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/A1GaAs 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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