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Chinese Journal of Luminescence

Calculation of Nonlinear Intersubband Optical Absorption in Asymmetric Quantum Wells

Peng Tan

Published Jan 1, 2006• 0 citations

Abstract

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.

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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.

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.

Infrared intersubband optical absorption between the quantized subbands and the Stark effects is of considerable interest because of their potential applications in high-speed IR modulators and photodetectors. Recently, we calculated the linear1 and third-order nonlinear2 intersubband optical absorptions with an applied electric field for the infinite quantum-well model with an effective well width (which gives the same ground state energy of a given finite quantum well). The observed intersubband absorption has a large dipole strength suggesting large optical nonlinearities which are in good agreement with our calculation based on the simple model. Distinct features of the intersubband absorption are as follows: (a) The absorption peak for the intersubband absorption increases in energy with increasing electric field over a wide range of the electric field because the energy difference between the two lowest subbands increases with the electric field. (b) The absorption peak for the intersubband absorption may (1) increase in magnitude with an increasing electric field if the intrasubband relaxation time τin is assumed to be constant or (2) decrease with an increasing electric field if the field broadening of the linewidth is taken into account. The nonlinear optical absorption coefficient with the electric field dependence is discussed.

The analytic forms of the linear and the third-order nonlinear optical intersubband absorption coefficients were obtained for general asymmetric quantum well systems using the density matrix formalism.Based on the model,the linear and the third-order nonlinear intersubband optical absorptions in electric-field biased hyperbolic quantum wells were studied.The numerical results were presented for a typical AlxGa1-xAs/GaAs electric-field biased hyperbolic quantum wells.The results show that the contributors to the nonlinear absorption coefficient are due to the electric field,the shape of quantum well and the optical intensity.

In this article, we have investigated the optical properties of intersubband transitions in an asymmetric AlGaAs/GaAs coupled quantum wells system. We solved the Schrödinger equation numerically using homemade finite difference codes to determine the electronic structure. The susceptibilities were calculated in frame of density matrix equations. The effect of relative phase variation between applied fields, on the linear absorption coefficients, relative refractive index changes, and group velocity has been investigated. The results show that the linear optical properties are extremely phase-dependent. By adjusting the phase, it is possible to obtain absorption curves with dispersion-like profile and vice versa.

Linear, nonlinear, and total refractive index changes are investigated theoretically in asymmetric coupled quantum wells. The analytical expressions for the linear and third-order nonlinear refractive index changes are obtained based on the density matrix method and the iterative approach. Numerical calculations are performed for typical GaAs/Al(subscript x)Ga(subscript 1-x)As asymmetric coupled quantum wells. The calculated results reveal that a large variation of the refractive index near the transition energy can be obtained in asymmetric coupled quantum wells, and that the incident optical intensity and the structure parameters, such as the barrier width and the right-well width, have great effects on the total refractive index changes.