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In this paper we will analyze the propagation of the angular spectrum of theelectromagnetic field through a finite length uniaxial crystal. We solve theboundary conditions of the fields at an interface of an isotropic medium and anuniaxial anisotropic medium with the optical axis in an arbitrary direction andsoon after we choose the optical axis in a plane formed by the direction ofpropagation (z-axis) and the x-axis . We show how the couplings occur betweenthe components of the field and in what situations we can give a vector orscalar treatment for the propagation

Propagation of the angular spectrum of electromagnetic fields in uniaxial crystals of finite length in the regime of the paraxial approximation