
Figure 4.1:
Experimental setup for parallel optical injection. TL tuneable laser, V.A.
variable attenuator, PC1 and PC2 polarisation controllers, PBS polarising
beamsplitter, OC optical coupler, PM power meter.
25
4.2 Dependence on the Injected Power
We choose a bias current of
I
= 3
.
05 mA which is on the order of twice the threshold
current. In the previous chapter we have seen, that according to measurements from
sections 3.2.2 and 3.3 we do not observe any switching or intrinsic bistable behaviour at
this current. Two spectra of our free running VCSEL at
I
= 3
.
05 mA are given in figures
4.2, taken with BOSA and OSA, respectively.
Wavelength [nm]
1540.4 1540.6 1540.8 1541 1541.2 1541.4
Signal [dBm]
-70
-60
-50
-40
-30
-20
-10
0
(a) BOSA spectrum (b) OSA image
Figure 4.2: Free running VCSEL at I= 3.05 mA
In the BOSA spectrum we can only see one clear peak, which is the parallel (also denoted
as
x
) polarisation of the VCSEL emitting at
λ
= 1540
.
91 nm. The OSA also shows us the
suppressed orthogonal (also denoted as
y
) polarisation due to better amplitude resolution,
which is shifted 0.26 nm to the short wavelength site and suppressed by about 30 dB.
Hence the birefringence of our VCSEL corresponds to 33 GHz. We classify the parallel
polarisation as the one that appears at a smaller frequency, and the orthogonal as the
one that appears at the higher, when both are present. The two peaks on the left side of
the OSA spectrum correspond to higher order transverse modes, which are not visible in
the BOSA due to the limited resolution. The two slightly different center wavelengths in
both pictures correspond to calibration differences between the two analysers.
4.2.1 Increasing Injected Power
At first we fix a detuning and increase the injected power in our system in order to classify
different behaviours of the oscillator under parallel optical injection. Figure 4.3 shows
the spectra for five different injected powers at a detuning of
ν
=
−
8
.
4 GHz. The spectra
are normalised in a way that the parallel polarisation of the free-running VCSEL defines
ν
= 0. Our signal is the coherent addition of the VCSEL emission and the reflection of
the optical injection from the front surface of the VCSEL.
For
Pinj
= 133
µ
W (4.3a) we observe periodic dynamics in the parallel polarisation and
26
Frequency [GHz]
-20 -10 0 10 20 30 40
Signal [dBm]
-70
-60
-50
-40
-30
-20
-10
(a) Pinj = 133 µW
Frequency [GHz]
-20 -10 0 10 20 30 40
Signal [dBm]
-70
-60
-50
-40
-30
-20
-10
(b) Pinj = 209 µW
Frequency [GHz]
-20 -10 0 10 20 30 40
Signal [dBm]
-70
-60
-50
-40
-30
-20
-10
(c) Pinj = 416 µW
Frequency [GHz]
-20 -10 0 10 20 30 40
Signal [dBm]
-70
-60
-50
-40
-30
-20
-10
(d) Pinj = 833 µW, averaged
Frequency [GHz]
-20 -10 0 10 20 30 40
Signal [dBm]
-70
-60
-50
-40
-30
-20
-10
(e) Pinj = 1056 µW
Figure 4.3:
Spectra corresponding to different injected powers at a detuning of
ν
=
−
8
.
4 GHz. All spectra were obtained by using a sweep average, in order to
obtain a better image of the relaxation oscillations. Slight peak broadening
is seen in all figures due to this averaging.
27
already an excited orthogonal. With an increase of the total power these dynamics
disappear and for
Pinj
= 209
µ
W (4.3b) we find the parallel polarisation slightly sup-
pressed and an increase in the orthogonal. For
Pinj
= 416
µ
W (4.3c) the free-running
parallel polarisation at 0 frequency is fully suppressed and the orthogonal fully excited.
Figures 4.3a - c show that with an increase of the injected power the free-running parallel
polarisation gets more and more suppressed while in the same time the orthogonal gains
more energy. Figure 4.3c shows injection locking and polarisation switching achieved at
the same time. We will denote this state as IL+PS. If we further increase the injected
power (4.3d,
Pinj
= 833
µ
W), we find a situation where the orthogonal polarisation is
accompanied by two small peaks. These peaks deviate by 1.45 GHz from the main peak.
