Twist defects in helical sonic structures.

We analyze theoretically both the acoustic wave propagation in periodic media made of anisotropic materials whose stiffness tensor is uniformly rotating along a given axis x(3) and the defect mode produced by twisting about x(3) one part of the helical structure with respect to the other. Within the Bragg band of the periodic structure, the twist defect gives rise to a resonant mode that is a superposition of two standing waves: one localized with exp(-gamma|x(3)|) dependence centered at the defect and the other extended over the whole sample. The ratio between the amplitudes of the localized and nonlocalized waves depends sharply on both the twist angle and the elastic anisotropy, and can assume huge values. The defect mode and the resonance frequency omega(0) are defined by fully analytical and very simple expressions. Finally, we discuss how around omega(0), a finite sample acts as a frequency filter for circularly polarized shear waves, whose bandwidth can be changed by many orders of magnitude by varying the sample thickness, the twist angle, or the elastic anisotropy.

Open problems in the optics of crystals: the role of multiple scattering.

The thickness b of the transition boundary layer, always present in crystals and giving still unsolved problems for the boundary conditions, is shown to be essentially determined by the multiple scattering of light, due to the inhomogeneity of any periodic structure. The parameter b depends on the orientation theta of the boundary plane with respect to the crystal lattice, and diverges for some critical orientations where strong macroscopic effects are found, which cannot be interpreted by any macroscopic model based on bulk and boundary equations. Our analysis exhaustively defines the limits of validity of macroscopic models for periodic nanoscale structures and solid crystals.

Bloch wave approach to the optics of crystals.

The Bloch wave method is used to find the effective permittivity tensor epsilon of periodic liquid crystals and artificial structures whose period p is short with respect to the light wavelength lambda and whose optical properties are defined by a permittivity field epsilon(r). The main role of the multiple scattering within the periodic medium is evidenced, and very general expressions of epsilon, based on expansions in ascending powers of the ratio p/lambda and of the light wave vector k, are found. Such expansions allow to discuss the general properties of epsilon, to clarify the role of the spatial dispersions, i.e., to separate the part of epsilon explicitly depending on k from its k-independent part, and to find some interesting properties of crystals that are (i) periodic in only one direction, or (ii) locally isotropic. Finally, the limits of validity of the macroscopic model are discussed. Within these limits only a few terms of the power expansions are required, and their expressions are explicitly given. The obtained results are also useful to better understand the macroscopic optical properties of solid crystals.

Acoustic wave propagation in structurally helical media.

A theoretical analysis is given of the acoustic wave propagation in periodically nonhomogeneous media made of a solid material whose stiffness tensor is uniformly rotating along a given axis. In the last years, such media have been studied theoretically as well as experimentally, in particular for what concerns sample preparation and possible applications. A detailed analysis of their acoustical properties is given here, based on fully analytic and simple propagation equations. For axial propagation: (i) the dispersion curves of media where the transversal field components and the longitudinal ones are not coupled show only one forbidden band, that gives selective Bragg diffraction; in the opposite case they show at least a second forbidden band, that involves the quasilongitudinal and one of the quasitransversal eigenmodes; (ii) in the first case (absence of coupling), the medium gives pure acoustical rotation for p<>lambda; (iii) in the presence of the coupling, regions of mode exchange between the longitudinal component and a transversal one are generally present. The cases of lossy media and of quasiaxial propagation are also considered, and the analogies between optical and acoustical properties discussed.

Direct measurement of the two principal refractive indexes of a nematic liquid crystal slab.

A new technique to measure the principal refractive indexes of a nematic liquid crystal is presented. The method is based on an indirect measurement of the refraction angle by determining the direction of a magnetic field which minimizes the light scattering. With this technique one can perform different light scattering experiments, which require a knowledge of the refractive indexes, on the same crystal slab. The accuracy is better than +/-0.15%. A discussion about the systematic error due to the distortion of the director profile near the holder edges and the relative correction is given.