双轴晶体主平面上倍频的相位匹配

从折射率椭球方程和折射率椭球面出发，讨论光束在双轴晶体中传播及偏振的特性、主平面倍频共线相位匹配（PM）问题，得到了双轴晶体主平面内激光所有可能PM倍频的8种偏振组合及其相应的PM角公式、有效非线性（NL）系数deff的一般表达式。结果表明：得到的公式简单，可大大简化PM参数计算及优化设计；折射率椭球面是单层曲面，比双层的折射率面简单；基于折射率椭球面寻找所有可能PM的类型、偏振组合的方法物理图像简明，易于理解，大大降低了双轴晶体PM问题分析的难度。

Phase Matching for SHG in Principal Planes of Biaxial Crystals

Characteristics of light propagation and polarization,collinear phase matching (PM) problems and methods in the principal planes are discussed based on indicatrix equation for SHG in biaxial crystals.8 polarization combinations for all the possible collinear PM SHG in the principal planes,the PM angle formulas and the general expressions of the effective nonlinear (NL) coefficient d eff are given.The results obtained are prety simple and greate to simplify calculatation and optimum design for the PM.In contrast to a Fresnel surface with double sheets,an indicatrix one is simple.The PM methods searching for all the possible PM polarization combinations of 3 WM which have clearly physical picture,are much simple and easy to be understood based on the indicatrix surface.