设计了组分为Al0.5Ga0.5As/GaAs/Al0.2Ga0.8As阶梯形量子阱结构,其导带子带能级可与中红外双波长CO2激光器的泵浦光光子能量共振.计算了此量子阱对两束泵浦光的二阶非线性差频系数χ(2)DFG及三阶非线性系数χ(3)ω1和χ(3)ω2的表达式；在导带分别为抛物线形和非抛物线形两种条件下,对比研究了三个非线性系数随两束泵浦光波长的变化.χ(2)DFG、χ(3)ω1和χ(3)ω2随两束泵浦光波长λp1和λp2都是呈现出先增大后减小的变化趋势,对应不同泵浦波长,存在一个峰值；相比于导带为抛物线形,在非抛物线条件下三个非线性系数随短波长的泵浦光λp1的变化出现“红移”现象,而随长波长的泵浦光λp2的变化峰值位置基本相同；由量子限制效应导致的两种导带情况下子带能级变化,即与泵浦光光子共振条件发生变化,是出现“红移”的原因；而峰值数值上的差异,主要由量子阱子带能级间的跃迁矩阵元和两种导带条件下不同的能级差决定.

Based on resonant subband transitions, the second-order and third-order nonlinear optical effects in an asymmetric quantum well (AQW) with the structure of GaAs/Al0.2Ga0.8As/Al0.5Ga0.5As have been theoretically investigated on the conditions of parabolic and non-parabolic bands. With the increase of two pump wavelengths λp1 and λp2 separately, the second-order nonlinear difference frequency susceptibility χ(2)DFG and the two third-order nonlinear susceptibilities χ(3)ω1 and χ(3)ω2 increase to a maximum value, and then drops down rapidly. In comparison with the condition of parabolic subband, the curves of χ(2)DFG, χ(3)ω1 and χ(3)ω2 show obvious red-shift as a function of the short pump wave λp1 on the condition of nonparabolic subband. However, with the increase of long pump wave λp2, no changes of peak position have been discovered. The physical origin of all red-shift in nonlinear optical effects is the different energy level gaps on the two conditions of subband, which causes the changes in resonant condition. The primary reason for different peak values is the different transition matrix elements, and the other reason is energy level gaps.