Twofold gain enhancement by elongation of QDs in polarization preserving QD-SOAs [original]

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Greif, L. A. T., Mittelstädt, A., Jagsch, S. T., & Schliwa, A. (2019). Twofold gain enhancement by

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Ludwig A. Th. Greif, Alexander Mittelstädt, Stefan T. Jagsch, Andrei

Schliwa

Twofold gain enhancement by elongation

of QDs in polarization preservin

QD-SOAs

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Twofold gain enhancement by elongation of QDs in polarization

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Twofold Gain Enhancement by Elongation of

QDs in Polarization Preserving QD-SOAs

L A Th Greif,∗A Mittelstädt, S T Jagsch, and A Schliwa

Technische Universität Berlin, Institut für Festkörperphysik, Hardenbergstraße 36, 10623

Berlin, Germany

E-mail: [email protected]berlin.de

Abstract

The impact of quantum dot(QD) elongation

on key parameters of QD-based semiconductor

optical amplifiers(SOAs) is investigated using

a combination of 8-band k·p-theory including

strain and piezoelectricity up to second order

and a rate equation model describing the popu-

lation of QD ground, excited and wetting layer

states. By considering columnar QDs of se-

lected aspect ratios, we show that chip gain

and saturation gain can be enhanced by up to

+3.6dB via an increased elongation of the in-

dividual QDs while retaining polarization pre-

serving amplification and gain recovery times

below 700fs. Our results enable the optimiza-

tion of polarization preserving QD-SOA devices

which combine ultrafast gain recovery with high

gain and low power consumption.

Keywords

self-assembled quantum dots, semiconductor

optical amplifier, k·p-theory, gain enhance-

ment

1 Introduction

Since the first pioneering works predicted most

desirable electronic and dynamic properties for

quantum dots(QDs),1,2 they have been in the

focus of research for use in semiconductor op-

tical amplifiers(SOAs). Ultrafast gain recovery

and pronounced nonlinear effects3substantiate

the high potential of QD-SOAs in the fields

of high frequency signal amplification, all-op-

tical data processing and wavelength conver-

sion using four-wave-mixing(FWM)4–7. De-

vices with modulation frequencies exceeding

200GHz8and a 120nm broadband gain with

saturation output powers above 20dB facil-

itate wavelength division multiplexing9,10and

high efficiency symmetric FWM.11 Further-

more, several experimental and theoretical

works have shown that, using closely stacked

QDs, polarization preserving amplification can

be realized.12–18 A remaining drawback is the

lower chip gain of QD-SOAs when compared to

quantum well-based systems, requiring longer

or multiple gain devisions to achieve compara-

ble amplification.9

elongated [110]-axis

optical [110]-axis

Figure 1: Scheme of the active region of a QD-

SOA with closely stacked QDs, showing the axis

of elongation with respect to the optical axis.

In this paper, we study an approach to in-

Page 1 of 12 AUTHOR SUBMITTED MANUSCRIPT - SST-105492.R1

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crease the chip gain of a QD-SOA while simul-

taneously preserving the input signal polariza-

tion. The gain enhancement is realized using

c-plane QDs that are elongated perpendicular

to the optical [1¯

10]-axis of the device (figure 1).

Several growth studies have demonstrated that

such elongated QDs can be realized with molec-

ular beam epitaxy(MBE) as well as metalor-

ganic vapor phase epitaxy(MOVPE) via ad-

justing the growth temperature or including an-

nealing steps.19–21 However, the formation of a

uniform elongation of all QDs within one stack

is still challenging.22

Due to the asymmetric confinement in the

(001)-plane the QD ground state transition

dipole moment is rotated into the (1¯

10)-plane,

optimizing the alignment with the electric field

of the optical signal. Thereby, the polarization

of the amplified signal is preserved in the (1¯

10)-

plane. The results are not limited to this unique

configuration of optical axis and QD-axis but

can be generalized as long as the axis of elonga-

tion is orientated perpendicular to the optical

axis of the QD-SOA.

