Optical degeneracies in anisotropic layered media: Treatment of singularities in a 4×4 matrix formalism

Abstract

matrices have been used extensively to study the propagation of light in anisotropic layered systems whose principal optic axes have arbitrary orientation. We present a general theory for the propagation of light in arbitrarily anisotropic layered systems that is particularly suited for treating optical degeneracies that arise ͑1͒ when light propagates in an isotropic medium embedded within the anisotropic layers or ͑2͒ when light propagates along one of the optic axes in an anisotropic layer. Boundary conditions are applied explicitly to the electric and magnetic fields at each interface, and transfer matrices that relate the transmitted and reflected fields to the optical properties of the system are developed. Criteria are given for identifying the mathematical singularities caused by the degeneracies described above, and a method for treating the singularities in the relevant expressions is presented.

Generalized 4 × 4 matrix formalism for light propagation in anisotropic stratified media: study of surface phonon polaritons in polar dielectric heterostructures

“…However, the angle of incidence-dependent calculation of light propagation in a general multilayer structure rapidly becomes cumbersome, especially if optical anisotropy and absorption are taken into account. In order to solve this problem, many authors have presented 4 × 4 matrix approaches [11][12][13][14][15][16][17] based on Maxwell's equations. However, many of these methods consider only special cases of the dielectric tensor 11,14,15,17 or lead to discontinuous solutions 13,16 .…”

“…In order to solve this problem, many authors have presented 4 × 4 matrix approaches [11][12][13][14][15][16][17] based on Maxwell's equations. However, many of these methods consider only special cases of the dielectric tensor 11,14,15,17 or lead to discontinuous solutions 13,16 . These problems become particularly critical in the mid-and far-infrared Reststrahlen spectral region of polar dielectrics 18 , where surface phonon polaritons (SPhPs) can be excited [19][20][21][22] .…”

Reflection Properties of a Biaxially Anisotropic Dielectric Film in a Long-Wavelength Approximation

“…Finally, it might be well to point out that the approximate analytical approach works also in the situations of optical degeneracies [17] that arise when light propagates along one of the optic axes in an anisotropic layer. It is well known that in theses instances the conventional numerical methods turn out to be applicable for computation through the presence of mathematical singularities.…”

“…Solutions in this case have the common factor exp(ik x x). Therefore, a differential form of the Equation (10) may be written {by substituting Equations (17) and (18) into (13) …”

Generalized Ellipsometry Using a Rotating Sample

“…The formula for calculating (7) can be found elsewhere [6]. These expressions establish the relationships between the Jones matrix and the system's dielectric tensors and film thicknesses.…”