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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Four-wave mixing in intersubband transitions of a semiconductor quantum well structure

Emmanuel Paspalakis, Aggeliki Kanaki, Andreas Terzis

Published May 4, 2007• 7 citations
Publisher

Abstract

We study theoretically the phenomenon of four-wave mixing in intersubband transitions of a symmetric double quantum well structure. In the theoretical model we consider two quantum well subbands that are coupled by a strong pump electromagnetic field and a weak probe electromagnetic field, taking into account the effects of electron-electron interactions. For the description of the system dynamics we use the density matrix equations obtained from the effective nonlinear Bloch equations. These equations are solved numerically for a realistic semiconductor quantum well structure GaAs/AlGaAs. We show that the four-wave mixing spectrum can be significantly dependent on the frequency and the intensity of the pump field and on electron sheet density.

DOI
10.1117/12.722187

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We study theoretically the phenomenon of pulsed four‐wave mixing in intersubband transitions of a symmetric semiconductor quantum well structure. In the theoretical model we consider two quantum well subbands that are coupled by a strong pulsed pump electromagnetic field and a weak pulsed probe electromagnetic field. For the description of the system dynamics we use the density matrix equations obtained from the effective nonlinear Bloch equations. We calculate the time‐integrated four‐wave mixing spectrum for various pulse shapes and electron sheet densities and study the effects of pulse shape on four‐wave mixing.
We study theoretically the Kerr nonlinearity of a probe field in the presence of a near resonant pump field in a two-subband system in a semiconductor quantum well structure. In our study we take into account the effects of electron–electron interactions and consider the interaction of the two-subband system with rectangular electromagnetic fields. For the description of the system dynamics we use the nonlinear differential equations of the density matrix elements for the several nonlinear optical processes, under the rotating wave approximation. These equations are solved numerically for a GaAs/AlGaAs quantum well structure. We show that the Kerr nonlinearity of a driven two-subband system can be significantly dependent on the frequency and the intensity of the pump field and on electron sheet density.
We study theoretically the time evolution of nonlinear optical phenomena of a probe electromagnetic field pulse in intersubband transitions of a semiconductor quantum well structure under the influence of a pump electromagnetic field. More specifically, we take into consideration the effects of electron-electron interactions and consider the interaction of a two-subband system with rectangular electromagnetic fields. The spectral form of the linear absorption, dispersion, and nonlinear optical Kerr effect is described, from the time that the external field is applied up until the dynamics of the system has reached a steady state. In order to describe the dynamics of the system, the effective nonlinear Bloch equations are used, in which renormalized terms for the transition energy and the applied field have been added, due to the effects of electron-electron interactions. These equations are properly combined, and the differential equations of the density matrix elements for the several optical phenomena up to third order are derived. These are solved numerically in the whole time range up to the steady state for a GaAs/AlGaAs quantum well structure. We show that the form of the several optical spectra studied here has a significantly altered evolution over time, according to the value of the frequency of the pump field and of electron sheet density. Even in the case in which the spectral form in the steady state case is almost identical for two different sets of parameters, their evolution can be quite different, according to the precise value of these parameters.
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We study the linear and nonlinear optical response of intersubband transitions in a semiconductor quantum well. We describe the coupling of the quantum well structure with the electromagnetic field by using the nonlinear density matrix equations, in the two-subband approximation. We provide proper approximate analytical solutions to these equations that are used for the closed-form determination of the optical susceptibilities χ(1), χ(3), and χ(5). We also explore the dependence of χ(1), χ(3), and χ(5) on the electron sheet density for a specific double GaAs/AlGaAs quantum well.
We study the interaction of chirped electromagnetic pulses with intersubband transitions of a double semiconductor quantum well. We consider the ground and first excited subbands and give emphasis to controlled intersubband population transfer. The system dynamics is described by the nonlinear density matrix equations that include the effects of electron-electron interactions. These equations are solved numerically for various values of the electron sheet density for a realistic double GaAs/AlGaAs quantum well, and the efficiency of population transfer is discussed.