Semi-parabolic Quantum Research Articles

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.

Exciton effects on nonlinear electro-optic effects in semi-parabolic quantum wires

The nonlinear electro-optic effects in quasi-one-dimensional semi-parabolic quantum wires are studied, in which the exciton effects are taken into account. The analytical expression of the electro-optic co-efficient is derived by compact density-matrix approach. Finally, the numerical results are presented for GaAs/AlGaAs semi-parabolic quantum wires. The results show that the electro-optic coefficient is over two times bigger than that obtained by without considering exciton effects. Furthermore, the electro-optic coefficient is related to the relaxation time.

Photoluminiscence excitation spectrum of a semiparabolic quantum well

The calculation of the energy levels of a semiparabolic quantum well are presented using two approximations: the direct numerical solution of the Schrödinger equation for the one parabolic band EFA model by a transfer matrix technique and the simplified two band Kane's model. The comparison of the results is given. The transition probability per unit time is calculated and the results are compared with the photoluminescent excitation spectrum of the quantum well. The assignment of transitions for different peaks in the spectrum is given and compared with the one given by Gossard et al.