Anisotropic transition dipole moments caused

by anisotropic nanostructures were already

used in InAs/InP quantum dash lasers and

SOAs.23–25 Quantum dashes represent an in-

termediate structure between QDs and quan-

tum wires with at least one dimension sig-

nificantly exceeding the exciton Bohr radius

and thus exhibit only two-dimensional quantum

confinement.26 Due to the bigger volume com-

pared to QDs, the threshold current is usually

slightly higher than in QD based structures27

and although polarization insensitive amplifica-

tion seems achievable28 to our best knowledge

it has not been demonstrated so far.

The paper is organized as follows. After intro-

ducing the device structure, a brief paragraph

discusses the method for calculating the spa-

tially resolved radiation intensities of a stack

of QDs. QD stacks with a vanishing degree of

polarization(DOP) in the (1¯

10)-plane are then

calculated for five different horizontal aspect ra-

tios ARh=d[110]/d[1¯

10](elongations), where di

is the length of the diagonal [i] in the basis

plane. Subsequently, the results are used to de-

termine the impact of the QD elongation on the

stimulated emission rate as well as other key

properties of the QD-SOA, such as chip gain,

saturation gain and gain recovery time(GRT).

2 Structure Details

Typical QD-SOA designs use the tilted ridge

waveguide geometry,5,29,30 where the cross sec-

tion provides refractive index nguiding along

the vertical and gain guiding in lateral direc-

tion (figure 2). Following Jayavel et al.,31 we

use Al0.5Ga0.5As for the cladding (n= 3.1) and

GaAs (n= 3.3) as matrix material in order to

realize the index guiding.

Figure 2: Schematic QD-SOA with pump cur-

rent I, a resulting current injection region of

width W, height of the active region LW, cav-

ity length Land nllayers of quantum dots, each

separated by a barrier of width wbarrier.

Figure 2 shows the active region composed

of seven layers of closely stacked QDs aligned

along the c-axis. The QDs are placed on a two-

monolayer(ML)-thick wetting layer (included

in the QD height). The barrier width wbarrier is

set to zero ML, as experimental findings suggest

that columnar QDs stay in contact with each

other along the growth direction.12,14,15 The in-

dividual QDs are modeled as truncated InAs-

pyramids with a side-wall angle of 30◦and di-

mensions given in table 1.

As shown in [13,32,33], elongation affects the

polarization properties of single and stacked

QDs. Thus, when changing the QD elongation,

Page 2 of 12AUTHOR SUBMITTED MANUSCRIPT - SST-105492.R1

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Table 1: Geometric specifications of the indi-

vidual QDs.

ARhQD height d[110] [nm]

1.0 1.13 12.39

1.5 1.13 11.19

2.0 1.41 12.39

2.5 1.70 12.39

3.0 1.13 7.59

adjustments in the geometry of the individual

QDs are necessary to preserve polarization in-

sensitivity of the stacks. Differences in the QD

volume are of no particular significance as only

the spatial radiation pattern enters the subse-

quent simulations of the QD-SOA dynamics as

discussed in section 3.2.

Device and operational parameters are

adapted from [34,35] and listed in table 2.

3 Method of Calculation

In order to connect macroscopic device prop-

erties like electric current and photon density

with the elongation of the zero dimensional

QDs, we use the rate equation model described

in [34–37] accompanied by numerically obtained

QD emission characteristics. In a first step, the

radiation pattern of the QD stacks with differ-

ent elongations are calculated using an 8-band

k·p-model including strain and strain-induced

piezoelectricity.38,39 Subsequently, the radiation

pattern is used to determine the ratio of pho-

tons spontaneously emitted into the waveguide,

known as β-factor

β=# spon. emitted along the waveguide

# all spon. emitted .

(1)

This figure of merit enters the rate equation

model and allows us to qualitatively study the

impact of the QD elongation on the device prop-

erties via its influence on the electron and hole

wavefunctions.

