Electromagnetic propagation in periodic porous structures

A variational technique is employed to compute approximate propagation constants for electromagnetic waves in a dielectric structure which is periodic in the X - Y plane and translationally invariant in the Z-direction. The fundamental cell, in the periodic structure, is composed of a pore and the surrounding host media. The pore is a circle of radius R-0 filled with a dielectric epsilon(1) and the host dielectric characterized by epsilon(2). The size of the cell is characterized by the length A which is similar toR(0). Two limiting cases are considered. In the first, the pore size is assumed to be much smaller than the wavelength; this limit is motivated by microwave heating of porous material. The approximate propagation constants are explicitly computed for this case and are shown to depend upon the two dielectric constants, the relative areas of the two regions in the cell, and on a modal number. They are not given by a simple mixture formula. In the second limit, the pore size is taken to be of the same order as the wavelength; this limit is motivated by the propagation of light in a holey fiber. In this case our argument directly yields the dispersion relationship recently derived by Ferrando et al. [Opt. Lett. 24 (1999) 276], using intuitive and physical reasoning. Thus, our method puts theirs into a mathematical framework from which other approximations might be deduced. (C) 2002 Elsevier Science B.V. All rights reserved.