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Born, M. and Wolf, E. (1970) Principles of Optics. Pergamon, Ox-ford.


  • 标题: 双轴晶体中基于角度计算的相位匹配研究The Study of Phase Matching Based on Angle Calculation in Biaxial Crystals

    作者: 霍广文, 陈恒, 李险峰

    关键字: 相位匹配, 双轴晶体, 计算, 折射率梯度Phase Matching, Biaxial Crystale, Gradient of Refractive Index

    期刊名称: 《Applied Physics》, Vol.6 No.8, 2016-08-30

    摘要: 本文介绍了一种通过角度投影方法计算双轴晶体中相位匹配参数的有效方法。该方法利用日本数学家小平邦彦对角度概念的推广,借助两个光轴与光波矢量之间的角度关系,通过角度投影方法确定了折射率计算所需角度参量的解析表达式,可直接用于相位匹配条件。文章以双轴晶体BIBO为例,数值模拟自发参量下转换过程中I类、II类相位匹配的角度关系和有效非线性系数。通过进一步对比自发参量下转换和倍频过程,讨论了角度表象下折射率梯度的物理意义。该方法在求解参量过程中的相位匹配参数时,避免了求解二阶菲涅尔方程过程,理论计算更便捷。 We present an effective method to calculate the phase matching parameters based on angle pro-jection in biaxial crystal. By exploiting the angle definition introduced by Japanese mathematician Kodaira Kunihiko, we deduce the angular relations in geometry and obtain the expressions of refractive indices depending on angular orientation of wave vector and optical axis angle. It can be directly applied in phase matching conditions. Taking biaxial crystal BIBO as an example, we calculate the relations of phase matching angles and effective nonlinear coefficient in Spontaneous Parametric Down-Conversion process (SPDC) for the type I and type II. We further compare the SPDC with double frequency process, and discuss the physical meaning of angular gradient of refractive index. This approach is convenient to calculate phase matching parameters without solving the quadratic Fresnel equations.