3.1 Beta-Factor and Spontaneous

Emission Rate

In order to obtain the rate of photons emitted

by the QDs within the waveguide structure, we

use Fermi’s golden rule

Γi→f()∝ |· hf|∇|ii |2.(2)

The polarization dependent transition rate

Γi→f()can be derived with the help of the 8-

band k·pelectron and hole wavefunctions |fi

and |ii, respectively. Following [40], Γi→f()

is transformed into a function of the propaga-

tion direction k. Only photons whose propa-

gation direction k(φk, θk)fulfills the following

equations41 are confined within the waveguide

θk≤arccos ˆn2

ˆn1=θlim,(3)

φk≤arctan W

2(L−x)=φlim.(4)

Here, ˆn1,ˆn2are the refractive index of the ma-

trix and cladding material, respectively, Wis

the width of the injection region, Lis the SOA

length and xis the position in the SOA along

the optical axis. We eliminate the spatial de-

pendence of (4) by averaging the limit angle

φlim over the active region

φlim =1

LZL

dx φlim(x).(5)

With the help of the calculated limit angles, the

β-factor can be derived as the ratio of the sum

of all photons emitted within the limit angles

to the total sum of emitted photons.

3.2 Rate Equation Model

The rate equation model is adapted from

[34,35,37] with corrections suggested by Li and

Li in [36]. The model describes the temporal

evolution of the charge carrier densities within

the wetting layer NW, the QD excited state

N2=˜

NQn2and ground state N1=˜

NQn1.

Here, n2and n1are the occupation proba-

bilities of excited state and ground state, re-

spectively. Occupation probabilities and carrier

Page 3 of 12 AUTHOR SUBMITTED MANUSCRIPT - SST-105492.R1

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densities are connected to the QD volume den-

sity ˜

NQ=NQ/LWvia the QD surface density

NQ.

Lifetimes for the capture τW→2and intradot

relaxation τ2→1are calculated considering

phonon-mediated and Auger processes42

τi=1

Ai+CiNW

, i = (W→2),(2 →1),

(6)

where Aiand Ciare the coefficients of phonon-

and Auger-assisted interaction, respectively.

The lifetimes are connected to the excitation

τ1→2and escape process τ2→Wvia a quasi-Fermi

equilibrium condition42 at T= 300 K,

τ2→W=τW→2

2ρ2NQh2

4πm∗

ekBTexp EW−E2

kBT,

(7)

τ1→2=τ2→1

ρ1

ρ2

exp E2−E1

kBT.(8)

Here, ρ1and ρ2denote the ground and ex-

cited state degeneracy without spin, his the

Planck constant, m∗

eis the effective electron

mass, kBis the Boltzmann constant and EW,

E2,E1are the energies of the wetting layer,

excited and ground state. For the considered

wetting layer carrier concentrations NWthe re-

laxation and excitation processes are mainly

phonon- (NW<1e17cm−3) or Auger-assisted

(NW>1e17cm−3), while the escape and cap-

ture processes are dominated by phonon cre-

ation/annihilation, showing nearly no NWde-

pendence (figure 3). Considering the internal

losses αint, the optical power within the SOA

can be calculated with the propagation equa-

tion43

P(z) = Pin exp((g−αint)z).(9)

The dependence of the modal gain gon the

ground state occupation probability n1can be

written as g=gmax(2n1−1).43 In various stud-

ies gmax is treated as a constant parameter de-

pending only on structural properties of the

specific device.34–36 As we want to compare QD-

SOAs with differently elongated QDs, a descrip-

tion of gmax as function of the elongation, or ef-

1e1

1e0

1e-1

NW [cm-3]

lifetime [ps]

Pin : 0.1 mW

ARh: 1.0

1e13

1e-2

1e2 1 2

1e14 1e15 1e16 1e17 1e18 1e19 1e20



2 1



2 W



W 2



Figure 3: Lifetimes of capture (W→2), re-

laxation (2→1), escape (2→W) and excitation

(1→2) processes for different wetting layer car-

rier concentrations NW.

fectively as function of the β-value, is necessary.

