C. Oldano

Symmetry properties of anisotropic dielectric gratings

We consider the exact equations, obtained by application of the Bloch–Floquet theorem, that describe the propagation of light in anisotropic dielectric gratings with an arbitrary variation of the dielectric tensor along the longitudinal direction. On the basis of these equations we determine the scattering matrix and the corresponding grating efficiencies. The conditions for electromagnetic energy conservation are derived and an energy representation for the field inside the grating is defined, thus permitting determination of reciprocity relations that give rise to particular symmetries of the grating efficiencies if one neglects the reflections at the boundaries. Finally, by exploiting the symmetry properties of the matrix that describes the propagation of the electromagnetic field inside the grating, we discuss the polarization properties of the diffracted beams in chiral C smectics in the phase-grating configuration and in the periodic structures induced in certain nematic liquid crystals by the application of static magnetic or electric fields.

Multiplet structure of the defect modes in 1D helical photonic crystals with twist defects

We theoretically analyse the defect modes generated by equispaced twist defects in 1D helical (cholesteric-like) structures within their frequency gap which is such that only the first two of the four eigenwaves 1±, 2± are exponentially attenuated. n0 identical defects generate n0 different defect modes, each one represented by a linear combination of the four eigenwaves. The components 1+ and 1− are by far the dominant ones and they are localized near the defect planes. We give exact analytic expressions for the elements of the transfer and scattering matrices of the defect planes, for the functions defining the defect mode when n0 = 1, and for the defect frequencies when n0 = 1, 2, 3. In the particular case n0 = 2 and twist angle θ = π/2, the difference between the two defect wavelengths λd2, λd1 depends exponentially on the distance z1 between the defect planes, going to zero for z1 → ∞ and becoming as large as the entire frequency gap for z1 → 0.

Optical Properties of Cholesteric Liquid Crystals at Oblique Incidence

Abstract The optical properties of a periodic structure characterized by a uniform rotation of the dielectric tensor about a given axis are theoretically analyzed. The electromagnetic wave is described as a superposition of elementary modes having the form of Bloch waves. Each elementary mode is represented by a sum of plane waves elliptically polarized, whose wavevectors are the solutions of a characteristic equation. This equation, presented in a preceding paper, is furtherly analyzed, in order to obtain the wave vectors in terms of a power series of a small parameter δ, representing the anisotropy of the dielectric tensor. The coefficients of the series up to terms containing δ6 are explicitly given, and the corresponding truncation errors computed. The spectral composition and the polarization states of the Bloch waves are also analyzed and discussed for different values of the incidence angle in the frequency range containing the lower reflection bands. In particular it is shown that in the regions b...

Reduced-Order Model Technique for the Analysis of Anisotropic Inhomogeneous Media: Application to Liquid-Crystal Displays

Electromagnetic wave propagation in anisotropic inhomogeneous media is computed by a novel reduced-order model technique, which is based on the restriction of the Marcuvitz-Schwinger equations on Krylov subspaces and on the application of the singular-value decomposition. The model is derived from the standard coupled-wave method and includes both wide-angle diffraction and light scattering at dielectric interfaces. The method, currently implemented for two-dimensional problems, was applied to the analysis of different liquid-crystal test cells. Numerical results are compared with those obtained through the application of the coupled-wave method and the Jones method and with experimental microscopic measurements.

Polarization Transfer-matrix For the Transmission of Light Through Liquid-crystal Slabs

The polarization properties of the light transmitted through an optically anisotropic stratified medium are discussed in terms of a 2 × 2 matrix approach, which can be followed in all cases when the intensity of the reflected waves is negligible. The starting point of the treatment is Berreman’s equation, involving a 4 × 4 matrix. A generalized Jones vector is obtained by applying a suitable transformation to Berreman’s vector. An equation for the propagation of the Jones vector is easily derived. It involves another 4 × 4 matrix, obtained from the Berreman one, whose elements describe the propagation and the mutual coupling of forward-and backward-traveling solutions. In particular, the upper 2 × 2 block corresponds to the Jones matrix of the problem. The Jones equation is solved by making use of an interaction-matrix treatment derived from the perturbation methods of quantum mechanics. A transfer matrix is obtained, describing the effect of the optical medium on the transmitted light. Such a procedure holds and gives good results, for the arbitrary incidence of light. Simple, analytical expressions for the transfer-matrix elements are obtained for quasi-normal incidence of light. This approximation retains its validity for incidence angles as large as 30° (in air). The case of the twisted nematic cell is discussed in detail. The effect of multiple reflections at the surfaces of the optical medium (or at interfaces between adjacent media) is shown to be correctly accounted for within the proposed approach.

4 × 4 matrix approach to chyral liquid-crystal optics

A new approach is proposed for studying the optical properties of anisotropic stratified media that makes use of a suitable perturbative treatment of Berreman’s 4 × 4 matrix, which describes light propagation in these structures. The method consists in finding a new basis for the 4 × 4 matrix in which a specific problem may be treated in a more convenient way. This allows one easily to obtain information about quantities of immediate physical meaning and to find simple approximate expressions for the optical properties having particular interest in experiments. The case of light propagation in cholesteric and chyral smectic liquid crystals at small incidence angles is studied in detail.

Dynamics of flexoelectric surface oscillations in a nematic liquid crystal

New dynamical aspects have been investigated in the flexoelectrically excited angular waves of a nematic liquid crystal by means of a modulation ellipsometry technique. At low frequency (f < 1 Hz) the gradient flexoelectric torque dominates and causes an out of phase electrooptical effect. At high frequency (f > 1 kHz), the surface friction is responsible for a new dynamical behavior. The surface viscosity is evaluated to be 3 (DOT) 10-5 erg(DOT)s/cm2.

Numerical methods for light propagation in large LC cells: a new approach

Accurate numerical methods for the propagation of light in large 3D samples with strong lateral variation of the director field require prohibitive amounts of time. We consider and compare a standard spectral method and the Finite Difference in Frequency Domain method, showing that the CPU time can be reduced by one or two orders of magnitude using a perturbation approach or a recently developed Reduced Order Method. The equations obtained are applied to liquid crystal cells with in-plane switching, illuminated by a large incoherent source. The developed formalism, based on numerically exact equations, is particularly suitable for treating magnetic or optically active media and for extending to such media the well known approximations based on the 4 × 4 (Berreman) or 2 × 2 (Jones) matrices.

On the Approximate Methods for Linear Optics of Liquid Crystals

Abstract Several approximate methods have been proposed so far to treat electromagnetic wave propagation in stratified anisotropic media, such as liquid crystals or aperiodic structures. Despite the complete equivalence among many of them, however, a comparison between different results is often made difficult by the complexity of the adopted formalism. In this paper, an exact propagation equation is given for a plane e.m. wave travelling within a stratified medium. On such a basis, various types of already known approximate results are discussed and generalized in a very simple way.

Optical properties of short pitch cholesteric liquid crystals

The optical properties of short pitch cholesteric liquid crystals are theoretically analysed in the framework of an effective medium theory. It is shown that such properties are well described by a very simple homogeneous model, defined by an effective permittivity tensor having uniaxial symmetry, that is expanded in a power series of the ratio p/λ0 between the helix pitch and the light wavelength. The linear term is identically zero. This fact gives short pitch cholesterics very unusual properties for their optical activity, which is related to the scaling terms as (p/λ0)m, with m odd and greater than 1. Some problems related to the presence of these terms and concerning boundary effects are discussed but not fully resolved. The limits of validity of the different approximations, obtained by considering only a limited number of terms, are also found.