In 1998 Ebbesen et. al. (Nature 391, 667) reported on extraordinary optical transmission through sub-wavelength hole arrays in metallic films. Sharp peaks were observed in the transmission spectrum at wavelengths as large as ten times the diameter of the cylindrical holes. The transmission enhancement was attributed to resonant interaction of the incident light with surface plasmons via the grating coupling.

Continuing this idea, we studied such systems in the presence of an in-plane static magnetic field. In order to go beyond the quasistatic approximation, we use the generalized Ohm's law (GOL) scheme. The idea behind the GOL is to reduce the entire physics of a 3D inhomogeneous film, which is described by the full set of Maxwell equations, to a set of coupled quasi-static-like equations on a 2D reference plane. These quasi-static equations can be decoupled in many cases to two conductivity-like problems with the same microgeometry, for which extensive theory already exists.

Using the GOL method we find that magnetic-field-dependent transmission spectrum can be calculated in doped semiconductor films with modulated surfaces. The most significant effect of the static in-plane magnetic field occurs in the frequency domain of the surface plasmon resonances, where the frequency of the transmission peak and its intensity depend on both the magnitude of the applied in-plane magnetic field and on its direction. The possibility of observing these effects in doped In-As films is considered in detail.