Following the microscopic derivation of gmax in

[ 43,44] a linear dependence on βis revealed.

Defining g0

max for a QD-SOA with unelongated

QDs the rate equation model is given as

∂NW

∂t =J

eLW

+N2

τ2→W

−

NW(1 −n2)

τW→2

−NW

τWR

(10)

∂N2

∂t =NW(1 −n2)

τW→2

+N1(1 −n2)

τ1→2

−

τ2→W

−N2(1 −n1)

τ2→1

(11)

∂N1

∂t =N2(1 −n1)

τ2→1

−N1(1 −n2)

τ1→2

−

N1n1

τ1R

−g0

max β(2n1−1) ¯

β0σhν ,

(12)

with the injection current density J=I/(L W),

the elementary charge e, the thickness of the

active layer LW, the radiative lifetime in the

wetting layer and GS, τWR,τ1R, the spatial av-

erage of the optical power within the SOA ¯

the total cross section of the QDs σ=VQDs/L,

with the total volume of the QDs VQDs.36

Equations (10)-(12) are solved using the

fourth-order Runge-Kutta method and an in-

cremental time step of 1e−4ps except for

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Table 2: Parameters used in the rate equation model and the lifetime calculation.

parameter physical meaning value

Iinjection current 2e-7A - 20A

LWthickness of effective active layer 200nm

LWL thickness of wetting layers 3.5nm

Llength of the SOA 2mm

Wwidth of current injection region 10µm

NQsurface QD density 5e10cm2

AW→2phonon assisted trans. coeff. 1e12s−1

CW→2Auger assisted trans. coeff. 1e-14m3s−1

A2→1phonon assisted trans. coeff. 1e11s−1

C2→1Auger assisted trans. coeff. 7e-12m3s−1

ρ2ES degeneracy (w/o spin) 2

ρ1GS degeneracy (w/o spin) 1

m∗

eeffective electron mass 0.0223me

EW−E2energy splitting W →280meV

E2−E1energy splitting 2→160meV

τWR spon. radiative lifetime in wetting layer 10ps

τ1R spon. radiative lifetime in GS 400ps

αint internal losses 3cm−1

max modal gain of a QD-SOA with unelongated QDs 11.5cm−1

the gain recovery calculations which were per-

formed with a time step of 1e−5ps.

Finally, the power of the amplified signal Pout

is calculated

Pout =Pin exp((g−αint)L),(13)

which defines the chip gain Gin dB

G= 10 log10(Pout/Pin).(14)

The absolute energies of all states shift with

different elongations as shown in [39]. But con-

sidering the more important energy spacings,

the bandgap as well as the conduction inter-

band spacing of the ground and first excited

state are relatively constant. However, the in-

terband spacing for higher states as well as the

energy difference to the wetting layer reservoir

is much more complex. This work constitutes a

proof of concept and thus we refrain from sim-

ulations of the extended wetting layer and also

from an explicit treatment of several higher ex-

cited states which would introduce a large num-

ber of unknown parameters.

In our opinion, such a simplified electronic

picture is most suitable to first prove the im-

pact of the elongation onto the basic device dy-

namics. Thus, except for the β-factor which

is directly calculated using the QD stack wave-

function, all parameters are treated as constant

for all considered QDs (table 2) with values sim-

ilar to those used in [34,35].

4 Results

Using single-particle states of the 8-band

k·p-simulations, the DOP and the β-factor

can be determined for each elongation of the

stacked QDs. Table 3 shows how the β-factor

of the QD stack increases with the elonga-

tion of the individual QDs, while maintaining

near-isotropic polarization through the stack

aspect ratio. The increase of the β-factor is

most pronounced for slightly elongated struc-

tures between ARh=1.0 and 1.5 and saturates

rapidly for higher aspect ratios. In combination

with the monotonous increase of βonly a small

number of elongations has to be considered to

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Table 3: DOP and β-factor of differently elon-

gated QD stacks.