These frequency peaks are close to relaxation oscillations, which should be located at
2.0 GHz. The polarisation switching is maintained for a range of injected powers, we find
injection locking (IL) at
Pinj
= 1056
µ
W (4.3e). A complete theoretical description of
this situation can be found in [13].
Now we measure the output power evolution over the injected power for several detunings.
A complete set of measurement results for ν=−8.6 GHz is presented in figure 4.4.
Injected Power [µW]
200 400 600 800 1000 1200 1400
Power [µW]
0
10
20
30
40
50
60
70
80
90
100
Parallel Polarisation Px
Orthogonal Polarisation Py
Parallel with Reflection Px+r
Total Power Ptot
Figure 4.4:
Output power evolution over injected power for
ν
=
−
8
.
6 GHz, IL+PS regime
extends from Pinj = 180 µW to Pinj = 1050 µW
For these measurements we have to take the reflection of the VCSEL into account. We fix
a value of detuning and at the three different output ports of our system, we measure
Pinj
,
Px+reflection
(from now on denoted as
Px+r
or ’parallel with reflection’) and
Py
. In order to
obtain the true power in the parallel polarisation
Px
, we conduct in the following a second
measurement where we turn the VCSEL off and just measure the power in the parallel
port of the beamsplitter for different injected powers as shown in figure 4.5a. The reflected
28
power (from now on denoted as
Pr
) is linear with
Pinj
. We now compute
Px
=
Px+r −Pr
.
This procedure can be applied, because following from equation 2.6 the phase difference
the reflected injected light and the
X
polarisation equals 90
◦
. Furthermore we multiply
the orthogonal polarisation power
Py
by 1.68 for all measurements. This is due to the
ratio of parallel to orthogonal polarisation loss of 2.25 dB. Hence the true value of the
power in the orthogonal polarisation is Py=Py, measured ·10(2.25/10) =Py, measured ·1.68.
Injected Power [µW]
0 200 400 600 800 1000 1200 1400
Power [µW]
0
5
10
15
20
25
30
35
(a) Reflected power for parallel polarisation
Injected Power [µW]
200 400 600 800 1000 1200
Power [µW]
48
48.5
49
49.5
50
50.5
51
(b) Detail of the total power, IL+PS regime only
Injected Power [µW]
200 400 600 800 1000 1200
Power [µW]
0
5
10
15
20
25
30
(c) Detail of Px, IL+PS regime only
Injected Power [µW]
200 400 600 800 1000 1200
Power [µW]
20
25
30
35
40
45
50
(d) Detail of Py, IL+PS regime only
Figure 4.5: Power evolution over injected power for ν=−8.6 GHz, zooms of figure 4.4
Before the IL+PS regime, the total power as well as
Px
respectively
Px+r
emit at a power
of about 40
µ
W. After the switching the total power increases to 50
µ
W. In theory we
expect a constant total power along with a linear decrease of
Py
and a linear increase of
Px
in the IL+PS state according to equations 2.4 and 2.5. Linear fits for the
Px
and
Py
are presented in figure 4.5c and d. We find
R2
(
Px
)=0
.
9965 and
R2
(
Py
)=0
.
9983 hence
we consider our data in agreement with the theoretically predicted linear behaviour. We
see however a slight increase (
∼
3%) of
Ptot
(figure 4.5b) along with the other expected
behaviours. A trend for
Ptot
seems to be present in nearly all our measurements and
29
at this point we have no explanation for this deviation from theory. After switching to
complete IL we detect again a decreased total power and nearly no activity in Py.
In order to map the power evolution of our laser, we conduct several measurements for
different detunings in a range of
−
11 to +2 GHz for a range of
Pinj
up to 1
.
3
·
10
3µ
W. All
power evolutions for different regions follow the same scheme. Examples for
ν
=
−
5
.
0 GHz
and
ν
= +1
.
7 GHz (only IL+PS regime, reflection corrected values) are presented in
figure 4.6. We see that measurements from the different regions are in accordance with
the one presented in figure 4.5 and hence conclude that our model seems to be agreeing
with the measured results.
Injected Power [µW]
50 100 150 200 250
Power [µW]
0
10
20
30
40
50
60
70
Parallel Polarisation
Orthogonal Polarisation
Total Power
(a) Detuning ν=−5.0 GHz
Injected Power [µW]
12345678
Power [µW]
0
10
20
30
40
50
60
70 Parallel Polarisation
Orthogonal Polarisation
Total Power
(b) Detuning ν= +1.7 GHz
Figure 4.6:
Power evolution over injected power, IL+PS regime only, parallel polarisation
reflection reduced.
