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Journal of Applied Physics

On the doubly resonant difference frequency mixing in an asymmetric quantum well structure

M. Zal użny

Published Aug 15, 1995• 4 citations
Publisher

Abstract

The effect of the depolarization field on the doubly resonant frequency mixing due to resonant intersubband transitions in asymmetric quantum wells, with only the ground subband occupied, is discussed. Calculations are performed in the framework of the perturbative density matrix formulation with relaxation time approximation. The results show that in the considered system the depolarization effect can be included by simple replacement (in the one-electron expression for the nonlinear susceptibility) of the intersubband energy by the depolarization shifted intersubband energy.

DOI
10.1063/1.360093

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The effect of the depolarization field on the doubly resonant frequency mixing due to resonant intersubband transitions in asymmetric quantum wells, with only the ground subband occupied, is discussed. Calculations are performed in the framework of the perturbative density matrix formulation with relaxation time approximation. The results show that in the considered system the depolarization effect can be included by simple replacement (in the one-electron expression for the nonlinear susceptibility) of the intersubband energy by the depolarization shifted intersubband energy.
The effect of the depolarization field on the nonlinear intersubband absorption spectrum of a rectangular quantum well (described by the two-subband model) is discussed. Calculations are performed in the framework of the density-matrix formulation with use of the relaxation-time approximation. Obtained results show that the depolarization effect not only shifts the peak by an amount depending on the intensity of the incident light but also leads to a significant distortion (asymmetry) of the line shape.
We investigate the interband difference-frequency-generation process arising from the three-wave interaction of resonant interband and intersubband coupling lights by theoretical estimation of the linear and the nonlinear susceptibilities of an asymmetric AlGaAs–GaAs quantum well. The three-level quantum-well system is analyzed by the perturbational density-matrix approach. The effect of the variation of carrier density in the quantum well on the interband mixing process is also considered. The nonlinear polarization induced by the intersubband coupling field is significantly enhanced in the case of doped structures. The peak second-order susceptibility estimated at the difference frequency is more than 2 orders of magnitude larger, whereas the coupling-field-induced third-order susceptibility is more than 4 orders of magnitude larger than that of bulk GaAs.
The problem of saturation of intersubband absorption and optical rectification in asymmetric quantum wells is discussed theoretically using the density matrix formalism. The effects of the electron-electron interaction are taken into account. It is shown that near the resonance the spectral shapes of the nonlinear optical absorption coefficient and the nonlinear optical rectification coefficient are very similar. In the absence of the electron-electron interaction the spectral responses are nearly Lorentzian. The electron-electron interaction plays an important role in heavy doped systems. In structures with large spatial separation of the ground and the excited states wave functions, the depolarization effect is small and the absorption spectrum is affected mainly by the electrostatic Coulomb interaction. This interaction shifts the absorption peak to higher energy by an amount depending on the intensity of the incident light and leads to the significant distortion (asymmetry) of the line.
The interband sum frequency generation process due to three-wave interaction of interband and intersubband coupling lights has been investigated in a semiconductor quantum well using the perturbational density matrix approach. The origin of the nonlinear process lies in the second-order susceptibility /spl chi//sub c2-h1//sup (2)/ arising due to the optical transition between the second conduction subband and the first heavy hole state. Both the sign and the magnitude of the second-order susceptibility of the well may be controlled by the carrier density level and the frequency of the intersubband field.
In the past few years advance in nanofabrication techniques have made it possible to make well-like compound semiconductor structures of low nanometer size.In these structures,the state of the electron in the direction perpendicular to the length of the well is quantized with sufficiently large separation in energy levels and the motion of the electron parallel to the length is that of a quasi-free electron.One of the most remarkable properties of these one-dimensional electron system is that the optical transitions between the size-quantized subbands are feasible.The result shows there is a large optical nonlinearities in asymmetric quantum wells.The problem of optical saturation of intersubband absorption has recently attracted considerable attention.The problem is very important to the development of superlattice devices such as fast infrared detectors and(modulators) because one needs to know the range of input optical intensities for which linear operation is(possible.) The analytical expression of the linear and the third-order nonlinear optical intersubband absorption coefficients are obtained in Pschl-Teller wells using the density matrix formalism taking into account the(intrasubband) relaxation.Since there are two adjustable parameters κ and λ in Pschl-Teller wells,the shapes of the wells will change with the change of the parameters κ and λ,accordingly the linear and the third-order nonlinear optical absorption coefficients will change with the parameters κ and λ.It is shown that the optical absorption coefficient depends on the parameter,and the optical intensity strongly. The absorption saturation will occur with I increase.Numerical results are presented for a typical AlGaAs/GaAs Pschl-Teller well.
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.