ARhDOP β[h]

1.0 0.08 1.10

1.5 -0.03 1.30

2.0 -0.01 1.41

2.5 -0.03 1.48

3.0 0.10 1.50

map the qualitative impact of ARhonto the

device properties.

According to (3) and (4), βalso depends on

the waveguide dimensions as well as the mate-

rial compositions. Therefore, the β-values may

vary for identical QD stacks in a waveguide with

different dimensions or refractive index.

4.1 Gain Enhancement

Having shown that we can efficiently tune the β-

factor using elongated QDs, we now investigate

the influence of the elongation on the chip gain,

the GRT and the saturation gain.

In figure 4 the QD occupation probabilities n2

and n1as well as the wetting layer carrier con-

centration NWare shown as functions of Jand

elongation for a constant optical input signal of

0.1mW. For J < 0.1A/cm2both QD states ex-

hibit constant occupations. Here, a small NW

below 1e14cm−3leads to small capture rates

NW(1 −n2)/τW→2and a long intradot relax-

ation time τ2→1(figure 3). Thus, the ground

state is mainly populated due to the constant

input signal, resembling an optically pumped

two-level system with a steady state occupation

of 0.5. In combination with a negligible excita-

tion process (1→2)n1significantly exceeds n2

(n2n1).

If NWis increased via an increased injection

current, the QD refilling takes place more effi-

ciently and thus n2increases to unity (n2>n1).

This point represents the formation of an in-

tradot relaxation bottleneck where n1is limited

by the finite intradot relaxation time. A larger

NWalso causes smaller intradot relaxation

and excitation times, changing the dominat-

ing mechanism from phonon- to Auger-assisted

(figure 3). Both processes exhibit different NW

dependencies which leads to the formation of a

shoulder in n1around J= 10 A/cm2. How-

ever, the relaxation always exceeds the exci-

tation processes, resulting in a net growth of

n1with increasing J. Ultimately, both states

are completely occupied (upper limit of the re-

laxation bottleneck) for current densities above

3e4A/cm2.

With QD elongation the transition dipole mo-

ment is increasingly aligned with the electric

field of the propagating optical signal in the

(1¯

10)-plane. Thus, the rate of stimulated emis-

sion increases, reducing n1. Elongation-induced

differences in the occupation probability can

solely be observed in the relaxation bottleneck

regime for the following reasons.

Firstly, for J < 0.1A/cm2, the ground state

is mainly occupied due to the resonant optical

signal resembling an optically pumped two-level

system. This means that absorption and emis-

sion processes exactly compensate each other.

Consequently, elongation-induced changes in

the rate of stimulated emission do not have any

impact on the QD state occupations.

Secondly, for J > 3e4A/cm2, the optical

losses are overcompensated by high capture

rates and fast intradot relaxation processes.

Thus, also in this regime no elongation depen-

dence of n1can be found.

In contrast to the QD occupation, the impact

of elongation on the chip gain Gis not limited

to the relaxation bottleneck regime but can be

observed as long as G > 0(figure 4b). Due to

the amplified signal-to-QD coupling, the rate of

stimulated emission is increased even for iden-

tical ground state occupations, leading to an

elongation-induced gain enhancement.

Figure 5a shows the QD occupation as a func-

tion of the signal output power. The QD oc-

cupation probabilities n2and n1are calculated

for a realistic operating current density of J=

5e2A/cm2and different QD elongations.10 For

a wide range of output powers (Pout <0.1mW)

the occupation is constant for all elongations

meaning that the complete inversion of the QD

ground states can be preserved (n1= 1) due

to the fast refilling dynamic on a femto- to pi-

cosecond timescale (figure 3).

