用分数维空间方法研究量子阱中激子效应对三次谐波产生的影响(英文)

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

运用分数维空间方法理论研究了GaAs/AlGaAs无限深和有限深方形量子阱中激子效应对三次谐波产生的影响。利用分数维空间模型获得波函数和束缚能级为空间维度的函数,而空间维度数是阱宽的函数。无限深方阱的维度数随着阱宽的减小从三维极限过渡到二维;而在有限深阱中,当维度数达到一个极值后,维度数随阱宽的减小而增大。采用密度矩阵和迭代法导出三次谐波的表达式。数值结果表明,考虑激子效应的三次谐波系数比只考虑电子状态的系数增大40%左右,并且三次谐波系数大小依赖于激子的受限程度。结果还表明在弛豫率较小情况下可以获得较大的三次谐波系数。

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.