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

Reflective liquid-crystal displays with asymmetric incident and exit angles

The 2 x 2 matrix methods are extended to calculate the optical behaviors of reflective liquid-crystal displays with asymmetric incident and exit angles. Both the unfolding method and the backward-eigenwave method are employed to derive the 2 x 2 matrix representations. The simulation results for symmetric incident and exit angles from these two methods are identical and agree well with those obtained from the 4 x 4 matrix method when the air-panel surface reflections are neglected. Further, the derived 2 x 2 matrix methods are applied to the asymmetric cases with different incident and exit angles. The simulated results on the normally black vertical alignment and normally white mixed-mode twisted nematic reflective displays show reasonably good agreement with the reported experimental data. In addition, a rubbing effect related to contrast values is observed and analyzed in asymmetric reflective cases. We also find that this effect has a significant influence on the contrast ratios once the difference between the incident and exit angles becomes large.

Simple recurrence matrix relations for multilayer anisotropic thin films

Generalized Abelès relations for one anisotropic thin film [E. Cojocaru, Appl. Opt. 36, 2825-2829 (1997)] are developed for light propagation from an isotropic medium of incidence (with refractive index n(0)) within a multilayer anisotropic thin film coated onto an anisotropic substrate. An immersion model is used for which it is assumed that each layer is imaginatively embedded between isotropic gaps of zero thickness and refractive index n(0). This model leads to simple expressions for the resultant transmitted and reflected electric field amplitudes at interfaces. They parallel the Abelès recurrence relations for layered isotropic media. These matrix relations include multiple reflections while they deal with total fields. They can be applied directly to complex stacks of isotropic and anisotropic thin films.

Simple expressions for transmission and reflection matrix elements of a biaxial thin layer at normal incidence

The extended Jones matrix method is applied for determination of the transmission and reflection matrices for a normally incident plane wave upon an homogeneous and lossless biaxial thin layer. The elements of these matrices are expressed by simple analytical relations. By using these relations one can express analytically the polarization-dependent optical parameters to be determined by generalized ellipsometry.

Generalized abelès relations for an anisotropic thin film with an arbitrary dielectric tensor: comments

The Cojocaru generalization of the 2 x 2 extended Jones matrix method, placed in a wider context of previous approaches to anisotropic optical thin films, is analyzed from a complementary perspective. This, contrary to initial belief, allows for a simple proof that one may include multiple reflections by taking into account total fields into the anisotropic film, and this therefore provides support for a more widespread use of the method.