Ren Ming-Liang, Li Zhi-Yuan
Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China.
Opt Express. 2010 Mar 29;18(7):7288-99. doi: 10.1364/OE.18.007288.
A versatile and accurate approach that combines a numerical iteration technique and a transfer-matrix method (TMM) is developed to solve the general problem of second harmonic generation (SHG) with pump depletion in quasi-phase-matched (QPM) nonlinear optical structures. We derive the iterative formulae from the nonlinear coupled wave equations and obtain the intensity distribution of fundamental wave and second harmonic wave by TMM. The approach shows quick numerical convergence of iteration and maintains perfect conservation of total energy. The simulation results show that the model coincides with the one under undepleted pump approximation very well when the SHG efficiency is small (well below 15%) and agrees very well with the effective nonlinear susceptibility model in handling general SHG problems even when the conversion efficiency is high up to 100%. Our method is applicable to general nonlinear optical structures, such as periodic, quasi-periodic, and aperiodic QPM structures, photonic crystals, and micro-cavities that might involve complicated modulation on the linear and nonlinear susceptibility.
开发了一种将数值迭代技术与传输矩阵法（TMM）相结合的通用且精确的方法，以解决准相位匹配（QPM）非线性光学结构中存在泵浦耗尽时二次谐波产生（SHG）的一般问题。我们从非线性耦合波方程推导出迭代公式，并通过TMM获得基波和二次谐波的强度分布。该方法显示出迭代的快速数值收敛，并保持了总能量的完美守恒。模拟结果表明，当SHG效率较小时（远低于15%），该模型与泵浦未耗尽近似下的模型非常吻合，并且即使在转换效率高达100%时，在处理一般SHG问题时也与有效非线性极化率模型非常吻合。我们的方法适用于一般的非线性光学结构，如周期性、准周期性和非周期性QPM结构、光子晶体以及可能涉及线性和非线性极化率复杂调制的微腔。
