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Dynamic Simulation of Mode-Locked Quantum-Dot Lasers

Dynamic Simulation of Mode-Locked Quantum-Dot Lasers

A. R. Rae, M. G. Thompson, R. V. Penty, I. H. White.

Electrical Engineering Division, University of Cambridge, 9 JJ Thomson Avenue, Cambridge, CB3 OFA, UK. ar410@https://www.sodocs.net/doc/278868225.html,

Abstract: A dynamic model of passive mode-locking in quantum-dot laser diodes is presented. It is found that in contrast with quantum-well lasers, rapid gain recovery is key for mode-locking of quantum-dot lasers.

?2008 Optical Society of America

OCIS codes: (140.5960) Semiconductor lasers; (140.4050) Mode-locked lasers.

In recent years there has been increasing experimental evidence that quantum-dot (QD) semiconductor lasers are well suited to short pulse generation. Mode-locked QD laser diodes routinely produce sub-picosecond pulse durations and low timing jitter [1]. Although there has been much speculation as to the underlining properties of QD lasers that make them superior to their quantum-well (QW) and bulk counterparts, there has been no systematic investigation into the dynamics of mode-locking in QD lasers. As a result, in this work we have sought to develop a greater understanding of the dynamics of QD mode-locking by developing a reliable and accurate QD mode-locked laser model that can be readily used to explain experimental results and allow for improved laser designs. By comparing QW and QD mode-locked lasers we show that there is a stark contrast in the underlying mechanisms that govern the mode-locking dynamics. In addition, we show that accurate modelling must take account of the electron occupation probabilities of the ground and excited states, and sweep out tunnelling.

To fully account for the ultra-fast carrier dynamics and phase locking of the longitudinal modes in mode-locking, a spatially resolved travelling wave model is implemented. Pulse propagation within the cavity is described by forward and reverse counter propagating fields, and the ultra-fast carrier dynamics are modelled using the three rate equations given below [2],

W

r W c E W

W D E

esc

E W

W N f N V V N eV I t

N τττη?

??+=??)1( (1a) E

r

E o e

G

E E

esc E G esc E G c E D W W E N f N N f N f V V N t N τττττ?????+?=??)1()1()1( (1b) S f f g v N f N f N t N h G e G mat g G r

G G esc E G e

G E G )1()1()1(max

0?+?????=??τττ

(1c)

where N W , N E , and N G are the carrier densities in the wetting layer, the QD excited state and the QD ground state

respectively. The carrier densities are normalised with respect to the active region volumes; V W for the wetting layer and V D for the QDs themselves. Current (I ) is injected directly into the wetting layer (with injection efficiency η), and carriers move between energy levels as a result of phonon and Auger scattering. The rate of capture into the excited and ground states are described by τc (1ps) and τo (150fs) respectively, and their associated escape times are

given by τE esc (60ps) and τG esc (2.2ps). The electron occupation probabilities of the ground ( f G e

) and excited ( f E ) states are calculated assuming a two fold degeneracy of the QD ground state and a four fold degeneracy of the QD excited

state. The model also considers the ground state hole occupation probability f G h

, and this is assumed to have a constant value of 0.4 in the gain section due to clamping of the quasi-Fermi levels in the valence band [3]. The rate of stimulated emission is proportional to the occupation of the electron and hole ground states, the maximum material gain g max (53.5cm -1), the group velocity v g , and the photon density in the cavity, S. Carrier recombination

occurs at rates τG r (1ns), τE r (100ps), and τW

r (5ns) for the ground state, excited state, and wetting layer respectively. A relatively short recombination time is used for the QD excited state in order to account for recombination in QDs that do not interact with the optical field.

Accurate modelling of the reversed biased absorber section requires an additional sweep-out term in equation 1c to account for tunnelling out of the QD ground state and enhanced thermal escape from the QDs [4]. This sweep-out rate is strongly dependent on the level of reverses bias and values for this parameter were taken from experimental measurements made by Malins et al. [4]. The maximum material absorption (at the central emission wavelength of 1280nm) was experimentally measured using a segmented contact technique and it was found to have an almost constant value of 40cm -1 for reverse bias voltages between 3-8V indicating that the Quantum Confined Stark effect does not have a significant effect at this wavelength.

