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Physical Review B

Linear and nonlinear pulse propagation in a multiple-quantum-well photonic crystal

Nils C. Nielsen, J. Kühl, Martin Schaarschmidt, Jens Förstner, A. Knorr, S. W. Koch, G. Khitrova, H. M. Gibbs, Harald W. Giessen

Published Aug 16, 2004• 30 citations
Publisher

Abstract

We investigate the temporal and spectral properties of subpicosecond pulses transmitted on the heavy-hole exciton transition through a multiple-quantum-well Bragg structure, exhibiting a one-dimensional photonic band gap. At low light intensities, a temporal propagation beating is observed. This beating is strongly dependent on the optical dephasing time ${T}_{2}$ which is dominated by the radiative interwell coupling. In an intermediate intensity regime, the Pauli-blocking nonlinearity leads to gradual suppression of the photonic band gap and vanishing of the linear propagation beating. For highly nonlinear excitation, we find signatures of self-induced transmission due to Rabi flopping and adiabatic following of the carrier density. Numerical simulations using the semiconductor Maxwell-Bloch equations are in excellent agreement with the experimental data up to intensities for which higher many-particle correlations become more important and self-phase modulation occurs in the sample substrate.

DOI
10.1103/physrevb.70.075306

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We investigate the temporal and spectral properties of subpicosecond pulses transmitted on the heavy-hole exciton transition through a multiple-quantum-well Bragg structure, exhibiting a one-dimensional photonic band gap. At low light intensities, a temporal propagation beating is observed. This beating is strongly dependent on the optical dephasing time T2{T}_{2}T2​ which is dominated by the radiative interwell coupling. In an intermediate intensity regime, the Pauli-blocking nonlinearity leads to gradual suppression of the photonic band gap and vanishing of the linear propagation beating. For highly nonlinear excitation, we find signatures of self-induced transmission due to Rabi flopping and adiabatic following of the carrier density. Numerical simulations using the semiconductor Maxwell-Bloch equations are in excellent agreement with the experimental data up to intensities for which higher many-particle correlations become more important and self-phase modulation occurs in the sample substrate.
We demonstrate that the temporal pulse phase remains essentially unaltered before separate phase characteristics are developed when propagating high-intensity pulses coherently on the exciton resonance of an optically thick semiconductor. This behavior is a clear manifestation of self-induced transmission and pulse breakup into soliton-like pulses due to Rabi flopping of the carrier density. Experiments using a novel fast-scan cross-correlation frequency-resolved optical gating (XFROG) method are in good agreement with numerical calculations based on the semiconductor Bloch equations.
We present phase-resolved pulse propagation measurements that allow us to fully describe the transition between several light-matter interaction regimes. The complete range from linear excitation to the breakdown of the photonic bandgap on to self-induced transmission and self-phase modulation is studied on a high-quality multiple-quantum-well Bragg structure. An improved fast-scanning cross-correlation frequency-resolved optical gating setup is applied to retrieve the pulse phase with an excellent signal-to-noise ratio. Calculations using the semiconductor Maxwell-Bloch equations show qualitative agreement with the experimental findings.
Linear time-resolved reflection on the heavy-hole exciton transition of high-quality multiple GaAs quantum-well Bragg samples reveals enhanced radiative emission and accelerated decay of the coherent optical polarization due to radiative interwell coupling. It is shown that this superradiant mode gradually vanishes with increasing excitation intensity. Microscopic calculations attribute this decoupling to the carrier-carrier Coulomb interaction in the individual quantum wells leading to excitation-induced dephasing. The intricate density dependence is discussed comparing computed results for the excitation-dependent decay in single quantum wells and multiple-quantum-well Bragg structures.
Time-integrated and spectrally resolved degenerate-four-wave mixing experiments at liquid helium temperature on the heavy- hole exciton resonance of a wedged (In,Ga)As/GaAs quantum well Bragg structure reveal a strong dependence of the dynamic and amplitude of the coherent nonlinear optical response in dependence on sample position. In the vicinity of the Bragg resonance the signal amplitude depends on both the rapid dephasing due to enhanced superradiant decay of the excitons and on the constructive interference of the signal amplitude in the backward Bragg reflection direction. We find that even in the presence of moderate inhomogeneous broadening of the excitonic resonance the superradiant decay dominates the excitonic nonlinearity at Bragg resonance. Our experimental results can be fairly well described by solutions based on the semiconductor Maxwell-Bloch equations taking disorder into account.
Time- and spectrally resolved reflectivity measurements on multiple-quantum-well structures excited by ultrashort laser pulses are presented. In Bragg structures, where the interwell distance amounts to half the optical wavelength at the exciton resonance, superradiant coupling of the polarization dynamics within different quantum wells leads to an enhancement of the reflectivity strength and linewidth. We show that the superradiance is not limited to the heavy-hole exciton but can be observed even on excited and light-hole exciton states as well as on correlated electron-hole pair states. These coupling effects grow with the number of quantum wells. For our samples containing 60 and 30 quantum wells, pronounced superradiant enhanced reflectivity is present even at high excitation intensities and high temperatures, showing the insensitivity of radiative coupling with respect to incoherent scattering processes. Our findings are in good agreement with solutions of the semiconductor Maxwell-Bloch equations.
We investigate the spectral properties of the excitonic nonlinear response in a GaAs quantum-well sample containing wells of different thicknesses. We observe both the heavy-hole biexciton and the light-hole biexciton in the transient four-wave mixing spectrum and estimate their binding energy dependence on well width. For moderate excitation densities the signal for negative delay at the heavy-hole exciton and biexciton resonances is due to two-photon transitions to the biexciton states through the exciton states. The temporal behavior of the transient four-wave mixing signal from the heavy-hole exciton resonance is strongly dependent on the spectral position of the laser. We show that this effect is due to interference phenomena and to excitation-induced dephasing.