Influence of multiple reflections on the transmission coefficients of uniaxial plane-parallel plates.

A study on the influence of multiple reflections on the transmission coefficients of uniaxial plane-parallel plates is presented. Two representative models are analyzed: one that considers only the first transmission, and a rigorous one, taking into account the multiple reflections within the plate. Modules, phases, and the interference between $p$ and $s$ transmitted fields are evaluated in a wide range of angles of incidence by means of three emblematic examples that illustrate the effects of thickness, birefringence, and optical axis orientation. For simplicity, whereas the optical axis can form an arbitrary angle with the interface, it is restricted to the plane of incidence. A complete theoretical framework is provided along with general reference guidelines derived from numerical examples.

Wide angle conoscopic interference patterns in uniaxial crystals.

The fringe pattern obtained when a divergent (or convergent) beam goes through a sample of birefringent crystal between two crossed polarizers contains information that is inherent to the crystalline sample under study. The formation of fringe patterns is analyzed from distinct approaches and with different degrees of approximation considering cones of light of large numerical aperture. We obtain analytic explicit formulas of the phase shift on the screen and compare them with the exact numerical solution. The results obtained are valid for arbitrary orientation of the optical axis and are not restricted either to low birefringence or to small angles of incidence. Moreover, they enable the extraction of the main features related to the characterization of uniaxial crystal slabs, such as the optical axis tilt angle and the principal refractive indices.

Determination of nongeometric effects: equivalence between Artmann's and Tamir's generalized methods.

This work shows that all first- and second-order nongeometric effects on propagation, total or partial reflection, and transmission can be understood and evaluated considering the superposition of two plane waves. It also shows that this description yields results that are qualitatively and quantitatively compatible with those obtained by Fourier analysis of beams with Gaussian intensity distribution in any type of interface. In order to show this equivalence, we start by describing the first- and second-order nongeometric effects, and we calculate them analytically by superposing two plane waves. Finally, these results are compared with those obtained for the nongeometric effects of Gaussian beams in isotropic interfaces and are applied to different types of interfaces. A simple analytical expression for the angular shift is obtained considering the transmission of an extraordinary beam in a uniaxial-isotropic interface.

Phase shift formulas in uniaxial media: an application to waveplates.

The calculation of phase shift and optical path difference in birefringent media is related to a wide range of applications and devices. We obtain an explicit formula for the phase shift introduced by an anisotropic uniaxial plane-parallel plate with arbitrary orientation of the optical axis when the incident wave has an arbitrary direction. This allows us to calculate the phase shift introduced by waveplates when considering oblique incidence as well as optical axis misalignments. The expressions were obtained by using Maxwell's equations and boundary conditions without any approximation. They can be applied both to single plane wave and space-limited beams.

Nonspecular transverse effects of polarized and unpolarized symmetric beams in isotropic-uniaxial interfaces.

We analyze the first-order nonspecular effects of three-dimensional beams in interfaces formed by two lineal dielectric media. We also analyze the dependence of the transverse effects on polarization and compare the results with those obtained for isotropic interfaces. In particular, we determine analytically the complex transverse lateral displacements of a beam with Gaussian distribution of intensity when it is reflected on an interface formed by an isotropic medium and a uniaxial anisotropic one and the mean direction of propagation of the beam is contained in each of the characteristic planes of the crystal.