Theory of light transmission through subwavelength periodic hole arrays

The existing theories which aim to explain the extraordinary optical transmission of a metallic film pierced by a two-dimensional subwavelength hole array [T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, Natural (London) 391, 667 (1998)] all have in common the following feature: instead of studying the two-dimensional crossed grating resulting from the hole array, they consider a one-dimensional grating with infinite slits. We show that such a simplification introduces an efficient channel for light transmission in lamellar gratings, which does not exist for hole arrays. Therefore in order to explain the relatively high transmission observed by Ebbesen et al., it is necessary to take into account the existence of the holes in the array. In this paper we develop a two-dimensional analysis of the experiment performed by Ebbesen et al. No simplification is introduced. This allows us to obtain theoretically the long-wavelength peak reported by Ebbesen et al. with the same grating thickness as the one used by these authors. We also review and study in detail the various contributions devoted to this very surprising effect.