Selective reflection by helicoidal liquid crystals. results of an exact calculation using the 4 x 4 characteristic matrix method

Abstract

2014 On présente un calcul exact de la réflexion de la lumière par un échantillon orienté de cristal liquide hélicoïdal (SmC* ou cholestérique) en utilisant la formulation matricielle 4 x 4 des équations de Maxwell pour les milieux anisotropes. On montre que la méthode approximative de Berreman et Scheffer est inadéquate, spécialement en ce qui concerne la région des faibles longueurs d'onde (nombre de pics, nombre de branches dans la bande de réflexion ainsi que leur dépendance avec les différents paramètres).Abstract 2014 The exact calculation of the reflection from single domain aligned samples of helicoidal liquid crystals (SmC* or cholesterics) is performed using the 4 x 4 matrix formulation of Maxwell equations in anisotropic media. We show that the expansion, approximation up to the 1st order of Berreman and Scheffer, is not adequate to describe the real situation, especially concerning the short wavelength region (heights of peaks, number of branches in the reflection band and their dependence on the different parameters). J. Physique 46 (1985) 815-825 MAI 1985, : Classification

Ellipsometry on Anisotropic Materials: Bragg Conditions and Phonons in Dielectric Helical Thin Films

“…In order to differentiate between bulk and interface related information, appropriate data acquisition and analysis procedures are necessary. A general calculus for data analysis was outlined previously, which allows for treatment of light propagation through anisotropic layers [1][2][3][4][5][6]. Optical effects due to interfaces, modeled as ultrathin layers of finite thickness, could be treated by this approach also.…”

“…In order to extract intrinsic physical quantities, such as the major indices of refraction and extinction coefficients, or orientation, length, and handedness of the helical structure, or the thickness of the DHTF from ellipsometry data model calculations, compromise numerical methods must stratify the cell into numerous virtually homogeneous anisotropic layers. This piecewise homogeneous approximation approach requires immense computational effort, but still delivers approximate results only [2,[32][33][34][35][36][37][38][39][40][41]. Convenient mathematical approaches for treatment of light incident not parallel to the helical axis have become available only very recently [42][43][44][45].…”

Combined optical and acoustical method for determination of thickness and porosity of transparent organic layers below the ultra-thin film limit

“…12 The major points are summarized here. Through a 4×4 matrix modeling approach, also known as the Berreman-formalism, 13,18,[23][24][25][26] a transfer matrix T can completely describe a linear optical system. T consists of an ordered product of partial transfer matrices (T p ), which describe homogenous constituent sublayers, and matrices that describe incident (ambient, L a ) and exit (substrate, L f ) mediums, such that…”

Lasing cholesteric capsules

“…7. Such a fine structure can be easily detected in well aligned thin cells [7]. One can expect that the fine structure in distorted, defective samples is also imperfect, such that the oscillation maximums do not necessarily decrease in their amplitude on departing from the PhBG edge, acquiring instead a random character.…”