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Analysis of the radiation properties of a planar antenna on a photonic crystal substrate
Author(s) -
Ammari Habib,
Béreux Natacha,
Bonnetier Eric
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.254
Subject(s) - photonic crystal , planar , substrate (aquarium) , antenna (radio) , radiation , patch antenna , mathematics , photonics , optics , symmetry (geometry) , radiation pattern , crystal (programming language) , physics , optoelectronics , mathematical analysis , geometry , telecommunications , computer science , oceanography , computer graphics (images) , programming language , geology
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 satisfies 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 behaviour of the corresponding Green's function. We also provide a mathematical justification of the use of a photonic crystal substrate as a perfect mirror at any incidence angle. Copyright © 2001 John Wiley & Sons, Ltd.
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