Theory of light transmission through subwavelength periodic hole arrays

The existing theories which aim to explain the extraordinary optical transm ission of a metallic film pierced by a two-dimensional subwavelength hole a rray [T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, Natur al (London) 391, 667 (1998)] all have in common the following feature: inst ead of studying the two-dimensional crossed grating resulting from the hole array, they consider a one-dimensional grating with infinite slits. We sho w that such a simplification introduces an efficient channel for light tran smission in lamellar gratings, which does not exist for hole armys. Therefo re 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 expe riment performed by Ebbesen et al. No simplification is introduced. This al lows us to obtain theoretically the long-wavelength peak reported by Ebbese n et nl. with the same grating thickness ns the one used by these authors. We also review and study in detail the various contributions devoted to thi s very surprising effect.