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Summary: Analysis of the Radiation Properties of a Planar
Antenna on a Photonic Crystal Substrate
Habib Ammari , Natacha Bereux , and Eric Bonnetier
Abstract
This paper is concerned with the rigorous investigation of the radiation properties
of a planar patch antenna on a photonic crystal substrate. Under the assumptions that
the driving frequency of the antenna lies within the band gap of the photonic crystal
substrate and that the crystal satis es a symmetry condition, we prove that the power
radiated into the substrate decays exponentially. To do this, we reduce the radiation
problem to the study of the well-posedness of a weakly singular integral equation on
the patch antenna, and to the study of the asymptotic behavior of the corresponding
Green's function. We also provide a mathematical justi cation of the use of a photonic
crystal substrate as a perfect mirror at any incidence angle.
Key words. photonic crystals, patch antennas, dielectric re
ectors, perfect mirrors, inte-
gral equations, Green's functions
AMS subject classi cations. 35Q60, 78A40
1 Introduction
A photonic crystal is a periodic dielectric structure that possesses the feature that electro-
magnetic waves of certain frequencies cannot propagate inside. The range of the prohibited
frequencies is called the complete band gap. The propagation of electromagnetic waves in
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