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Chinese Journal of Quantum Electronics

Exciton effects on third-harmonic generation in quantum wells via fractional-dimensional space approach

YU Feng-mei

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Exciton effects on the third-harmonic generation in GaAs/AlGaAs infinite and finite square quantum wells are calculated within the framework of the fractional-dimensional space approach.The wave functions and bound energies are obtained as functions of spatial dimensionality and the dimension is a function of the well width.For an infinite confining potential the dimension(D) has a transition from the 3D limit to 2D limit when the well width decreases.However,in a finite well,when the well width decreases below a given value,the dimension increases.The analytical expression of the third-harmonic generation is described using the compact density method and the iterative procedure.The numerical results show that the third-harmonic generation coefficient with considering exciton effects is 40%greater than the one without considering exciton effects and it is very sensitively dependent on the exciton confinement.In addition,the smaller the relaxation constant is,the larger the third-harmonic generation will be.

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Exciton effects on the third-harmonic generation in GaAs/AlGaAs infinite and finite square quantum wells are calculated within the framework of the fractional-dimensional space approach.The wave functions and bound energies are obtained as functions of spatial dimensionality and the dimension is a function of the well width.For an infinite confining potential the dimension(D) has a transition from the 3D limit to 2D limit when the well width decreases.However,in a finite well,when the well width decreases below a given value,the dimension increases.The analytical expression of the third-harmonic generation is described using the compact density method and the iterative procedure.The numerical results show that the third-harmonic generation coefficient with considering exciton effects is 40%greater than the one without considering exciton effects and it is very sensitively dependent on the exciton confinement.In addition,the smaller the relaxation constant is,the larger the third-harmonic generation will be.
Excitonic effects on the third-harmonic-generation coefficient for disclike parabolic quantum dots are studied, and an analytic formula for the third-harmonic-generation coefficient is obtained by using the compact-density-matrix approach and an iterative method. Numerical results are presented for typical GaAs/AlGaAs parabolic quantum dots. The results show that the third-harmonic-generation coefficient is greatly enhanced because the excitons are localized in the quantum dots - it is over three times that obtained by just considering electron states - and that it is very sensitively dependent on the exciton confinement. In addition, the third-harmonic-generation coefficient is related to the relaxation constant.
Third-order optical nonlinearities in semi-parabolic quantum wells are studied. The third-harmonic generation coefficient is obtained by using compact-density-matrix approach and iterative method, and the numerical results are presented for spical semi-parabolic quantum wells. The very large third-harmonic-generation coefficient is obtained in this semi-parabolic quantum wells and it is over 10 times bigger than that obtained in parabolic quantum wells. In addition, the relations among the third-harmonic-generation coefficient, the photons energy, the parabolic confinement frequency, and the relaxation constant are also investigated, respectively.
Abstrcat The linear and nonlinear susceptibilities had been obtained by the compact-density-matrix approach in presence of the multifrequency incident optical field. An analytic formula for third-harmonic-generation was presented by graphic technology(Feynman). Numerical results were presented for typical GaAs/AlGaAs Morse quantum well. The results showed that third-harmonic-generation increased with the enhancement of a and decreased with relaxation constant increasing. Therefore, if the parameter was increased or the relaxation constant was reduced with the effects on the system associated by environment and other factors limited to minimum,a large third-harmonic-generation coefficient would be obtained.
The third harmonic generation coefficients( THG) in quantum wells with a new potential are studied theoretically. We obtain eigenfunctions and energy eigenvalues by means of solving Schrodinger equation within the framework of effective mass approximation method. The analytic expressions of the third-harmonic generation coefficients can be got using the compact-density-matrix approach and iterative method. It is found that the THG coefficients are affected by the width of the quantum well d and the parameter U0.
Abstract In this theoretical work, we investigate how external fields like as electric, magnetic, and intense laser fields, as well as structural factors, affect the third harmonic generation (THG) coefficient of an AlGaAs/GaAs Manning-like double quantum well heterostructure. To achieve our goals, we numerically solve the time-independent Schrödinger equation using the diagonalization approach with the effective mass approximation and then derive the subband energy levels and corresponding wave functions of the structure. After that, we derive the mathematical expression of the THG coefficient by using the compact density matrix method. According to our results, the resonance peaks of the THG coefficient show shifting to the high-energy region with an increase in the field’s magnitude in cases where external fields (electric, magnetic, and intense laser) are applied separately. At the same time, increasing the depth (width) of the quantum well structure causes the THG peaks to shift to the high (low) energy region. We believe that the findings from this search will have a substantial impact on existing experimental device designs and applications.