REPRESENTATION OF BIREFRINGENT FILTERS BY DIRECTLY COMPOSED 4X4 MATRICES

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 there fore a simplified method to set up this matrix is proposed. It is dedu ced 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 interfac es. The refractive indices and the directions of polarization of the f our waves are calculated from the well-known dispersion relation in th e principal coordinate system and a coordinate transformation. Transmi ssion curves of Lyot filters made of uniaxial and biaxial materials ar e calculated in the cases of plane waves of finite or infinite lateral extension that are incident under Brewster's angle upon the filter po sitioned outside or within a laser resonator. The special examples giv en for a quartz filter and a YAlO3 filter are characterized by a high selectivity within a broad bandwidth if Fabry-Perot effects can be neg lected. Transmission curves of a quartz filter were verified by measur ements.