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IEEE Journal of Quantum Electronics

Pulse Amplification and Spatio-Spectral Hole-Burning in Inhomogeneously Broadened Quantum-Dot Semiconductor Optical Amplifiers

Dietmar W. Reschner, Edeltraud Gehrig, Ortwin G. Hess

Published Nov 25, 2008• 23 citations
Publisher

Abstract

We present a theoretical model for the description of carrier and light dynamics in a quantum dot semiconductor optical amplifier that includes the inhomogeneous broadening of the quantum dots (QDs) via a spatially resolved statistical approach. The model is based on Maxwell-Bloch equations and takes into account the scattering of charge carriers between 2-D wetting layer states and bound quantum dot states, the amplification, and the wave-guiding of the light fields in the optical cavity. Simulations allow the analysis of the occupation probability of the quantum dot levels at steady state and during optical excitation by a femtosecond pulse. The influence of homogeneously and inhomogeneously broadened quantum dot media on spatial and spectral hole burning is revealed and discussed. It is shown that spatially varying dot properties lead to the reshaping of the optical pulse in the active medium.

DOI
10.1109/jqe.2008.2004756

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We present a theoretical model for the description of carrier and light dynamics in a quantum dot semiconductor optical amplifier that includes the inhomogeneous broadening of the quantum dots (QDs) via a spatially resolved statistical approach. The model is based on Maxwell-Bloch equations and takes into account the scattering of charge carriers between 2-D wetting layer states and bound quantum dot states, the amplification, and the wave-guiding of the light fields in the optical cavity. Simulations allow the analysis of the occupation probability of the quantum dot levels at steady state and during optical excitation by a femtosecond pulse. The influence of homogeneously and inhomogeneously broadened quantum dot media on spatial and spectral hole burning is revealed and discussed. It is shown that spatially varying dot properties lead to the reshaping of the optical pulse in the active medium.
The dynamics of ultrashort pulses propagating in a quantum dot amplifier is determined by a complex nonlinear coupling and dynamic interplay of light fields and carriers in the spatially inhomogeneous quantum dot ensemble. Computational modeling shows that in spite of the large complexity the strong localization of the carrier inversion and the low amplitude phase coupling may allow the amplification and transmission of ultrahort light pulses with minimum deterioration of the pulse properties (e.g. pulse shape, duration). The theoretical description is based on spatially resolved Quantum Dot Maxwell-Bloch equations that describe the spatio-temporal light field and inter-/intra-level carrier dynamics in each quantum dot of a typical quantum dot ensemble. In particular, this includes spontaneous luminescence, counterpropagation of amplified spontaneous emission and induced recombination as well as carrier diffusion in the wetting layer of the laser. Intradot scattering via emission and absorption of phonons, as well as the scattering with the carriers and phonons of the surrounding wetting layer are dynamically included on a mesoscopic level. Spatial fluctuations in size and energy levels of the quantum dots and irregularities in the spatial distribution of the quantum dots in the active layer are simulated via statistical methods. Simulation results of the nonlinear pulse propagation in quantum dot optical amplifiers allow visualization and interpretation of fundamental nonlinear processes such as selective depletion and re-filling of quantum dot energy levels leading to a complex gain and index dynamics that affect the amplitude and phase of a propagating light pulse. Computational modelling thus may lay the foundation for an optimization and tayloring of pulse properties.
We numerically investigate the effect of inhomogeneous broadening caused by quantum-dot (QD) size fluctuations on the gain and phase recovery of QD semiconductor optical amplifiers (SOAs). We establish 1088 coupled rate equations to simulate the carrier dynamics of the inhomogeneously broadened QD ensembles as inhomogeneous broadening increases. When all the QD ensembles are identical and inhomogeneous broadening becomes zero, eight coupled rate equations are solved for the homogeneous QDs. The gain and phase recovery responses are calculated when an ultrashort pump pulse is injected into a QD SOA. As the inhomogeneous broadening increases, the slow component of the phase recovery at the QD ground state increases due to the enlarged contribution from the slow phase recovery of carrier reservoirs such as the QD excited states. By separately calculating the gain and phase recovery responses of the homogeneous QDs with different sizes, we identify how increasing inhomogeneous broadening affects the enlarged slow phase recovery components from carrier reservoirs. We also demonstrate that the effect of inhomogeneous broadening on the temporal variation of the α-factor is more significant compared to the injection pump power.
Summary form only given. Significant progress has been obtained on quantum dot (QD) lasers, but the possible advantages of QD amplifiers are not yet clear. We show here that a relatively slow coupling between the optically active QD carrier states and the surrounding carrier reservoir can lead to efficient gain modulation suitable for ultrafast signal processing. The basis of this property is that the process of spectral hole burning (SHB) can become very effective. We consider a traveling wave optical amplifier consisting of the dot states, which interact with the optical signal (no inhomogeneous broadening included), and the wetting layer (WL), where current is injected. Time evolution is described by two coupled rate equations. Carrier capture from WL to dots is characterized by the capture time /spl tau//sub 0/.
In this work, the ultrafast gain dynamics of a quantum dot (QD)-based semiconductor optical amplifier (SOA) is modeled on the basis of semiconductor Bloch equations that include microscopically calculated nonlinear scattering rates between QD carriers and the surrounding carrier reservoir. This enables us to separately study the dynamics of electrons and holes inside the device as well as the coherent effects related to the fast polarization dynamics. We show that the optical pulse power and the dephasing time of the polarization mainly affect the gain depletion inside the active region, while the electric injection current density and thus the internal carrier dynamics influence the gain recovery. We observe that carrier–carrier scattering is the source of desynchronized behavior of electrons and holes in the recovery dynamics of QD-based SOAs. The amplification of pulse trains in the SOA predicted by our model agrees well with experimental data.
We investigate the interplay of multiwave-mixing processes with the microscopically coupled spatiotemporal light field and charge carrier dynamics in broad-area semiconductor laser amplifiers. Our theoretical description is based on extended spatially resolved Maxwell-Bloch equations including on the microscopic level spatiotemporal multiwave-mixing processes. Performing a third-order expansion in terms of the microscopic carrier distribution, we include in our description both the effects of population pulsations of the total carrier density at the beat frequency and the spatiospectral interactions of the light fields leading to gain nonlinearities as well as spatial and spectral hole burning. Our simulations show that in a broad-area semiconductor laser amplifier, spatiotemporal wave-mixing processes occur in both transverse and propagation directions of the multifrequency optical beams employed in a typical excite-probe configuration.
Quantum dot (QD)-based semiconductor optical amplifiers offer unique properties compared with conventional devices based on bulk or quantum well material. Due to the bandfilling properties of QDs and the existence of a nearby reservoir of carriers in the form of a wetting layer, QD semiconductor optical amplifiers may be operated in regimes of high linearity, i.e. with a high saturation power, but can also show strong and fast nonlinearities by breaking the equilibrium between discrete dot states and the continuum of wetting layer states. In this paper, we analyse the interplay of these two carrier populations in terms of a simple rate equation model. Based on the steady-state and small-signal properties of the model, we analyse and discuss the optical modulation response and the four-wave mixing properties of QD semiconductor optical amplifiers, in particular emphasizing the role of ultrafast gain dynamics.