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Annual Meeting Optical Society of America

Nonlinear Intersubband optical absorption in a quantum well with an applied electric field

D. Ahn, S. L. Chuang

Published Jan 1, 1987• 1 citation
Publisher

Abstract

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.

DOI
10.1364/oam.1987.mr9

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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.
In multiple quantum wells system, a large dipole strength and a narrow band width were observed. This suggests that the intersubband optical transitions in a quantum well may have very large optical nonlinearities. The intersubband transition have potential for device applications in far-infrared laser amplifiers, photodetectors and high-speed electrooptical modulators. In device design, the region of input optical density for linear response is a very important parameter. And the optical saturation is related with tunnelling effects and the intersubband relaxations. So the intersubband nonlinear absorption is very valuble for a fundamental and a practical point of views. Recently, there are some works on this region [1], [2].
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 nonlinear intersubband optical transitions in a quantum well with an applied electric field are studied with the effects of screening taken into account. Recently, we calculated the linear and nonlinear intersubband optical absorptions in a quantum well with and without an applied electric field.1-3 Interesting Stark effects on the intersubband transitions in the conduction band of an Al- GaAs-GaAs quantum well have been predicted1 and confirmed by experiments.4 The saturation optical intensity in a quantum well has also been reported to be 2 MW/cm2,5 which agrees with our theoretical calculations using the methods in Refs. 2 and 3.
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 study, the effects of the external fields (electric and tilted magnetic fields) and well parameters on the optical absorption coefficients in GaAs/GaAlAs multiple (five) quantum wells under the applied electric and tilted magnetic fields has been investigated theoretically. Firstly, the energy eigenvalues and eigen functions of an electron confined in multiple quantum wells are calculated by analytically from Schrödinger equation using the transfer matrix method within the effective mass approximation, Secondly, the linear, nonlinear and total intersubband optical absorptions in GaAs/GaAlAs multiple quantum wells system are studied within the compact density-matrix approach. It is shown that the parameters such as strenghts of the external fields and θ-tilted angle values not only shift the peak positions in absorption spectrum but also considerably modify their potential heights. In generally, electronic and optical properties of the quantum wells are very sensitive to the applied external fields and well parameters. Therefore, we can conclude that the effect of the external fields can be used to tune and control the optical properties of interest in the range of the far-infrared electromagnetic spectrum.
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.