Page 6 of 12AUTHOR SUBMITTED MANUSCRIPT - SST-105492.R1

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Figure 4: a) Wetting layer carrier concentration NW(solid), steady state occupation probabilities

of the QD ground state n1(dashed) and excited state n2(dotted) as well as b) chip gain as function

of injection current density for QD-SOAs with differently elongated QDs at a signal input power of

0.1mW.

Figure 5: a) Wetting layer carrier concentration NW(solid), steady state occupation probabilities of

the QD ground state n1(dashed) and excited state n2(dotted) as well as b) chip gain as function

of output power for QD-SOAs with differently elongated QDs at an injection current density of

5e2A/cm2. Circles mark the saturation output power and the associated saturation gain.

For output powers in the range of 10 mW

the ground state occupation collapses and is

driven into transparency (n1= 0.5) represent-

ing a saturated gain medium. Like in an opti-

cally pumped two-level system (figure 4, J <

0.1A/cm2), optical gain and loss processes are

compensating each other and, again, n1does

not depend on the QD elongation. Solely for

the transition regime between 0.1mW < Pout <

10 mW the elongation-dependent increase in

signal-to-QD coupling results in slightly re-

duced occupation probabilities (figure 5a in-

set).

For output powers below 0.1mW, the chip

gain as a function of the output power (fig-

ure 5b) provides an elongation-induced gain

enhancement of up to +3.6dB. These results

are in good agreement with an investigation

Figure 6: Saturation power (grey circles) and

saturation gain (black diamonds) for QD-SOAs

with differently elongated QDs.

on quantum dash SOAs whose gain can be in-

creased by +3.0-4.1dB if the optical axis is

chosen perpendicular to the quantum dashes,

instead of being aligned.24

The enhancement is reduced with higher out-

Page 7 of 12 AUTHOR SUBMITTED MANUSCRIPT - SST-105492.R1

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put powers and completely disappears in the

saturated regime. In addition to the gain en-

hancement, the stronger signal-to-QD coupling

also shifts the transition to the saturated regime

towards lower output powers.

As a figure of merit for this transition the sat-

uration power Psat is calculated, defined as the

power for which Gis halfway between the low

and high power limit45

P=Psat ⇔G(P) = (Glow +|Ghigh|)/2

=Gsat.(15)

The saturation power and the saturation gain

are depicted in figure 5b and figure 6, respec-

tively, showing that the saturation gain can

be enhanced by +3.4dB even though the sat-

uration power decreases with QD elongation.

Strikingly, 70 % (+2.6dB) of the maximum

gain enhancement can be achieved already for

ARh= 2.

4.2 Reduction of Gain Recovery

Time

The gain recovery time is analyzed by simulat-

ing a monochromatic pump-probe experiment

(figure 7).34,35 To this end, a continuous wave

probe signal of variable optical input power

monitors the gain collapse and subsequent re-

covery following a pump pulse. A Gaussian

pump pulse with a FWHM of 150 fs and a peak

power of 0.01 mW is inserted after the electri-

cally driven system reaches a steady state. The

time evolution of the out-coupled probe signal

then determines the (90:10)% GRT as a func-

tion of output power and elongation.

The GRT is determined by the competition

between the intradot relaxation rate (Γ2→1), ex-

citation rate (Γ1→2), rate of stimulated (Γstim)

time

signal power

Ppump Pprobe

150 fs

amplified probe signal



GRT

0.1



0.9



Figure 7: Pump-probe scheme with time evolu-

tion of input (pump - dotted; probe - dashed)

and amplified probe signal (solid). The am-

plified probe signal declines by ∆Pdue to the

pump insertion. The time to recover from 10%

to 90% of ∆Pdefines the GRT.

and spontaneous emission (Γspon)

Γ2→1=N2(1 −n1)

τ2→1

,(16)

Γ1→2=N1(1 −n2)

τ1→2

,(17)

Γstim =gmax(2n1−1) ¯

σhν ,(18)

Γspon =N1n1

τ1R

.(19)

Except for the stimulated emission rate, all

rates depend on a specific lifetime and QD state

occupation probability. While the spontaneous

emission lifetime is treated as a constant, the

relaxation and excitation lifetimes depend on

the wetting layer carrier density (6)-(8).

