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978-1-4799-0683-3/13/$31.00 ©2013 IEEE 1

Semiconductor Optical Amplifier Based on a Quantum

Dot-in-a-Well (QDWELL) Structure

Y. Ben Ezra, B.I. Lembrikov

Department of Electronics and Electrical Engineering, Holon Institute of Technology

P.O. Box 305, 58102, 52 Golomb str., Holon, Israel

Tel: (9723) 502 6684, Fax: (9723) 502 6685, e-mail: borisle@hit.ac.il

ABSTRACT

Recently, אhe optical injection influence on lasers based on the QDs in a quantum well (QDWELL) structure has

been investigated. The optical injection results in the carrier dynamics synchronization and the QDWELL laser

performance improvement. In this paper, we for the first time studied theoretically a semiconductor optical

amplifier (SOA) based on the QDWELL structure where the probe wave plays a role of the optical injection.

We obtained the basic characteristics of a novel type of SOA based on QDWELL structure.

1. INTRODUCTION

Lasers based on InAs quantum dot (QD) grown in the strained InGaAs quantum well (QW) (QDWELL)

structure are characterized by an extremely low threshold current density of 42.6 A⋅cm-2

and a lasing wavelength

near 1.3 μm [1]. The QDWELL laser performance limitations are caused by the desynchronized dynamics of the

electrons and holes in QDs and QW [2]. Their dynamics is extremely complicated and determined by the

strongly nonlinear electron and hole scattering rates ,

,

in out

e hS for scattering in and out of QDs [2].

The performance of directly modulated semiconductor lasers can be improved by using the optical injection

locking (OIL) providing a single-mode regime with side-mode suppression, strongly enhanced RO frequency,

enhanced bandwidth, reduced nonlinearity, reduced relative intensity noise (RIN), reduced chirp, increased link

gain, and near-single-sideband modulation [3]. The optical injection influence on the QDWELL laser dynamics

has been recently investigated [4]-[6]. The theoretical model of the optically injected QDWELL laser is based on

the Lüdge-Schöll (LS) rate equations [5]. In particular, it has been shown that the optical pumping synchronizes

the electron and hole dynamics in QDs and QW due to the dominant fast stimulated transitions [6].

The QDWELL structure as a semiconductor optical amplifier (SOA) has not been investigated. The application

of a QDWELL structure as a novel type of a QD SOA is promising since the probe optical wave may play a role

of an optical pumping which would synchronize the electron and hole behavior. As a result, QDWELL SOA

may operate at high operation frequencies, it would have a strong gain, and fast gain recovery. In this paper, we

for the first time theoretically studied the QDWELL SOA operation using the LS rate equations for optically

injected QDWELL laser [5] modified for the amplifier regime [7].

2. THEORETICAL MODEL

Figure 1. The energy band structure of a QDWELL SOA.

The energy band structure of the QDWELL SOA in presented in Fig. 1. The QDWELL SOA dynamics is

described by the modified LS model rate equations. These equations for the electron and hole occupation

probabilities ,e h in the confined QD levels, the electron and hole densities ,e hw in the QW, the pumping

(probe) and signal wave photon densities per unit area , ,ph p sn and phases ,p s have the form

mod mod,

, ,

, , , ,

1 12 2

, , 1 ,

p g s ge h

e h ph p e h ph sQD QD

L a L a

in out

sp e h e h e h e h e h e h e h

g v g vn n

t a N a N

R S w w S w w

(1)

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,

, , , ,

0

2 , 1 ,e h QD in out

spe h e h e h e h e h e h

w jN S w w S w w R

t e

(2)

, , ,

mod , , , mod ,

,2 , ;

2

ph p s p s

p s ph p s p s

n zg n z g

z z

(3a,b)

Where the modal gain is given by [7]

mod , 0/ 2 1QD

p s L QD i e hg a N r d F (4)

QDr is the mean size of QDs, La is the number of self-organized QD layers, is the confinement factor,

1

2 2

0 0 21i res i T

is the cross section of interaction of photons of frequency ω₀ with carriers in

a QD at the transition frequency i ,

2

0 2 0/res rgT c n is the resonant cross section, μ is the associated

dipole moment of the optical transition, 1

2 hom2T is the dephasing time, hom is the homogeneous linewidth

(full-width at half maximum (FWHM)), 1 2 2exp /i iF

, ω is the average

transition frequency, Δω is related to the inhomogeneous linewidth FWHM hom 2 ln2in , 2κ are the

optical intensity losses, gv is the group velocity, / gt z v , QD

aN and QDN are the density per unit area of the

active QDs of lasing subgroup and the density per unit area of all QDs, respectively, c is the speed of light in

vacuum, j is the injection current density, 0 is the free space permittivity, e₀ is the elementary charge, the

factors Ssp e hR B w w and

e hR W describe the spontaneous emission in the QW and QDs, respectively, SB

is the band-band recombination coefficient, 2 3 3

0/ 3bg LW c is the Einstein coefficient for

spontaneous emission resulting from the incoherent interaction of the QD with all resonator modes, bg is the

static relative permittivity of the background medium, is the linewidth enhancement factor (LEF). Eqs. (3a,b)

yield for the averaged over the cavity length L pumping and signal wave photon densities

, , , , mod ,

0 0

12

L L

ph p s ph p s p sinn n dz dz g

L

(5)

phases , mod ,

0

/ 2

L

p s p sg dz , and chirp 1

, ,2 /p s p s

.

