Electromagnetic Wave Propagation in Periodic Porous Structures

We employ a homogenization procedure to describe the propagation of electromagnetic waves in a dielectric structure which is doubly-periodic in the X-Y plane and of arbitrary variation in the direction of propagation, Z. The fundamental cell is composed of an arbitrarily shaped pore filled with a dielectric and the host by another. Our analysis yields the structure of the electromagnetic fields at the micro level and gives an effective medium equation at the macro level. The latter contains a simple arithmetic average of the dielectric constants and a correction term which involves a line integral around the pore. The integrand of this integral depends upon the polarization of the wave and the solution to a canonical potential problem. We approximately solve this problem for small pore volumes and for large contrasts, the pore dielectric constant being much larger than the host. We also provide an equivalent variational formulation for the potential problem and use a simple Raleigh-Ritz procedure to determine an approximate solution. For all these approximations, we provide a simple macroscopic description of electromagnetic wave propagation in our structure.