Optical properties of anisotropic periodic helical structures

An optical model is considered describing a wide class of optically anisotropic media such as chiral smectic liquid crystals and, in the limiting cases, cholesteric liquid crystals and anisotropic homogeneous media. It describes a structure having a periodicity along a given axis generated by a uniform rotation of the dielectric tensor. Maxwell's equations for this model, studied so far only in particular cases, are here solved for the general case where the direction of the propagating waves and the orientation of the dielectric tensor make an arbitrary angle with respect to the rotation axis. The resolving procedure involves the evaluation of the eigenmodes of the electromagnetic wave, i.e. the Bloch waves intrinsic to the specific periodic structure, which reduce to the ordinary and extraordinary waves in the limiting case of anisotropic homogeneous structures. The dispersion relation for the eigenmodes is deduced, allowing the study of the optical properties of this structure on a general basis. The Bragg reflection bands are found to be constituted alternatively by singlets and triplets. In general the even order bands are triplets whose lateral peaks correspond to the Bragg instabilities of each eigenmode, while the central peak is common to both eigenmodes and gives total reflection with a mode exchange. The odd order bands are singlets whose characteristics are very similar to the central peak of the triplets. The polarization properties of the eigenmodes are studied in the particular case of locally uniaxial media, where the Bloch waves show an abrupt polarization change for a particular value of the angle between the optical axis and the rotation axis.On considère un modèle optique décrivant une large classe de milieux optiquement anisotropes tels que les cristaux liquides smectiques chiraux et, à la limite, les cristaux liquides cholestériques et les milieux homogènes anisotropes. Ce modèle décrit une structure présentant une périodicité le long d'un axe donné, engendrée par une rotation uniforme du tenseur diélectrique. Les équations de Maxwell étudiées jusqu'à présent seulement pour des cas particuliers sont résolues ici dans le cas général où la direction de propagation des ondes et l'orientation de l'axe de rotation du tenseur diélectrique forment un angle arbitraire. Le processus de résolution met en jeu le calcul des modes propres de l'onde électromagnétique, c'est-a-dire les ondes de Bloch propres à la structure périodique, qui se réduit aux ondes ordinaires et extraordinaires dans le cas limite d'une structure homogène anisotrope. De la relation de dispersion des modes propres ainsi déduits on tire les propriétés optiques de cette structure sur une base générale. Les bandes de réflexion de Bragg sont formées d'une alternance de singulets et de triplets. En général, les bandes d'ordre pair sont des triplets dont les pics latéraux correspondent aux instabilités de Bragg des modes propres considérés tandis que le pic central est commun aux deux modes propres et conduit à la réflexion totale avec échange de mode. Les bandes d'ordre impair sont formées de singulets dont les caractéristiques sont très voisines de celles du pic central des triplets. Les propriétés de polarisation des modes propres sont étudiées dans le cas particulier d'un milieu localement uniaxe pour lequel les ondes de Bloch présentent un brusque changement de polarisation à une valeur particulière de l'angle entre l'axe optique et l'axe de rotation

Esercizi di Fisica

CD-RO

Light Propagation in Antsotropic Stratified Media in the Quast Adiabatic Limit

We propose a new perturbative treatment of the equations for electromagnetic wave propagation in the adjabatic limit in liquid crystals where the director is continuosly rotatin through the sample with an arbitrary law. In this approach a simple, 2×2 Jones matrix is obtained by proper transformation of the conventional 4×4 Berreman matrix. An approximate propagation equation is deduced for the jones Vector giving the polarization state of the wave propagating in the forward direction. The results obtained by using this equation are compared with the exact ones and the limits of validity of the present approach are discussed

Some new results concerning the optical-properties of anisotropic stratified media

A general approach to the optics of anisotropic media, based on a new formalism is presented. It allows to straightforwardly obtain and generalize almost all previously known results in this research area

Optical properties of cholesteric liquid crystals at oblique incidence

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 between the reflection bands both the wave functions and the wavevectors can be evaluated with very good approximation by simple analytic expressions, while for an accurate evaluation of the reflection properties of the structure more involved expressions are needed

Frank constant determination in a nematic liquid crystal by light attenuation measurement

A simple method for measuring the elastic Frank constants of a nematic liquid crystal is described. The method consists in measuring the attenuation of a laser beam transmitted through the specimen as a function of the angle of incidence and making a best fitting by using the results of a theory developed in a previous paper. Some experimental results concerning MBBA liquid crystals are reported and discussed