3. SIMULATION RESULTS

We solved numerically the system of equations (1)-(5) for the typical values of parameters [5], [7], signal and

pumping wavelength of 1.55 µm and 1.53 µm, respectively, and the bias current density 2 thj j . The simulation

results are presented in Figs. 2-6. In the pulse regime with the pulse duration of 60 ps, the electron and hole

dynamics in QDs is desynchronized for the low pumping power as it is seen from Fig. 2.

Figure 2. The QW and QD carrier dynamics for a low pumping level of 10-6

W.

The situation significantly changes under the strong pumping of about 1mW as it is seen from Fig. 2.

Comparison of eqs. (1), (4) shows that the necessary condition for the amplification is 1/ 2e h , while the

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equilibrium state corresponds to 1e h . When due to the strong pumping the sum e h exceeds the unity,

the occupation of the QD levels is decreasing as it seen from Fig. 3. The synchronization of the electron and hole

dynamics in QW is provided by the bias current. The synchronization of carrier dynamics in QDs is not complete

due to the influence of the different electron and hole scattering rates ,

,

in out

e hS .

Figure 3. The QW and QD carrier dynamics for a high pumping level of 10-3

W.

Figure 4. The normalized input and output optical signals.

The time delay and slope difference of the input and output signal pulses shown in Fig. 4 are caused by the rise

time necessary for the filling of the QDs electron and hole levels and the transition from the absorption regime

to the amplification regime. The QD and QW carrier dynamics in the PRBS regime, the output signal and the

chirp for the case with a high repetition frequency of 50 GHz and comparatively high pumping wave power are

shown in Figs. 5, 6. The QD carrier dynamics exhibits a strong synchronization. It is seen that both e and

h start decreasing when 1e h . The output signal and the chirp of the QDWELL SOA demonstrate a

good performance without patterning effect due to the carrier synchronization by a pumping optical wave.

Figure 5. The QW and QD carrier dynamics for a PRBS input signal with the repetition frequency 50 GHz and

a power of 10-3

Watt (a pumping wave power of 10-4

W).

Figure 6. The output signal intensity and chirp for a PRBS input signal with the repetition frequency 50 GHz and

a power of 10-3

Watt (a pumping wave power of 10-4

W).

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4. CONCLUSIONS

We have shown theoretically that a QDWELL SOA can demonstrate a high performance due to the carrier

dynamics synchronization by a pumping (probe) optical wave.

REFERENCES

[1] A. Stintz, G.T. Liu, H. Li, L.F. Lester, and K.J. Malloy, "Low-threshold current density 1.3-μm InAs

quantum dot lasers with the dots-in-well (DWELL) structure", IEEE Photonic Technology Letters, vol. 12,

no. 6, pp. 591-593, Jun. 2000.

[2] K. Lüdge and E. Schöll, "Quantum-Dot lasers – Desynchronized nonlinear dynamics of electrons and

holes", IEEE Journal of Quantum Electronics, vol. 45, no. 11, pp. 1396-1403, Nov. 2009.

[3] E. K. Lau, Liang Jie Wong, and Ming C. Wu, "Enhanced modulation characteristics of injection-locked

lasers: A tutorial", IEEE Journal of Selected Topics in Quantum Electronics, vol. 15, no. 3, pp. 618-633,

May/Jun. 2009.

[4] D. Goulding, S.P. Hegarty, O. Rasskazov, S.Melnik, M. Hartnett, G. Greene, J.G. McInerney,

D. Rachinskii, and G. Huyer, "Excitability in a quantum dot laser with optical injection", Physical Review

Letters, vol. 98, no. 15, pp. 153903-1-4, Apr. 2007.

[5] J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Schöll and K. Lüdge, "Optically injected quantum dot lasers:

Impact of nonlinear carrier lifetimes on frequency-locking dynamics", New Journal of Physics, vol. 14,

pp. 1-20, 2012.

[6] Y. Ben Ezra, B.I. Lembrikov, "Synchronized carrier dynamics in quantum dot-in-a-well (QDWELL) laser

under an optical injection", IEEE Journal of Selected Topics in Quantum Electronics, 2013, Accepted for

publication.

[7] A.V. Uskov, T.W. Berg, and J. Mørk, "Theory of pulse-train amplification without patterning effects in

quantum-dot semiconductor optical amplifiers", IEEE Journal of Quantum Electronics, vol. 40, no. 3,

Mar. 2004, pp. 306-320.