The lifetimes show no variation with respect

to the elongation and only a small step-like in-

crease of up to 11% near the saturation power

(plots available in supporting informations)

τW→2= 18.25 ps to 18.26 ps,

τ2→W= 1.00 ps,

τ1→2= 1.58 ps to 1.72 ps,

τ2→1= 0.31 ps to 0.34 ps.

In contrast, the ground state occupation

probability n1exhibits an elongation depen-

dence (figure 5a inset) becoming smaller for

increasing elongation and intermediate output

powers 0.1mW< Pout <10 mW. For this rea-

son, the in-scattering rate Γ2→1increases while

Page 8 of 12AUTHOR SUBMITTED MANUSCRIPT - SST-105492.R1

Accepted Manuscript

the out-scattering rates Γ1→2and Γspon de-

crease. Considering the chip gain Gfor differ-

ently elongated QDs as a function of the output

power (figure 5b), we infer that the rate of stim-

ulated emission is increased with elongation as

long as Pout is lower than 10mW. Additionally,

Γstim is also proportional to ¯

Pand thus negligi-

ble for very low optical powers (Pout <0.1mW).

Figure 8: GRT as function of the output power

for QD-SOAs with differently elongated QDs.

Circles mark the saturation output power and

the associated saturation GRT.

Consequently, the GRT as function of optical

power and elongation (figure 8) exhibits neither

power nor elongation dependence for Pout lower

than 0.1mW or higher than 10 mW. For low

optical powers the GRT is significantly longer

than the excited state to ground state relax-

ation time τ2→1due to out-scattering processes.

This situation is reversed for high optical pow-

ers, since high photon absorption rates within

the quasi-two-level regime (discussed in section

A) result in a GRT much smaller than τ2→1.

In the intermediate regime, the GRT can be

reduced by 60fs by increasing ARhfrom 1to 3.

This reduction is caused by the net increase of

the sum of all rates, as the increased losses Γstim

are overcompensated by the elongation-induced

increase in in-scattering Γ2→1and the reduced

losses Γ1→2and Γspon.

Analogous to the saturation gain the sat-

uration GRT can be determined GRTsat =

GRT(Psat)(figure 9). In contrast to the GRT

for a given output power in the intermediate

regime, GRTsat is relatively insensitive to the

elongation.

Figure 9: Saturation power (grey circles) and

saturation GRT (black diamonds) for QD-

SOAs with differently elongated QDs.

5 Conclusion

We have shown how a more than twofold en-

hancement of both chip gain and saturation

gain of a QD-SOAs can be realized when using

elongated QDs, while retaining or even improv-

ing ultra-fast gain recovery dynamics. Strik-

ingly, a horizontal aspect ratio of 2 already

leads to a gain enhancement of +2.6dB repre-

senting 70 % of the overall observed enhance-

ment.

Furthermore, polarization insensitive signal

amplification is realized for all elongations

through stacking of QDs, forming a vertically

coupled confinement region with adjustable

emission directionality. As such, our approach

makes QD-SOAs more competitive with quan-

tum well-based devices, in particular for appli-

cations requiring ultra-fast modulation speeds.

Author Information

Corresponding Author

*lath@physik.tu-berlin.de

ORCID

LudwigA.Th.Greif: 0000-0002-6732-7062

AlexanderMittelstädt: 0000-0002-7587-9385

StefanT.Jagsch: 0000-0002-2365-0554

AndreiSchliwa: 0000-0001-7085-3680

Notes

The authors declare no competing financial in-

terest.

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Acknowledgement

The authors thank the Deutsche Forschungsge-

meinschaft(DFG) which founded this work in

the frame of the CRC 787.

Supporting Information Available:

Figures of the capture (W→2), escape (2→W),

excitation (1→2) and relaxation (2→1) life-

times as functions of the optical output power

for differently elongated QDs.

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