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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. OCIS codes: 060.2310, 060.2400, 230.1480, 230.7370.

Thin-film wavelets are further analyzed for the design of dichroic mirrors for ultrafast solid-state lasers that provide both high reflectance on the lasing wavelength range and high transmittance of the pump light. Discrete quarter-wave-thick dielectric thin-film structures of homogeneous refractive indices following a quintic-wavelet envelope are considered. Relations for the reflectance on the lasing wavelength range are given. Adding several index-matching quarter-wave layers to both sides of the discrete wavelet optimizes the transmittance of the pump light. The design is further optimized to get minimum phase distortion on the lasing wavelength range.

In case of tunable ultrashort-pulse lasers, besides the prism material, separation, and insertion, one may choose the central wavelength providing a better high-order dispersion compensation. Because of errors that accumulate in numerical iterations, the analytic approach may be preferable for high-order dispersion examination. Analytic expressions for the fourth--and the fifth--order dispersions of crossed prisms pairs, both at arbitrary and Brewster-angle incidences are presented. Examples are given for e-sapphire slabs and for one or two pairs of fused-silica prisms. Results are shown providing compensation of both the second-and the third-order dispersions, by keeping as low as possible the higher-order ones. OCIS codes: 230.5480, 260.2030, 350.5030, 160.4670, 140.3590, 140.7090.

Omnidirectional reflection from periodic and Fibonacci quasi-periodic multilayers that are embedded in an isotropic medium is further analyzed. Besides the isotropic structures, birefringent structures are considered that comprise uniaxial layers in the principal-axis system, alternating with isotropic layers so that the refractive index of isotropic layers is equal to the principal extraordinary refractive index of the uniaxial layers. The transfer-matrix method is applied, and the same formalism is used for both the isotropic and the uniaxial media in the principal-axis system. Simple and original relations are obtained for the invariant of the one-dimensional Fibonacci sequences at oblique incidence. Numerical examples are given comparatively for the isotropic and the birefringent structures in the case of periodic and Fibonacci quasi-periodic sequences at different values of the refractive indices. OCIS codes: 230.4170, 260.1180, 260.1440, 160.5470, 240.7040, 310.0310.

Periodic and quasi-periodic Cantor-like bandgap structures that bordered upon a medium of refractive index [n.sub.0] are analyzed. An immersion model is used with the assumption that each layer is embedded between two identical regions of refractive index [n.sub.0] and thickness [d.sub.0], where [d.sub.0] is set equal to zero. Transmittance and group velocity are determined Their dependence on [n.sub.0] is emphasized. Relations for the midgap value of the normalized group velocity are given. By use of these relations, diagrams are completed at different values of [n.sub.0], showing the pairs of quarter-wave-layer refractive indices at which there is an apparent superluminal tunneling through the finite periodic and quasi-periodic Cantor-like bandgap structures. OCIS codes: 230.4170, 240.7040, 310.6870, 350.5030, 230.1480, 120.2440.

Ray vector traces that can be obtained at the back of a biaxial crystal through crystal rotation are calculated numerically by variation of one of the three Euler angles. Negative and positive lossless biaxial crystals are considered at normal incidence. Interesting features of these traces are evidenced by reference to the circular ring that forms at internal conical refraction.

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 ace expressed by simple analytical relations. By using these relations one can express analytically the polarization-dependent optical parameters to be determined by generalized ellipsometry.

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 Abeles relations, and thus they may be considered as generalized Abeles 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.

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.

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.

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. Key words: Reflection, polarization, ellipsometry.

Single-layer coatings on total internal reflection boundaries that produce any specific phase retardation are analyzed. One- and two-reflection phase-retarding systems are considered. Simple quadratic equations are obtained for an unknown layer phase thickness at a given angle of incidence and phase retardation. Equations for specific multilayer coatings that are equivalent to single-layer designs are also deduced. Diagrams of solution zones for refractive indices are given comparatively for one- and two-reflection systems. Key words: Thin-film coatings, total internal reflection prisms, phase retarders.

Simple relations in terms of effective g parameters are given for linear resonators that contain laser rods with curved endfaces and for symmetrical and asymmetric ring resonators of solid-state lasers. The equivalence relationships of thick and thin lenses have been applied.

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' angle of incidence are comparatively analyzed both numerically and analytically.

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

The reflectance of an absorbing medium for incident light of arbitrary polarization can exhibit two extrema at angles of incidence [[Phi].sub.max] and [[Phi].sub.min]. The behavior of iso-[[Phi].sub.max] and iso-[[Phi].sub.min] contours in the complex plane of a dielectric constant for various incident polarizations is analyzed.

Simple algebraic expressions are presented for calculating the waist position measured from the vertex and the waist size of a Gaussian beam transmitted through thick lenses.

The relationships for refractive indices for zero-phase-shift quarter-wave coatings on metallic reflectors are given. Small variations in Lambda/4-layer phase thicknesses are also considered.

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.

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.

Forbidden gaps in Solc folded-type anisotropic periodic structures are analyzed. The azimuth angle in the first quadrant and unequal thicknesses of alternating uniaxial layers are considered. Unit-cell translation matrices are explicitly given at oblique and normal incidences. Implicit dispersion relations are obtained. Birefringence and normal group velocities are determined. Numerical examples make the distinction between the gaps determined by one root and those determined by two roots of the eigenvalue equation. When layers have unequal thicknesses, the gap determined by one root is much wider, but inside the gap the reflectivity is lower than unity, breaks appear, and an increased birefringence results. [C] 2001 Optical Society of America OCIS codes: 230.4170, 260.1180, 260.1440, 260.5430, 310.6870, 350.2460.

Recently it was shown theoretically [Opt. Commun. 174, 43 (2000)] that a Solc folded-type anisotropic dielectric structure under certain conditions exhibits omnidirectional reflection at any polarization over a wide spectral range. Here, omnidirectional reflection from Solc folded-type dielectric periodic structures is further analyzed. Transfer-matrix methodology is applied. Simple expressions are obtained for transfer matrices at interfaces and the unit cell translation matrix. Dispersion relations are determined. Numerical examples are shown comparatively for isotropic and Solc-type anisotropic periodic structures. The Solc-type structure has a wider band of omnidirectional reflection. The results demonstrate that anisotropic materials should be useful in photonic bandgap structures. [C] 2000 Optical Society of America OCIS codes: 230.4170, 260.1180, 260.1440, 260.5430, 310.6870, 350.2460.

The general case of obliquely incident plane-wave propagation in periodic anisotropic layered media is presented. Arbitrary permittivity tensors of the two alternating anisotropic layers are considered. An immersion model is used with the assumption that each layer is embedded between two isotropic regions that have the same index of refraction as the isotropic medium of incidence and a thickness that is set equal to zero. Then explicit relations are presented for normally incident plane waves in periodic structures that consist of alternating biaxial layers of arbitrary principal-axis orientation. Specific cases of alternating isotropic and biaxial layers are also considered. Unit cell translation matrices are presented for both traveling directions, from the left to the right and vice versa. Dispersion relations that contain information regarding the propagation bands and the forbidden gaps in periodic anisotropic structures are presented. OCIS codes: 230.4170, 230.1480, 260.1180, 260.2030, 260.5430, 310.6870.

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 [n.sub.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.sub.0]. 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. [C] 2000 Optical Society of America OCIS codes: 310.0310, 160.1190, 160.3820, 160.4760, 260.1180, 260.1440.