Propagation of an electromagnetic wave in an absorbing anisotropic medium and infrared transmission spectroscopy of liquid crystals

Abstract

The theory of absorbance is developed for the entire electromagnetic spectrum of radiation in a semi-infinite anisotropic medium with a second rank dielectric tensor, the elements of which are complex and frequency dependent. The theory of the absorbance A (?,?) of an optically anisotropic liquid in an infrared (IR) test cell is then outlined and applied to IR transmission experiments. A formula for the dependence of A (?,?), on ? (? being the angle between the electric vector and the principal optical axis) is derived from first principles. The formula, for radiation of angular frequency ?, viz, A (?,?) =- log10 [10-A (?,0) cos2 ?+ 10-A (?,? 2) sin2 ?] is in agreement with that proposed by Jang, Park, Maclennan, Kim, and Clark [Ferroelectrics 180, 213 (1996)] and confirms some of the work of Kocot, Wrzalik, and Vij [Liq. Cryst. 21, 147 (1996)]. The comments on this formula by Jang, Park, Kim, Glaser, and Clark [Phys. Rev. E 62, 5027 (2000)], and by Kocot are discussed. The absorbance A (?,0) and A (?,? 2) have been expressed in terms of the optical properties of the material and the dimensions of the cell.