Electromagnetic fields in layered-inhomogeneous uniaxial media: Validation criterion and higher-order solutions of the geometrical-optics approximation

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Abstract
We study the electromagnetic fields in layered-inhomogeneous uniaxial planar structures using the geometrical-optics approximation (GOA). Explicit expressions for the fields in the higher- (first-) order GOA are obtained. We also obtain the validation criterion for the zeroth-order GOA. There results are important for studying the true significance of the geometrical-optics approximation and the extension of its usefulness. The GOA solution shows that when total internal reflection occurs in the medium, the field amplitudes become zero and the angle of refraction becomes π/2. The azimuthal dependence of the ray direction and total internal reflection is discussed. The results are applied to a wave propagation in a hybrid oriented uniaxial nematic liquid crystal in an external field.