Maria C. Simon

Ray tracing formulas for monoaxial optical components

A formalism which allows finite ray tracing through monoaxial crystals was developed starting from Maxwells equations. The derived formulas were applied to a Wollaston prism in convergent light and spot diagrams were obtained.

Reflection and transmission coefficients in uniaxial crystals

Abstract In this work we present a detailed deduction of the general solution of the boundary conditions for an isotropic medium-uniaxial birefringent crystal interface. The reflection and transmission coefficients are defined with reference to a polarization perpendicular or parallel to the incidence plane of the incident ray. The explicit expressions and curves of these coefficients are obtained as functions of the incidence angle, and they are discussed comparing them with the isotropic case.

Wollaston prism with large split angle

The image formation through a Wollaston prism with large split angle is studied. Formulas for the split angle, approximate calculations of aberrations, and ray tracings are used. The most important aberrations found are astigmatism and anamorphic distortion. Tilting the Wollaston with respect to the incident beam may reduce these aberrations, and if the orientation of the optical axis in the first element is varied it is possible to cancel one of the two aberrations for both images simultaneously, while the other one is substantially reduced. With an adequate adjustment of all the construction parameters the images become sharp enough to allow the use of large split angles (approximately 15 degrees).

Internal reflection in uniaxial crystals. I: Geometrical description

Abstract We give a vector formulation to calculate the direction of the internally reflected rays in a uniaxial crystal. The vector formulae obtained can be applied in general to any direction of the optical axis and any direction of incidence. The reflective indices are also defined, and formulae for them are given in terms of the angle of incidence and of the optical properties of the crystal.

Inhibited reflection in uniaxial crystals

When an ordinary or extraordinary ray that propagates through a birefringent crystal is reflected it gives rise to two reflected rays whose directions may be calculated with formulas similar to Snells law for refraction. When the reflection angle is greater than the incidence angle there is a critical angle for which the reflected ray is grazing, and for values of the incidence angle greater than this critical value the reflected ray no longer exists. We call this phenomenon inhibited reflection. We show how the critical angles may be calculated, and an experiment that visualizes the phenomenon shows good agreement with theory.

Optical path in birefringent media and Fermat's principle

In this paper we propose a definition for the optical path in birefringent crystals. We apply this definition to light refraction in a crystal-crystal interface by means of Fermats principle. The result obtained is confirmed by applying Snells law generalized for crystals and the relation obtained from Maxwells equations between the direction normal to the wavefront and the ray.

Reflection and Refraction in Uniaxial Crystals with Dielectric and Magnetic Anisotropy

Abstract The formulae for the refractive indices and the reflection coefficients for a discontinuity surface between an isotropic medium and a birefringent one with dielectric and magnetic anisotropy were developed. In the case considered the symmetry axis forms an arbitrary angle with the interface. The curves obtained for the cases of dielectric, magnetic or both anisotropies are compared.

Internal reflection in uniaxial crystals. II: Coefficients of transmission and reflection for an ordinary incident wave

Abstract The boundary condition at the interface between a crystal and an isotropic medium have been solved in a general form for the situation when an ordinary ray is incident from the crystal and gives rise to two reflected rays besides the refracted ray. With the formulae obtained, the reflection and transmission coefficients have been calculated as functions of the incidence angle, and a pseudo-Brewster angle was observed to exist for each one of the reflected rays.

Fringe localization in interferometers illuminated by a succession of incoherent line sources

Abstract It is well known that interference fringes formed by an interferometer that is illuminated with a point source are non-localized and, when it is done with an extended source, they are localized. Nevertheless, when the interferometer is illuminated with a discrete succession of points or lines, the localization of the fringes presents some characteristics that are different from those obtained with the former, for example the discrete number of localization surfaces. In this work we obtain the conditions to find the position of the surfaces of localization of these planes for an arbitrary interferometer. Then we apply this method to a wedge interferometer and compare the experimental and theoretical results.

Goos-Hänchen effect of an ordinary refracted beam

When there is total reflection on an isotropic or an anisotropic interface, the reflected ray suffers a displacement on the interface. This effect, which is known as the Goos-Hänchen effect, has been studied by a great number of authors. If an isotropic-uniaxial interface is considered, the condition of total reflection for one of the refracted rays can be fulfilled whereas the other subsists as a propagating wave. In this paper, we analyse and determine analytically the complex displacement that the ray associated with this propagating wave suffers. Representing the ray by a beam with a Gaussian distribution of amplitudes, we show how this displacement is modified by different configurations of the interface and of the incident waves.