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Periodic Fréedericksz transition for nematic-liquid-crystal cells with weak anchoring
No full textLonberg and Meyer [Phys. Rev. Lett. 55, 718 (1985)] have recently discovered in polymer nematics the existence of a critical value rc=0.303 for the ratio r=K2/K1 between the twist and splay Frank elastic constants, below which a periodic splay-twist distortion is energetically favored with respect to the well-known aperiodic splay distortion which appears in a Fréedericksz transition. In this paper the effect of weak-anchoring conditions on the critical r value and on the other parameters of interest is theoretically investigated. Analytical expressions between these parameters are given. It is shown that the periodic transition is not allowed in the range 0.5<r<2. Outside this range either the periodic or aperiodic transition appears, according to the surface treatment, the sample thickness, and the direction of the magnetic field. Hence the critical value of r can be controlled in a wide range
Optical properties of cholesteric liquid crystals at oblique incidence
No full textThe 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
Jones Matrix Treatment of Electromagnetic-wave Propagation In Anisotropic Stratified Media
No full textLight Propagation in Antsotropic Stratified Media in the Quast Adiabatic Limit
No full textWe 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
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