Properties of conically propagating electromagnetic and elastodynamic waves in periodic media

Sebastien Guenneau, Chris Poulton and Alexander Movchan

University of Liverpool
Department of Mathematical Sciences
M & O Building, Peach Street
Liverpool, L69 3BX

This talk presents analysis of electromagnetic and elastodynamic waves conically propagating through a doubly periodic array of cylindrical fibres. A new method, based on a multiple scattering approach, has been proposed to reduce these spectral problems for partial differential equations to certain algebraic problems of the Rayleigh type: its matrix elements decay exponentially away from the main diagonal, giving rise to higher-order multipole coefficients that decay similarly quickly. We obtain a formulation in terms of an eigenvalue problem that enables us to construct the high-order dispersion curves and to study both photonic and phononic bang gap structures in oblique Incidence [1]. We also address the question of a singular perturbation induced by the conical incidence parameter for both electromagnetic and elastic modes. We finally discuss some effective properties for ferro-magnetic photonic crystal fibres in the long wavelength limit [2].


[1] Guenneau, S., Poulton C. G. and Movchan, A. B. Oblique propagation of electromagnetic and elastic waves for an array of cylindrical fibres, Proc. Roy. Soc. (submitted)
[2] Poulton, C. G., Botten, L. C., McPhedran, R. C., Nicorovici, N. A., Movchan, A. B. Non-commuting limits in electromagnetic scattering: asymptotic analysis for an array of highly conducting inclusions, SIAM J. Appl. Math., 61 (2001) 1706-1730