0030-400X/00/8904- $20.00 © 2000 MAIK “Nauka/Interperiodica” 0631 Optics and Spectroscopy, Vol. 89, No. 4, 2000, pp. 631–638. Translated from Optika i Spektroskopiya, Vol. 89, No. 4, 2000, pp. 685–692. Original Russian Text Copyright © 2000 by Gevorgyan. INTRODUCTION An exact solution of the problem of propagation of an electromagnetic wave in media with a helical struc- ture is considered in papers [1–6] and the papers cited therein. However, these papers analyze only the case where either the permittivity tensor or the permeability tensor is a multiple of the unit tensor and an electro- magnetic wave travels along the helix axis. In some papers, the problem is analyzed taking into account the anisotropy of both the permittivity and the permeability [7–10]. In [10], the authors consider the general case where the principal axes of local permittivity and per- meability tensors and and the helix axes are arbi- trarily oriented to one another. However, in these papers, the propagation of an electromagnetic wave in a medium in the absence of boundaries or the reflection from a half-space were analyzed. The next step will be to analyze the propagation of light (or an electromag- netic wave) through a layer of a medium under consid- eration. This problem is closer to the experimental sit- uation because layers of finite thickness are commonly used in experiments and practical applications. More- over, as shown in [11], in particular, for a cholesteric liquid crystal, under certain conditions, an exact solu- tion of this boundary problem for a layer has a simpler and clearer form than the solution of the boundary problem for reflection of light from a half-space. It is likely that this is caused by a higher symmetry of the first problem. In this paper, the case where the local axes of and coincide with one another and one of them repre- sents the helix axis is considered. This case is of addi- tional importance because basic specific features of helical media caused by the presence of both dielectric and magnetic anisotropies manifest themselves here. ε ˆ μ ˆ ε ˆ μ ˆ One can produce helical structures with anisotropy of permeability by adding chiral molecules to a fer- ronematic [12]. Moreover, helical media can be pro- duced artificially [13, 14]. In [14], the possibility of producing an artificial medium possessing both dielec- tric and magnetic helicities is discussed. The problem studied here is of a certain theoretical importance, in particular, for generalizing the results obtained. Note that interest in the interaction of light with helical structures, including structures with vari- ous specific features, has increased in the recent years [15–23]. PROPERTIES OF CHARACTERISTIC SOLUTIONS. THE BOUNDARY PROBLEM FOR A HALF-SPACE Consider the propagation of light in media possess- ing dielectric and magnetic helicities, with the principal axes of and coinciding with one another and one of them (the z-axis) being coincident with the helix axis: (1) where ε m = (ε 1 + ε 2 )/2, μ m = (μ 1 + μ 2 )/2, δ ε = (ε 1 – ε 2 )/(ε 1 + ε 2 ), δ μ = (μ 1 – μ 2 )/(μ 1 + μ 2 ), ε 1 , ε 2 are the prin- ε ˆ μ ˆ ε ˆ z () ε m 1 δ ε 2 az cos + δ ε 2 az sin 0 δ ε 2 az sin 1 δ ε 2 az cos – 0 0 0 1 δ ε – ⎝ ⎠ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎛ ⎞ , = μ ˆ z () μ m 1 δ μ 2 az cos + δ μ 2 az sin 0 δ μ 2 az sin 1 δ μ 2 az cos – 0 0 0 1 δ μ – ⎝ ⎠ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎛ ⎞ , = Reflection and Transmission of Light for a Layer with Dielectric and Magnetic Helicities. I. Jones Matrices. Natural Polarizations A. A. Gevorgyan Yerevan State University, Yerevan, 375049 Armenia e-mail: yndanfiz@sun.ysu.am Received February 25, 1999 Abstract—Transmission and reflection of light normally incident on a layer of a medium with dielectric and magnetic helicities is studied. The axes of local tensors and and the helix axis are parallel to one another and perpendicular to the boundary surfaces. Jones matrices are constructed. Reflection and transmission coef- ficients, the rotation of the plane of polarization, and the ellipticity of polarization are calculated. Specific fea- tures of natural polarizations and the character of reflection and passage of waves with natural polarizations are studied. © 2000 MAIK “Nauka/Interperiodica”. ε ˆ μ ˆ PHYSICAL AND QUANTUM OPTICS