宽波带二次谐波产生过程中误差函数的研究

Research on error function in broadband second harmonic generation

在无泵浦损耗近似(undepleted pump approximation,UPA)下用模拟退火算法设计的非周期光学超晶格(aperiodi optical superlattice,AOS)中实现了1.06~1.08μm波长范围内高转换效率的宽波带二次谐波产生(second harmonic generation,SHG),并且在该结构中研究了已有文献所提出的误差函数对宽波带SHG过程的适用性。该文献提出的误差函数可以用来很好地估计SHG过程中UPA的适用范围,并且指出误差函数只跟SHG的转换效率有关。研究结果表明:宽波带SHG过程中的误差函数曲线与该文献提出的误差函数曲线(本文中称其为标准曲线)是有偏离的,也即该文献提出的误差函数曲线并不适用于宽波带SHG过程。这是因为在实现宽波带SHG的结构中并不能达到好的准相位匹配(quasi phase matching,QPM),该文献提出的误差函数曲线只有在满足完美的QPM的情况下才完全适用。并且还发现在宽波带SHG过程中,误差函数不仅与SHG的转换效率有关,与入射的基频波波长也有关系;对于某些误差函数曲线与标准曲线偏离不大的波长,该文献提出的误差函数曲线可以近似地用来估计UPA的适用范围。

The high conversion efficiency broadband broadband second harmonic generation （SHG）in the wavelength range of 1.06 -1.08 μm can be achieved in the aperiodic optical superlattice （AOS）,and the AOS was designed by simulated annealing algorithm under undepletion pump approximation （UPA）.The applicability of error function pro-posed in a published literature for broadband SHG in AOS structure is investigated.Error function proposed in a pub-lished literature can well estimate application range of UPA in SHG and is only related to the conversion efficiency of SHG.The results show that error function curves presented in a published literature are not suitable for broadband SHG because the structure of broadband SHG can not reach good quasi phase matiching （QPM）.Only under the con-dition of perfect QPM,error function curves presented in a published literature can completely be suitable for broad-band SHG.Furthermore,error function is related to the conversion efficiency of SHG and is also related to the wave-length of incident fundamental wave.