We use all these results to give a map of the IL+PS region of our VCSEL for
I
= 3
.
04 mA
(figure 4.7). We plot the injected power against the frequency detuning
νi
. Points corre-
spond to the points where a switch in behaviour is seen. The enclosed area corresponds to
the IL+PS regime. A theoretically computed stability map is given in figure 4.8. Details
on the theoretical description of this system are given in [13].
Good qualitative agreement between theory and experiment is found. We identify a
stable IL+PS region for our VCSEL for positive as well as negative detunings. The
region for negative detunings is bigger than the region for positive values as expected.
Smaller detunings, in both positive and negative regions are more difficult to measure
because they are subject to less stable detunings and more chaotic behaviour is found.
This makes a distinction between the different states more difficult. Admittedly in this
work only the IL+PS state is analysed and a complete characterisation of other states of
the system is subject to future investigations.
30
νi [GHz]
-10 -8 -6 -4 -2 0 2
Injected Power [µW]
100
101
102
103
104
Figure 4.7:
Map of the IL+PS region for
I
= 3
.
05 mA obtained by increase of
Pinj
for
fixed detunings. Injected power in logarithmic scaling.
-10 -8 -6 -4 -2 0 2
10
-4
10
-3
10
-2
10
-1
10
0
P
inj
i
(GHz)
Figure 4.8:
Theoretical map of the IL+PS region for
I
= 3
.
05 mA, injected power in
logarithmic scaling obtained according to [13].
31
4.2.2 Decreasing Injected Power
In section 3.2.2 we show that our VCSEL itself is subject to optical bistability without an
injecting system. Now we want to analyse the bistability of the IL+PS region. Therefore
we conduct a similar measurement as before and now decrease
Pinj
(Figure 4.9). We
choose only to investigate the negative detuning region because the total IL+PS regime
is greater and more stable in this part.
νi [GHz]
-10 -8 -6 -4 -2
Injected Power [µW]
101
102
103
Up
Down
Figure 4.9:
Map of the IL+PS region for
I
= 3
.
05 mA obtained by decrease (blue, down)
and increase (grey, up) of Pinj for fixed detunings.
We find that now our upper boundary of the IL+PS region is significantly shifted to
lower injected powers for greater detunings. In this case the master laser is able to lock
the VCSEL oscillation for smaller powers, once locking is already achieved. The rate
equations (eq. 2.1) predict the upper boundary to be bistable, which is in agreement
with our results. For detunings on the order of -4 GHz the locking regime is similar, it
is even possible to achieve locking for a detuning where we did not observe locking in
the case of power increase. For small detunings we also experience a shift of the lower
boundary. The area of the IL+PS regime is decreased by a significant amount.
4.3 Dependence on the Frequency Detuning
We choose to investigate the dependency of the stability of our system on the change
of the frequency detuning. Therefore we set again a bias current of
I
= 3
.
05 mA and
now fix the injected power while varying the detuning of our system. We concentrate on
sweeping only the negative detuning region. We measure
Pinj
and
Py
with PMs and
Px
with the OSA because we see fluctuation in the parallel polarisation. The OSA allows us
the possibility of direct sweep averaging. We reduce the reflection of the system again
and multiply
Py
by 1.68 due to the beamsplitter losses.
Px
is manipulated to compensate
for different calibrations of the OSA and the PMs.
32
νi [GHz]
-8.5 -8 -7.5 -7 -6.5 -6
Power [µW]
0
10
20
30
40
50
60
70 Parallel Polarisation
Orthogonal Polarisation
Total Power
Figure 4.10: Power evolution over detuning for Pinj = 151 µW, IL+PS regime only
A measurement for
Pinj
= 151
µ
W is presented in figure 4.10. During measurements the
initial detuning is always decreased to obtain a minimum detuning in the end. For figure
4.10 a sweep average of 10 is conducted for every
Px
. Again we expect a constant total
power. Theory predicts curvature in the parallel as well as in the orthogonal polarisation
accordingt to equations 2.4 and 2.5. Figures 4.11a and b show detailed pictures of parallel
and orthogonal evolution, respectively. A linear slope fit shows the presence of curvature
in the averaged
Px
and
Py
values. The
Px
and
Py
curves both cross the linear fit twice
which supports the existence of some curvature in both polarisation. Measurements
for other currents (figure 4.12)
Pinj
= 39
µ
W (4.12a, b) and
Pinj
= 78
µ
W (4.12c, d),
respectively, show similar behaviour.
