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REPRESENTATION OF BIREFRINGENT FILTERS BY DIRECTLY COMPOSED 4X4 MATRICES

机译：直接组成4X4矩阵表示双折射滤光片

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摘要

The interaction of an obliquely incident plane wave with an arbitrary birefringent plane structure can be described exactly by a so-called 4 x 4 layer matrix. However, its formation is rather complex, and therefore a simplified method to set up this matrix is proposed. It is deduced from the boundary conditions for the tangential components of the E and the H fields at the interfaces of the birefringent layer and the phase shifts of the four waves within the layer between both interfaces. The refractive indices and the directions of polarization of the four waves are calculated from the well-known dispersion relation in the principal coordinate system and a coordinate transformation. Transmission curves of Lyot filters made of uniaxial and biaxial materials are calculated in the cases of plane waves of finite or infinite lateral extension that are incident under Brewster's angle upon the filter positioned outside or within a laser resonator. The special examples given for a quartz filter and a YAlO3 filter are characterized by a high selectivity within a broad bandwidth if Fabry-Perot effects can be neglected. Transmission curves of a quartz filter were verified by measurements. [References: 21]
机译：斜入射平面波与任意双折射平面结构的相互作用可以通过所谓的4 x 4层矩阵精确描述。但是，其形成相当复杂，因此提出了一种简化的方法来建立该矩阵。它是从双折射层界面处的E和H场的切向分量的边界条件以及两个界面之间的层内四波的相移得出的。根据主坐标系中的众所周知的色散关系和坐标变换来计算四波的折射率和偏振方向。在以布鲁斯特角入射到位于激光谐振器外部或内部的滤波器上的有限或无限横向延伸平面波的情况下，可以计算出由单轴和双轴材料制成的Lyot滤波器的透射曲线。如果可以忽略法布里-珀罗效应，则石英滤光片和YAlO3滤光片的特殊示例的特点是在宽带宽内具有高选择性。通过测量验证了石英滤光片的透射曲线。 [参考：21]

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