Analytical theory of plane electromagnetic wave reflection from a layer or half-space of a particulate photonic crystal is introduced. The photonic (artificial) crystal is formed by small complex-shaped dielectric or metallic inclusions arranged in the nodes of a regular three-dimensional lattice with parallelepipedal elementary cell of general kind. The dipole model and the local-field approach are used for description of electromagnetic interaction between inclusions. Frequency-dependent polarizabilities are used for description of inclusions polarization. The interaction between adjacent layers is considered using the Floquet representation including evanescent modes. Using an analytical theory of dispersion for the crystals under consideration it becomes possible to make predictions for dipole moments distribution deep inside the layer. Additional corrections for distribution in the surface layers and amplitudes of predicted modes have been found numerically from a linear system of equation. This method needs much less computational time comparing with the same method without prediction of distribution and can be applied for calculation of reflection coefficient for much more thicker layers or for a half space. Also, a simple analytical single mode propagation theory for reflection from layer and half-space of particulate crystal is presented. It does not take into account the surface effects, but it is numerically shown for microwave crystal of loaded wires that this theory gives an excellent correspondence with exact one in the case of single mode propagation.

Date Published: 6 November 2001
PDF: 12 pages
Proc. SPIE 4453, Materials and Devices for Photonic Circuits II, (6 November 2001); doi: 10.1117/12.447653

Published in SPIE Proceedings Vol. 4453:
Materials and Devices for Photonic Circuits II
Mario Nicola Armenise, Editor(s)