νi [GHz]
-8.5 -8 -7.5 -7 -6.5 -6
Power [µW]
4
4.5
5
5.5
6
6.5
7
7.5
8
(a) Detail of Px
νi [GHz]
-8.5 -8 -7.5 -7 -6.5 -6
Power [µW]
47
47.5
48
48.5
49
49.5
50
50.5
51
51.5
(b) Detail of Py
Figure 4.11:
Power evolution over detuning for
Pinj
= 151
µ
W, IL+PS regime only, Detail,
zoom of figure 4.10
33
νi [GHz]
-4.6 -4.4 -4.2 -4 -3.8 -3.6
Power [µW]
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
(a) Pinj = 39 µW, detail of Px
νi [GHz]
-4.6 -4.4 -4.2 -4 -3.8 -3.6
Power [µW]
35.2
35.4
35.6
35.8
36
36.2
36.4
36.6
36.8
(b) Pinj = 39 µW, detail of Py
νi [GHz]
-6.5 -6 -5.5 -5 -4.5
Power [µW]
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
(c) Pinj = 78 µW, detail of Px
νi [GHz]
-6.5 -6 -5.5 -5 -4.5
Power [µW]
27.5
28
28.5
29
29.5
30
30.5
31
(d) Pinj = 78 µW, detail of Py
Figure 4.12:
Power evolution over detuning for
Pinj
= 39
µ
W (a, b) and
Pinj
= 78
µ
W (c,
d), IL+PS regime only, Detail
With the previous hints supporting our theoretical assumption of curvature, nonlinear
regression fits of the data set for
Pinj
= 151
µ
W using eq. 2.4 and 2.5 are computed.
Results are presented in figure 4.13.
Starting with equations 2.4 and 2.5 we use the relations
Px
=
c· Px
and
Py
=
c· Py
to
link the normalised values form theory to our measurement data. In order to estimate
c
we use previously estimated values for
γa
,
κ
,
µ
and
α
. Assuming
κ∼
33 GHz,
µ∼
2
.
29,
γa∼ −
0
.
5 GHz and
α∼
2
.
8 we estimate
c∼
40
µ
W. Computed values can be obtained
from table 4.1.
34
Fit of Px
κ2·Pinj/4 2.31 ·103±0.80 ·103GHz2
γa−2.13 ±0.30 GHz
Table 4.1: Computed values from fit of Pxusing equation 2.4.
νi [GHz]
-8.5 -8 -7.5 -7 -6.5 -6
Power [µW]
4.5
5
5.5
6
6.5
7
7.5
8
8.5
(a) Detail of the parallel polarisation, fit with equa-
tion 2.4
νi [GHz]
-9 -8.5 -8 -7.5 -7 -6.5 -6
Power [µW]
46.5
47
47.5
48
48.5
49
49.5
50
50.5
51
(b) Detail of the orthogonal polarisation, fit with
2.5
Figure 4.13:
Power evolution over detuning for
Pinj
= 151
µ
W, IL+PS regime only, Detail,
fit with eq. 2.4 and 2.5, zoom of figure 4.10
A comparison of the IL+PS areas obtained for the variation of
Pinj
can be obtained
from figure 4.14. Measurements for
Pinj
= 151
µ
W, 78
µ
W and 39
µ
W are included. A
measurement for
Pinj
= 1322
µ
W is excluded because it gave inconclusive results on the
boundaries of the region.