The model is validated against experimental results recorded from a 2mm long QD device incorporating a 390μm long absorber section. The details of the experimental measurements can be found in [1] and the results are

reproduced in figure 1. Figure 1 shows the typical increase in pulse-width and peak output power with gain current (figures 1a and 1b) along with the typical decrease in pulse-width with reverse bias (figure 1c). It is clear from figure 1 that the model predictions are in excellent agreement with the experimental results. The model is able reproduce trends in pulse-width and output power for a wide range of gain currents and absorber reverse bias, thus giving

Fig.1. a) Pulse-width vs. gain current for a reverse bias of 8V b) Pulse peak power vs. gain current for a reverse bias of 8V e) Minimum pulse-width (for optimum gain current) vs. reverse bias.

To gain a further insight into

the underlying mode-locking dynamics and to draw a contrast with QW mode-locked lasers, figure 2 compares the temporal gain and absorption dynamics for QW and QD mode-locking. Figure 2a shows typical QW mode-locking dynamics published in [5] while figures 2b and 2c show the dynamics of our QD laser model for mode-locking at 8V reverse bias and 4V reverse bias respectively. These figures show a significant difference between the pulse generation mechanisms in QD mode-locked lasers compared to those from previously reported simulations for QW mode-locked lasers [5].

Fig.2. Comparison of the mode-locking dynamics for QW and QD lasers a) temporal gain and absorption simulated using a QW laser model [5] b) temporal gain and absorption simulated using the QD laser model for 8V reverse bias c) temporal gain and absorption simulated using the QD laser model for 4V reverse bias.

If we first consider the mechanisms of mode-locking within the QW device, figure 2a, we can see that a window of net gain forms initially as the absorption saturates more quickly than the gain. As the pulse continues to form it proceeds to saturate the gain and the net window of gain ultimately closes due to the fast recovery of the absorber. As can be seen from figures 2b and 2c the dynamics for the QDs are quite different. First of all, both the absorption and the gain saturate quickly and with similar time constants, and thus the window of net gain is initially opened by the ultra-fast recovery of the gain, and is then closed by the slower recovery of the absorption. Therefore, in QD mode-locked lasers the window of net gain is determined by the ultra-fast response of both the gain and the absorption dynamics. Even for Figure 2c where the ultra-fast recovery of the gain and absorption is not so prominent, the pulse forming region is due to the same window. The dependence of both the start and end of the window on controllable recovery rates explains that the ability of QD lasers to generate a wide range of picosecond and sub-picosecond pulses, and also for the pulse parameters to be largely independent of harmonic mode-locking level [6].

In summary, an experimental and theoretical comparative study of a passively mode-locked QD laser diode has been presented. This study shows that in contrast to QW mode-locking, QD mode-locking is greatly dependant on the fast time constants of both the gain and the absorption, thus explaining known experimental phenomena.

[1] Thompson et al., “Absorber Length Optimisation for Sub-Picosecond Pulse Generation and Ultra-Low Jitter Performance in Passively Mode-Locked 1.3μm Quantum-Dot Laser Diodes,” presented at OFC 2006, Anaheim, USA.

[2] Berg et al., “Ultrafast Gain Recovery and Modulation Limitations in Self-Assembled Quantum-Dot Devices,” PTL 13, pp. 541-543 (2001). [3] Smowton et al., “Gain in p -doped quantum dot lasers,” JAP 101, 013107 (2007).

[4] Malins et al., “Ultrafast electroabsorption dynamics in an InAs quantum dot saturable absorber at 1.3μm,” APL 89, 171111 (2006). [5] Williams et al., “Long-wavelength monolithic mode-locked diode lasers,” NJP 6, 179 (2004).

[6] Rae et al., “Harmonic Mode-Locking of a Quantum-Dot Laser Diode,” presented at LEOS 2006, Montreal, Canada.

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