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Dyakonov surface waves (DSWs) at the interface of an isotropic dielectric material and a biaxial dielectric crystal were considered in the case in which two principal axes of the biaxial crystal lie in the plane of the interface. Both x-cut and y-cut biaxial crystals were considered, and all permittivity scalars were assumed to be real and positive. A rather simple expression to relate the components of the wave vector of a DSW was derived, and analytical expressions for the limit angles at which the DSWs can propagate and the Poynting vector components of the DSWs were obtained. These expressions were numerically investigated for several biaxial materials. Different conditions for the relative permittivity scalars at which the DSWs can exist were identified. As an example, DSWs can exist not only for the positive, but also for the negative y-cut biaxial crystals.

Zero-reflectance conditions for quarter-wave-thick, high-spatial-frequency, rectangular-groove dielectric gratings are analyzed further at oblique incidence by a combination of the effective medium theory and the anisotropic thin-film theory. Numerical examples are given for gratings on glass and silicon substrates with refractive indices of 1.5 and 3.5, respectively.

An analysis is given of the designs of thin-film coatings on totally reflecting boundaries that produce half-wave, quarter-wave, and half-quarter-wave phase retardations. Particular single-layer, double-layer, and symmetrical triple-layer coatings that contain only one non-quarter-wave layer are considered. Simple quadratic equations are presented for the non-quarter-wave-layer phase thickness. Useful diagrams of the solution zones for layer refractive indices are obtained.

Theoretical performances of single-wavelength thin-film polarizing cubes, Brewster polarizers, and polarizing plates at a 45 degrees angle of incidence are comparatively analyzed both numerically and analytically.

The design of quarter- and half-wavelength layer coatings to preserve light polarization on total reflection is approached analytically. Simple relations for refractive indices are given.

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.

Theoretical formulas are presented for calculating the trajectory of the extraordinary ray at the back of a rotating uniaxial birefringent plate.

Dispersion of the fundamental confined modes in hollow-core all-silica Bragg fibers with nanosupports is analyzed. The transfer-matrix formalism is applied. Anomalies in the group-velocity dispersion are evidenced at long wavelengths, toward the upper limit of the bandgap. The results confirm that, as in microstructured photonic crystal fibers, this anomalous dispersion is due to prevention of the confined hollow-core modes from crossing the surface modes, the avoided crossings are more apparent in the variation of group velocity with wavelength. The dependence of these avoided crossings on the hollow-core radius and the layer thicknesses is briefly analyzed.

Generalized Abeles 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 n0) 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 n0. This model leads to simple expressions for the resultant transmitted and reflected electric field amplitudes at interfaces. They parallel the Abeles 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.

Extraordinary-wave propagation within homogeneous uniaxial media is analyzed in the case of an arbitrary optic-axis orientation. Unit vectors along the electric- and magnetic-field directions are represented by direction cosines and vectorial relations. The extraordinary-ray path is determined simply by direction cosines. Numerical examples are given for extraordinary-ray tracings within a plane-parallel uniaxial plate. It is shown that a symmetrical convergent beam is asymmetrically imaged when it is incident normally and passes through the uniaxial plate with an arbitrary optic-axis orientation.

Three special angles associated with the external reflection of light at the surface of an absorbing medium are well known: the principal angle, the pseudo-Brewster angle, and the second Brewster angle. Another significant angle has been identified recently by Azzam and El-Saba [Appl. Opt. 28, 1365 (1989)]. At this angle, the slope of the differential reflection phase shift with respect to the angle of incidence is maximum negative. For convenience it is called the third Brewster angle. The nature of the contours of the constant third Brewster angle in a complex dielectric constant plane is considered both analytically and graphically in comparison with the other constant special-angle contours.

A specific triple-layer antireflection coating with equal refractive indices and thicknesses of the first and third layers is considered. Simple formulas for coating layer thicknesses are derived for nonabsorbing materials at normal incidence.