It is significant, that again we can see comparable values for the lower boundary of our
region and decreased values in the bistable boundary to the IL region. This substantiates
the theoretical assumptions. Furthermore the computed IL+PS area is nearly completely
embedded in the area that was obtained for the variation of the injected power. The
most probable reason for the IL+PS regime to be smaller than in the case of a constant
detuning might lie in the measurement process. We denote a generally higher instability
in the system for measurements of detuning variation, which could cause the system to
switch into the IL state. Also the general measurement process is less stable. Due to
internal jittering of the VCSEL and a slight instability of our tuneable laser a variation
of
νi
is harder to implement than a variation of
Pinj
. It is also not possible to monitor
detuning constantly over the measurement process. In order to obtain the steps of
detuning which are taken, a step is set in the TL and the initial detuning is measured
with the BOSA. Then the output is switched to the PMs and OSA, respectively. Data is
taken according to the detuning values displayed by the TL. After the measurement is
35
νi [GHz]
-10 -8 -6 -4 -2
Injected Power [µW]
101
102
103
Constant νi
Constant Pinj
Figure 4.14:
Map of the IL+PS region for
I
= 3
.
05 mA obtained by decrease of the
detuning νifor fixed Pinj (blue) and Pinj for fixed detunings (grey).
completed detuning is measured again with the BOSA. If there are differences between
the estimated and measured detuning, the measured detuning is chosen as the termination
value. The process of connecting and disconnecting the fibers between the PMs and
BOSA could have a so far unknown influence on the measurement parameters.
4.4 Dependence on the VCSEL Bias Current
Now we investigate the influence of the bias current of the VCSEL on the IL+PS region
under parallel optical injection. We keep the setup similar and first fix a bias current
of
I
= 6
.
00 mA. Later we repeat the measurement for
I
= 7
.
00 mA. Figure 4.15 shows
a comparison of the theoretically obtained IL+PS areas for 3.05 and 6.00 mA by using
the model of reference [
14
]. The theoretical curve for
I
= 7
.
00 mA can not be considered
similar to the one for
I
= 6
.
00 mA. We have seen in section 3.2.2 that a polarisation
switching takes place. This switching will influence the
γa
significantly and hence we
arrive to a different situation in the theoretical map, which is not given in this work.
For simplicity we will just deal with qualitative phenomena in the case of
I
= 7
.
00 mA.
Deviations from
I
= 3
.
05 mA for the
I
= 6
.
00 mA case are a shift of the IL+PS area in
the negative detuning domain to the left, hence the state is no longer visible for small
negative detunings. We also see a broadening of this region, where the lower boundary
stays constant but the upper, bistable boundary increases. In the positive domain we still
expect to obtain the IL+PS state for detunings close to 0. The region broadens as both
boundaries upper and lower increase. A stable IL+PS is expected for larger detuning
values than before.
36
-10 -8 -6 -4 -2 0 2 4
10
-4
10
-3
10
-2
10
-1
10
0
P
inj
i
(GHz)
3.05 mA
6 mA
Figure 4.15: Theoretical map of the IL+PS region for I= 3.05 and I= 6.00 mA.
In the case of
I
= 6
.
00 mA we conduct 4 measurements for each current, two in the
positive and two in the negative region to characterise the behaviour of our system at
this current. We choose again to increase the injected power for a constant detuning. In
the IL+PS regime we see the same behaviour as for
I
= 3
.
05 mA, illustrated in figure
4.16a. Linear fits for Pxand Pygive R2(Px) = 0.9990 and R2(Py) = 0.9992.
Injected Power [µW]
50 100 150 200 250 300 350 400
Power [µW]
0
20
40
60
80
100
120
140
Parallel Polarisation
Orthogonal Polarisation
Total Power
(a) νi=−6.1 GHz, IL+PS regime only
Injected Power [µW]
0 50 100 150 200 250 300 350
Power [µW]
0
20
40
60
80
100
120
140
Parallel Polarisation
Orthogonal Polarisation
Total Power
(b) νi=−5.2 GHz
Figure 4.16:
Power evolution over injected power, parallel polarisation reflection reduced
Figure 4.16b illustrates how the evolution changes in the presence of another dynamical
polarisation state. IL+PS is achieved for
Pinj ∈
[40
,
155]
µ
W. For
Pinj ∈
[155
,
281]
µ
W
the behaviour changes.
Ptot
is no longer constant but shows greater variation while
Px
and
Py
show curvature. Analysis of this behaviour in the BOSA showed that some kind
of periodic dynamics are present in this region, before IL starts at Pinj = 305 µW.
37
A map of the obtained IL+PS regions compared with the ones for 3.05 mA is given in figure
4.17. Our characterisation is consistent with theory. For a detuning of
νi<−
6
.
2 GHz we
can no longer close the IL+PS region with our available injected power. For
νi
=
−
6
.
2 GHz
we see a similar lower boundary of the region as for 3
.
