Semi-parabolic Quantum Wells Research Articles

Calculation of linear and nonlinear intersubband refractive‐index changes in an asymmetrical semiparabolic quantum well with applied electric field

AbstractBy using the displacement harmonic variant method and the compact density matrix approach, the linear and nonlinear intersubband refractive‐index changes (RICs) in a semiparabolic quantum well (QW) with an applied electric field have been investigated in detail. Simple analytical formulae for the linear and nonlinear RICs in the system were also deduced. The effect of the band nonparabolicity has been taken into account. Numerical calculations of typical GaAs semiparabolic QWs were performed. The dependence of the linear and nonlinear RICs on the incident optical intensity, the frequency of the confined potential of the semiparabolic quantum well, and the strength of the applied electric field were discussed under both conditions of considering and ignoring the band nonparabolicity. Results reveal that the RICs in the semiparabolic quantum‐well system sensitively depend on these factors. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electric field effect on the linear and nonlinear intersubband refractive index changes in asymmetrical semiparabolic and symmetrical parabolic quantum wells

By using the displacement harmonic variant method and the compact density matrix approach, the linear and nonlinear intersubband refractive index changes (RICs) in a semiparabolic quantum well (QW) with applied electric field have been investigated in detail. The simple analytical formulae for the linear and nonlinear RICs in the system were also deduced. The symmetrical parabolic QWs with applied electric fields were taken into account for comparison. Numerical calculations on typical GaAs QWs were performed. The dependence of the linear and nonlinear RICs on the incident optical intensity, the frequencies of the confined potential of the QWs and the strength of the applied electric field were discussed. Results reveal that the RICs in the semiparabolic quantum well system sensitively depend on these factors. The calculation also shows that the semiparabolic QW is a more ideal nonlinear optical system relative to the symmetric parabolic QW systems.

Studies on the Second-Order Nonlinear Optical Properties of Parabolic and Semi-parabolic Quantum Wells with Applied Electric Fields**The project supported by Natural Science Foundation of Guangdong Province of China

Within the framework of compact density matrix approach and iterative procedure, a detailed procedure for the calculation of the second-harmonic generation (SHG) susceptibility tensor is given in the electric-field-biased parabolic and semi-parabolic quantum wells (QWs). The simple analytical formula for the SHG susceptibility in the systems is also deduced. Numerical results on typical AlGaAs/GaAs materials show that, for the same effective width, the SHG susceptibility in semi-parabolic QW is larger than that in parabolic QW due to the self-asymmetry of the semi-parabolic QW, and the applied electric field can make the SHG susceptibilities in both systems enhance remarkably. Moreover, the SHG susceptibility is also related to the parabolic confinement frequency and the relaxation rate of the systems.

Calculation of Linear and Nonlinear Intersubband Optical Absorptions in Electric-Field-Biased Semiparabolic Quantum Wells

By using the compact density matrix approach and iterative procedure, a detailed procedure for the calculation of the linear and nonlinear intersubband optical absorption coefficients is given in the electric-field-biased semi-parabolic quantum wells (QWs). The simple analytical formulas for the linear and nonlinear optical absorption coefficients in the systems are also deduced. Numerical result on typical GaAs materials shows that, the linear and nonlinear optical absorption coefficients sensitively depend on the applied electric field and the confined potential frequency of the semiparabolic QW systems as well as the incident optics beam intensity.

Electric field effect on the second-order nonlinear optical properties of parabolic and semiparabolic quantum wells

By using the compact-density-matrix approach and iterative procedure, a detailed procedure for the calculation of the second-harmonic generation (SHG) susceptibility tensor is given in the electric-field-biased parabolic and semiparabolic quantum wells (QW's). The simple analytical formula for the SHG susceptibility in the systems is also deduced. By adopting the methods of envelope wave function and displacement harmonic oscillation, the electronic states in parabolic and semi parabolic QW's with applied electric fields are exactly solved. Numerical results on typical ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{Al}/\mathrm{GaAs}$ materials show that, for the same effective widths, the SHG susceptibility in semiparabolic QW is larger than that in parabolic QW due to the self-asymmetry of the semiparabolic QW, and the applied electric field can make the SHG susceptibilities in both systems enhance remarkably. Moreover, the SHG susceptibility also sensitively depends on the relaxation rate of the systems.

Bound States and the Third Harmonic Generation in an Electric Field Biased Semi-parabolic Quantum Well**The project supported in part by Guangdong Provincial Natural Science Foundation of China

Within the framework of the compact density matrix approach, the third-harmonic generation (THG) in an electric-field-biased semi-parabolic quantum well (QW) has been deduced and investigated. Via variant of displacement harmonic oscillation, the exact electronic states in the semi-parabolic QW with an applied electric field have also been obtained and discussed. Numerical results on typical GaAs material reveal that, electric fields and confined potential frequency of semi-parabolic QW have obvious influences on the energy levels of electronic states and the THG in the semi-parabolic QW systems.

Bound states and third-harmonic generation in a semi-parabolic quantum well with an applied electric field

Within the framework of the compact density-matrix approach, the third-harmonic generation (THG) in an electric-field-biased semi-parabolic quantum well (QW) has been deduced and investigated. Via the method of displaced harmonic oscillation, the exact solution for the electronic states in a semi-parabolic QW with an applied electric field have also been determined. Numerical results on typical GaAs material show that electric field and confined potential frequency of semi-parabolic QW have obvious influences on the energy levels of electronic states and the THG in the semi-parabolic QW systems.

Third‐order nonlinear optical properties of parabolic and semiparabolic quantum wells

AbstractA detailed procedure for the calculation of the third‐harmonic‐generation susceptibility tensor is given in parabolic and semiparabolic quantum wells, and an analytic formula for the third‐harmonic‐generation susceptibility is obtained by the compact density matrix approach and an iterative procedure. Finally, numerical results are presented for typical GaAs/AlGaAs parabolic and semiparabolic quantum wells. The calculated results show that the third‐harmonic‐generation susceptibilities in parabolic quantum wells are over one order of magnitude greater than in semiparabolic quantum wells, and are over eight orders of magnitude greater than in bulk GaAs. In addition, the third‐harmonic‐generation susceptibilities are related to the parabolic confinement frequency and the relaxation rate.

ELECTRO-OPTIC EFFECT IN A SEMI-PARABOLIC QUANTUM WELL WITH AN APPLIED ELECTRIC FIELD

By using the compact density matrix approach, the electro-optic effect (EOE) in a semi-parabolic quantum well (QW) with an applied electric field has been theoretically investigated. Via a variant of displacement harmonic oscillation, the exact electronic states in the semi-parabolic QW with an applied electric field are obtained. Numerical results on typical GaAs material reveal that the electro-optic effect nearly linearly increases with the increasing of magnitude of the electric field, but it monotonously decreases with the increasing of confining potential frequency of the semi-parabolic QW. The EOE in the model investigated is 102 times larger than that in the symmetric parabolic QW under the same electric field and the same frequency of parabolic confining potential, which is due to the self-asymmetry of the system and the electric field effect.