Brewster and pseudo-Brewster angles of uniaxial crystal surfaces and their use for determination of optical properties

Abstract

M. Elshazly-Zaghloul and R. M. A. Azzam, "Brewster and pseudo-Brewster angles of uniaxial crystal surfaces and their use for determination of optical properties," J. Opt. Soc. Am. 72, 657-661 (1982) Brewster and pseudo-Brewster angles are defined for surfaces of transparent and absorbing uniaxial crystals parallel and perpendicular to the optic axis. Two Brewster angles of a transparent uniaxial crystal surface parallel to the optic axis, measured when the optic axis is oriented perpendicular and parallel to the plane of incidence, readily determine the ordinary and extraordinary indices No and Ne. N 0 and Ne can also be obtained from two Brewster angles measured on a surface perpendicular to the optic axis in contact with two media of different refractive indices. Conditions for the existence of two Brewster angles are discussed. The complex No and Ne of an absorbing uniaxial crystal can be derived from pseudo-Brewster-angle and minimum-reflectance data obtained in two symmetrical orientations of a surface parallel to the optic axis. An approximate, but accurate, explicit inversion procedure is presented for this purpose.

Explicit expression of the pseudo-Brewster angle for anisotropic metamaterials

“…Substituting Eqs. (1) and (2) into Eq. (3) and after some tedious algebra, we obtain the following approximation for the PBA,…”

“…The pseudo-Brewster angle (PBA) refers to the incident angle of electromagnetic (EM) wave at the surface of an imperfect dielectric at which the magnitude of the reflection coefficient for a wave polarized within the plane of incidence becomes a minimum value [1]. The PBA differs from the Brewster angle in that the dielectric medium's absorbance has been taken into consideration.…”

Internal Reflection in Uniaxial Crystals II: Coefficients of Transmission and Reflection for an Ordinary Incident Wave

“…µou(SO -x) 4 . Coordinate transformations So far, we have only obtained the relations between the fields of a plane wave propagating in a uniaxial crystal or an isotropic medium .…”

“…For this reason the problem must be treated in vector form, for which purpose we shall use the notation and the method introduced in some earlier works [2,3] . Elshazly-Zaghloul and Azzam [4] obtained the reflection coefficients for three symmetry planes when the light is incident on a crystal from the isotropic medium, and determined the existence of a 'pseudo-Brewster' angle . In the present work, we develop for the general case the formulae for the electric and magnetic fields of the reflected and refracted waves as functions of the fields of the incident wave when the light is incident from the birefrigent medium and the incident ray is the ordinary one .…”

Biaxial thin-film coated-plate polarizing beam splitters

“…Index matching, n A ϭ n B , is trivial and not useful in stacks of isotropic materials, but it can be effective in stacks of birefringent materials. [3][4][5] The purpose of this paper is to show that the 45°c oated-plate design is possible by using a pair of formbirefringent 2,6 materials in a periodic structure. Such a stack of films can yield independent optical outputs for p-polarized and s-polarized light.…”