05 mA and an increased upper
boundary. This is again very consistent with previous results and our assumption of
a bistability region at the upper boundary of the zone. For 5 GHz we measure similar
values as for the 3
.
05 mA case. At
νi
=
−
4 GHz we can no longer see the IL+PS regime.
This is consistent with an earlier closing of the area. For positive detunings we find
strongly increased values for
νi
= +1
.
4 GHz compared to the situation for 3
.
05 mA. At
νi
= +2
.
9 GHz we measure a smaller IL+PS region again which is consistent with the
fact that the maximum of the positive region has shifted. At
I
= 3
.
05 mA it was not
possible to measure any IL+PS state at this detuning value. The increase is consistent
with figure 4.15. For νi≥+4.0 GHz IL+PS is no longer present.
νi [GHz]
-10 -8 -6 -4 -2 0 2
Injected Power [µW]
100
101
102
103
104
3.04 mA
6.00 mA
Figure 4.17:
Map of the IL+PS region for
I
= 3
.
05 mA (grey) and exemplary measure-
ments at
I
= 6
.
00 mA (blue), obtained by increasing
Pinj
for fixed detunings.
In the case of
I
= 7
.
00 mA we have to consider the polarisation switching that takes place
at
I∼
6
.
5 mA. Hence the orthogonal polarisation is the initially dominant one while the
parallel is the inferior. Parallel and orthogonal are again defined as the one with the
lower (parallel), respectively higher (orthogonal) frequency. We still consider parallel
optical injection, which means injection parallel to the dominant polarisation. Hence
now we inject with a detuning with respect to the orthogonal polarisation. Results for
38
the power evolution are shown in figure 4.18. Only negative detunings were investigated
because for positive detunings too many regions of periodic dynamics in the spectra made
the location of the IL+PS regime difficult. A detailed classification should be subject to
further investigations.
Injected Power [µW]
200 400 600 800 1000 1200 1400
Power [µW]
0
20
40
60
80
100
120
140
Parallel Polarisation
Orthogonal Polarisation
Total Power
(a) νi=−5.8 GHz
Injected Power [µW]
0 200 400 600 800 1000
Power [µW]
0
20
40
60
80
100
120
140
160
Parallel Polarisation
Orthogonal Polarisation
Total Power
(b) νi=−5.1 GHz
Figure 4.18:
Power evolution over injected power
I
= 7
.
00 mA, IL+PS regime only,
parallel polarisation reflection reduced
In the negative detuning domain we see similar behaviour as before. No IL+PS is
found for detunings
νi<
6
.
0 GHz. Measurements for
νi
=
−
5
.
1 GHz (figure 4.18a) and
νi
=
−
5
.
8 GHz (figure 4.18b) are presented. The total power can be considered linear
with deviations on the order of several percent. The dominant orthogonal polarisation is
suppressed and linearly increasing with
R2
(
Py,−
5
.
2) = 0
.
9938 and
R2
(
Py,−
5
.
8) = 0
.
9982
while the parallel polarisation is the dominant one over the IL+PS region and linearly
decreasing with
R2
(
Px,−
5
.
1) = 0
.
9955 and
R2
(
Px,−
5
.
8) = 0
.
9524. For
νi
=
−
4
.
5 GHz
we can only observe dynamics.
39
5 Summary and Outlook
In this work we have conducted several measurements to classify the polarisation of
a VCSEL subject to parallel optical injection under different conditions. First we
have characterised our free-running VCSEL. Our VCSEL has a threshold current of
Ith
= 1
.
618
±
0
.
014 mA and saturation at about 9 mA. Our possible wavelength range is
1540 - 1544.5 nm, the birefringence of the device is 33 GHz. We find an internal quantum
efficiency of η= 0.1882 ±0.0006 and a differential gain of GN= (1.64 ±0.2) ·104Hz.
We inject light from a tuneable laser via a three port optical circulator into the VCSEL.
Polarisation of the VCSEL output and the injected light is controlled by Fiber U-Bench
polarisation controllers. The output is divided into a parallel and orthogonal polarisation
part by a polarising beamsplitter. We analyse the output under three different conditions,
first by keeping the detuning constant and changing the injected power, second by setting
a constant injected power and varying the detuning and third by changing to different
bias currents while keeping the detuning constant and modifying the injected power. For
all measurements, unless denoted differently, we use
T
= 25
±
0
.
