Reducing Berreman's 4 x 4 formulation of liquid-crystal-display optics to 2 x 2 Jones vector equations

Modeling the reflection from cholesteric liquid crystals using modal analysis and mode matching

The reflection and transmission spectra from right-handed cholesteric liquid crystals are computed in the visible region for a linearly, circularly, or elliptically polarized incident plane wave at oblique incidence. The liquid crystal cell is sandwiched between dielectric layers of certain thickness and refractive index. The underlined formulation is based on a modal analysis of the governing field expressions in the dielectric and liquid-crystal regions. A representative matrix system is obtained after enforcing the continuity of the tangential electric and magnetic fields at the material interfaces. Solution of the governing matrix system results in the reflectance and transmittance for a given wavelength. Numerical results for both normal and oblique incidence were obtained and compared with data published in the literature. The underlined formulation is effective, accurate, robust, versatile, and computationally efficient.

Generalized Abelnus relations for an anisotropic thin film of an arbitrary dielectric tensor

The extended Jones matrix method is applied to one dielectrically anisotropic, homogeneous thin film at oblique incidence. Standard boundary conditions are imposed on resultant electric- and magnetic-field vectors at interfaces. Thus simple matricial relations are obtained for transmitted and reflected electric-field amplitudes at the two interfaces. In the limits of isotropy, they reduce to four well-known Abelès relations, and thus they may be considered as generalized Abelès relations for dielectrically anisotropic thin films. These matricial relations include multiple reflections while dealing with total fields. Thus they provide new insights into the 2 x 2 extended Jones matrix formalism.