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用紧致密度矩阵和弛豫时间近似方法，研究在非对称半抛物量子阱中的二阶光学非线性．该非线性是由子能带间的共振跃迁引起的，在波长为１０．６μｍ时，光学整流系数可达０．１０４ｍｍ／Ｖ（比ＧａＡｓ晶体中高１０５倍），二次谐波产生系数可达３．１μｍ／Ｖ（比ＧａＡｓ晶体中高１０４倍）．在相同条件下，比阶梯阱模型的结果大一个数量级，比“极化球”模型的结果大两个数量级．
The second order optical nonlinearity in an asymmetric semi-parabolic quantum well is studied by compact density matrix and relaxation time approximation. The nonlinearity is caused by the resonant transition between the sub-bands. At a wavelength of 10.6μm, the optical rectification coefficient can reach 0.104mm / V (105 times higher than GaAs crystals) and the second harmonic generation coefficient can reach 3 .1 μm / V (104 times higher than in GaAs crystals). Under the same conditions, it is an order of magnitude larger than the result of the ladder-trap model and two orders of magnitude larger than the result of the “polar-sphere” model.