05
◦
C and a bias current
of I= 3.05 mA as standard parameters.
At first we classify different behaviours of our system under variation of
Pinj
(for details,
see figure 4.3). We find periodic dynamics and an excitation of the orthogonal polarisa-
tion, a suppressed free-running parallel polarisation along with an excited orthogonal, a
new state where injection locking is achieved at the same time as polarisation switching
(denoted as IL+PS) and complete injection locking (IL). This is the first time to our
knowledge that the IL+PS state is observed and investigated. Next we analyse the output
power evolution of our system for different constant detunings while varying the injected
power. Before the IL+PS regime we find the parallel polarisation (
Px
) and the total output
power (
Ptot
) to be equal while the orthogonal (
Py
) is completely suppressed. During the
IL+PS regime the total power increases,
Py
is at first completely excited and then decays
linearly anticorrelated to
Px
which is initially suppressed. We conclude that our system
behaves according to our theoretical expectations. Following the theoretically estimated
map of the output power evolution for several detunings we find similar behaviour. A
complete map of the IL+PS region for
Pinj
up to 1
.
3
·
10
3µ
W and
νi∈
[
−
11
,
+2] GHz
is given (figure 4.7). Our map is in good qualitative agreement with the theoretical
results. All previous measurements were obtained by increasing the injected power. In
order to investigate the optical bistability of our system we map the IL+PS region for
negative detunings while decreasing
Pinj
. We find the upper boundary of the IL+PS
regime significantly shifted towards lower injection powers while the lower boundary
can be considered approximately constant. This is in agreement with theoretical predic-
41
tions, which assume that bistability can be found in the transition between IL+PS and IL.
To further investigate the system bistability we set a constant bias current and vary
the detuning. For the IL+PS regime we find again a constant total power and an
initially excited
Py
along with an initially suppressed
Px
. This time we however expect a
nonlinear decrease following equations 2.4 and 2.5. We can identify nonlinear behaviour
for measurements of
Pinj
= 39
,
78 and 151
µ
W. We present a map of the IL+PS region
for this measurement in a range of
Pinj ∈
[39
,
151]
µ
W and
νi∈
[
−
9
,−
3] GHz (figure
4.14). We find again a decreased upper boundary and an approximately constant lower
boundary. The total IL+PS region is however smaller, we think that this is related to a
greater instability in measurements with changes in detuning.
In a third step we investigate changes in the IL+PS region arising form a change
in bias current. Again we set a fixed detuning and increase the injected power. At
I
= 6
.
00 mA we find a similar power evolution behaviour than for
I
= 3
.
05 mA. We
present a map of the estimated IL+PS region. Consistent with theory we see again an
increase in the upper boundary and a constant lower boundary for negative detuings
and an increase in both boundaries for positive detunings. Moreover we investigate
the case of
I
= 7
.
00 mA, where we find a different initial situation. Now
Py
is the
initially dominant polarisation while
Px
is initially suppressed before the IL+PS regime.
We now inject in the orthogonal polarisation, with a detuning with respect to
Py
. We
find qualitatively matching results for the power evolution in the negative detuning region.
In order to check the generality of our previously obtained results, we employ a different
VCSEL with a birefringence of 12 GHz, hence about one third of the birefringence of the
previous one. For detunings of
νi
=
−
7
.
4 and
−
4
.
1 GHz we can again identify polarisation
switching and an IL+PS regime. Also a bistability in the IL+PS to IL boundary is again
observed. The state could however not be identified for previous stability analysis of a
VCSEL with a birefringence of 60 GHz [12].
Summarising, we have observed and investigated the IL+PS regime under several cir-
cumstances. Further investigations should consider other states such as period doubling
or chaotic behaviour in order to classify them better. Better classification of the differ-
ent states will lead to more accurate maps because one of our future objectives is the
experimental and theoretical study of nonlinear dynamics of this system. Also a more
detailed look at other devices with different birefringence would be desirable to classify
the generality of our results.
