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 .
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 .
 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)
 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