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arXiv:1409.5990 · Physical Review B

Nonlinear pulse propagation in InAs/InP quantum dot optical amplifiers: Rabi oscillations in the presence of nonresonant nonlinearities

Ouri Karni, Akhilesh Kumar Mishra, G. Eisenstein, Johann Peter Reithmaier

Published Mar 9, 2015• 16 citations
arXivHTMLPDF

Abstract

There is interest in what happens to ultrashort light pulses propagating through a quantum-dot semiconductor optical amplifier waveguide. In this experiment, the influence of nonresonant propagation effects, such as linear dispersion, two-phonon absorption, and Kerr-like, on the intensity and frequency profile of the pulses is shown to be strong enough that they must be included in any modeling.

DOI
10.1103/physrevb.91.115304

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There is interest in what happens to ultrashort light pulses propagating through a quantum-dot semiconductor optical amplifier waveguide. In this experiment, the influence of nonresonant propagation effects, such as linear dispersion, two-phonon absorption, and Kerr-like, on the intensity and frequency profile of the pulses is shown to be strong enough that they must be included in any modeling.
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 report direct observations of Rabi oscillations and self-induced transparency in a quantum dot optical amplifier operating at room temperature. The experiments make use of pulses whose durations are shorter than the coherence time which are characterized using Cross-Frequency-Resolved Optical Gating. A numerical model which solves the Maxwell and Schrödinger equations and accounts for the inhomogeneously broadened nature of the quantum dot gain medium confirms the experimental results. The model is also used to explain the relationship between the observability of Rabi oscillations, the pulse duration and the homogeneous and inhomogeneous spectral widths of the semiconductor.
Using the Foreman effective mass Hamiltonian for strained In/sub x/Ga/sub 1-x/As--In/sub y/Ga/sub 1-y/As/sub z/P/sub 1-z/ quantum wells, the propagation of subpicosecond pulses in a 1.55-/spl mu/m optical amplifier was calculated. The multisubband carrier dynamics as well as the polarization dynamics were taken into account. Carrier heating and coherent light-carrier interactions as well as the interplay of these nonlinear processes and the amplifier dispersion are studied. Strong Rabi oscillations occur in the optical field of a propagated pulse, its frequency chirp, as well as in the carrier density and temperature. While the Rabi oscillation imposes negative frequency chirp and hence red-shifts the pulse spectrum, positive frequency chirp can occur due to the local gain dispersion, where the higher frequency components of the pulse have larger gain. Due to the Rabi oscillation, the spectrum of the amplified pulse is considerably distorted and sidebands emerge. For a linearly chirped input pulse, the spectrum of the output pulse can be either red-shifted or blue-shifted with respect to its center frequency, depending on its initial chirp. For strong pulse propagation, a pronounced pulse break up occurs when a 175-fs pulse propagates in the gain regime, while a significant pulse compression occurs when the pulse propagates at the transparency point.
Using a self-consistent delay-differential-equation model for the description of the nonlinear light propagation in InAs/InGaAs quantum-dot-in-a-well semiconductor optical amplifiers, we analyze the amplifier in a four-wave-mixing setup in terms of the conversion efficiency. Our model allows us to extract the hierarchy of nonlinear effects that constitute the four-wave-mixing process. We show that spectral hole burning in the quantum-dot medium facilitates wavelength conversion over a spectral detuning of several THz, whereas the effect of carrier heating and global carrier-density pulsations is found to be negligible. Furthermore we show that for high optical field amplitudes the emergence of Rabi oscillations leads to a flattening of the conversion efficiency, potentially allowing for ultra-broadband wavelength conversion and frequency comb generation.
We present a numerical study of coherent control in a room temperature InAs/InP quantum dot (QD) semiconductor optical amplifier (SOA) using shaped ultra-short pulses. Both the gain and absorption regimes were analyzed for pulses with central wavelengths lying on either side of the inhomogeneously broadened gain spectrum. The numerical experiments predict that in the gain regime the coherent interactions between a QD SOA and a pulse can be controlled by incorporating a quadratic spectral phase (QSP) in the pulse profile. The sequential interaction with the gain medium of different spectral components of the pulse results in either suppression or enhancement of the coherent signatures on the pulse profile depending upon their proximity to the gain spectrum peak. In the absorption regime, positive QSP induces a negative chirp that adds up to that of a two photon absorption induced Kerr-like effect resulting in pulse compression while negative QSP enhances dispersive broadening of the pulse.
We investigate the optical properties of a Coulomb-coupled double-quantum dot system excited by coherent light pulses. Basic effects of Coulomb coupling regarding linear and nonlinear optical processes are discussed. By numerically solving the Heisenberg equation of motion we are able to present the temporal evolution of the system's density matrix for a wide range of coupling parameters. The two main coupling effects in dipole approximation, biexcitonic shift and F\"orster energy transfer, are investigated and their qualitative and quantitative influence on absorption spectra, Rabi oscillations, and single- and two-pulse excitation is discussed. We present simulated differential transmission spectra to allow for comparison with recent experimental studies.