Journal of the European Optical Society - Rapid publications, Vol 6 (2011)

The exact theory for scattering of waves by thick holes in a slab and other objects with non-separable geometries

B. J. Hoenders


The theory for scattering of electromagnetic waves is developed for scattering
objects for which the natural modes of the field inside the object
do not couple one-to-one with those outside the scatterer. Key
feature of the calculation of the scattered fields is the
introduction of a new set of modes. As an example, we calculate the
reflected and transmitted fields generated by an electromagnetic
plane wave that impinges upon a multilayer slab of which the layers
are stacked perpendicular to the boundary planes.
As this is the geometry of a thick plate with slits our theory encompasses the exact scattering theory of electromagnetic waves by a thick plate with slits.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2011.11011s]

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P. M. Morse, and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

V. D. Kupradze, Randwertaufgaben der Schwingungstheorie und Integralgleichungen (Deutscher Verlag der Wissenschaften, Berlin, 1956).

P. H. Moon, and D. E. Spencer, Field theory handbook: including coordinate systems, differential equations and their solutions (Springer-Verlag, Berlin, 1988).

S. S. S. Vinogradov, P. Smith, and E. D. Vinogradova, Canonical Problems in Scattering and Potential Theory, Part 2; Acoustic and Electromagnetic Diffraction by Canonical Structures (vol. 127 of Monographs and Surveys in Pure and Applied Mathematics, Chapman Hall, London, 1981).

M. Born, and E. Wolf, Principles of Optics (Seventh Edition, Springer-Verlag, Berlin, 1999).

B. J. Hoenders, M. Bertolotti, and R. Uitham, "Set of modes for the description of wave propagation through slabs with a transverse variation of the refractive index" J. Opt. Soc. Am. A 24, 1189-1200 (2007).

E. Hilb, "ber Reihenentwicklungen, welche aus speziellen Randwertproblemen bei gewnlichen linearen inhomogenen Differentialgleichungen entspringen" Journ. reine. angew. Math. 140, 205-229 (1911).

B. J. Hoenders, and M. Bertolotti, "Coherence theory of electromagnetic wave propagation through stratified N-layer media" J. Opt. Soc. Am. A 22, 1143-1150 (2005).

P. Yeh, Optical Waves in Layered Media (Wiley series in pure and applied optics, John Wiley and Sons, Chicester, 1988).

P. Yeh, A. Yariv, and C.-S. Hong, "Electromagnetic propagation in periodic stratified media. I. General theory" J. Opt. Soc. Am. 67, 423-438 (1977).

D. G. Stavenga, S. Foletti, G. Palasantzas, and K. Arikawa, "Light on the moth-eye corneal nipple array of butterflies" Proc. R. Soc. B 273, 661-667 (2006).