42
Bibliography
[1]
Iga, K.: Vertical-Cavity Surface-Emitting Laser: Its Conception and Evolution. In:
Japanese Journal of Applied Physics 47, 1 (2008), S. 1–10
[2]
Michalzik, R.: VCSELs: Fundamentals, Technology and Applications of Vertical-
Cavity Surface-Emitting Lasers. Springer Verlag, 2013. – ISBN 978–3–642–24985–3
[3]
Koyama, F.: Recent advances of VCSEL photonics. In: Journal of Lightwave
Technology 24, 12 (2006)
[4]
Demtr
¨
oder, W.: Experimentalphysik 3 - Atome, Molek¨ule und Festk¨orper. Springer
Verlag, 2005. – ISBN 3–540–21473–9
[5]
Saleh, B. ; Teich, M.: Fundamentals of Photonics. John Wiley and Sons, 2007. –
ISBN 978–0–471–35832–9
[6]
Quirce, A.: Doctoral Thesis: Din´amica de polarizaci´on y modos transversales de
VCSELs sometidos a inyecci´on ´optica, Universidad de Cantabria. 2012
[7]
P
´
erez, P. ; Valle, A. ; Noriega, I. ; Pesquera, L.: Measurement of the Intrinsic
Parameters of Single-Mode VCSELs. In: Journal of Lightwave Technology 32, 8
(2014), S. 1601–1607
[8]
Noriega, I.: Trabajo de Fin de Carrera: Medida de par´ametros est´aticos y
din´amicos de un l´aser de semiconductor de emisi´on de cavidad vertical, Universidad
de Cantabria. 2015
[9]
Moser, P. ; Lott, J.A. ; Wolf, P. ; Larisch, G. ; Li, H. ; Bimberg, D.:
Temperature-Stable Oxide-Confined 980 Nm VCSELs Operating Error-Free at 46
Gb/s and 85◦C. In: 2014 International Semiconductor Laser Conference (2014)
[10]
Ohtusbo, J.: Semiconductor Lasers: Stability, Instability and Chaos. Springer
Verlag, 2013. – ISBN 978–3–642–30147–6
[11] Hurtado, A. ; Henning, I.D. ; Adams, M.J.: Differences in the injection locking
bandwidth in 1550nm-VCSELs subject to parallel and orthogonal optical injection.
In: IEEE Journal Selected Topics in Quantum Electronics 15, 19 (2009), S. 585–593
[12]
Hurtado, A. ; Qurice, A. ; Valle, A. ; Pesquera, L. ; Adams, M.: Nonlinear
dynamics induced by parallel and orthogonal optical injection in 1550 nm Vertical-
Cavity Surface-Emitting Lasers (VCSELs). In: Optics Express 18, 9 (2010), S.
9425
43
[13]
Quirce, A. ; P
´
erez, P. ; Popp, A. ; Valle, A. ; Pesquera, L. ; Hong, Y. ;
Thienpont, H. ; Panajotov, K.: Two-Polarization mode emission in single-mode
VCSELs subject to parallel optical injection. In: Submitted to Optics Letters (2016)
[14]
Friart, G. ; Gavrielides, A. ; Erneux, T.: Analytical stability boundaries of
an injected two-polarization semiconductor laser. In: Physical Review 91 (2015), S.
042918
[15]
P
´
erez, P. ; A.Valle ;L.Pesquera: Polarization-resolved characterization of
longwavelength vertical-vacity surface-emitting laser parameters. In: Journal of the
Optical Society of America B 31,11 (2014), S. 2574–2580
[16]
Deen, M. ; Kumar, S.: Fiber Optic Communications: Fundamentals and Applica-
tions. John Wiley and Sons, 2014. – ISBN 978–0–470–51867–0
[17]
BeyondtechInc:Fiber optic connector guide.
http://beyondtech.us/blogs/beyond-blog/46105025-fiber-optic-connector-guide
.
Version: December 2015
[18]
AragonPhotonics:Product descriptions: Bosa 100 and 200 Series.
http://aragonphotonics.com/models/. Version: December 2015
[19]
OZ-Optics:Product descriptions: Attenuators.
http://www.ozoptics.com/products/attenuators.html
. Version: December
2015
[20]
Estand
´
ıa, S.: Trabajo de Fin de Grado: Din´amica de L´aseres de Semiconductor
Sometidos a Retroalimentaci´on ´
Optica, Universidad de Cantabria. 2015
[21]
Martin-Regalado, J. ; Prati, F. ; Miguel, M. S. ; Abraham, N.B.: Polarization
Properties of Vertical-Cavity Surface-Emitting Lasers. In: IEEE Journal of Quantum
Electronics 33, 5 (1997), S. 765–783
44
