(1) Institut Henri Poincaré, 86 Bis Route de Croissy, 78110 Le Vésinet, France
Abstract:
Thinking of photonic crystals, we investigate the theory of
electromagnetic wave
propagation in a perfectly conducting semi-cylinder endowed with a periodic
permittivity along its axis while its circular base is illuminated by an
harmonic Bessel beam, symmetric around the cylinder axis. We prove that the
Floquet-Bessel expansions of electromagnetic fields whose Floquet parts are
solutions of a Mathieu equation. is a suitable tool to handle this kind of
problems.