Control of extraordinary light transmission through perforated metal films using liquid crystals

We calculate the effective dielectric tensor of a metal film penetrated by cylindrical holes filled with a nematic liquid crystal (NLC). We assume that the director of the NLC is parallel to the film, and that its direction within the plane can be controlled by a static magnetic field, via the Freedericksz effect. To calculate the effective dielectric tensor, we consider both randomly distributed holes (using a Maxwell-Garnett approximation) and a square lattice of holes (using a Fourier technique). Both the holes and the lattice constant of the square lattice are assumed small compared to the wavelength. The films are found to exhibit extraordinary light transmission at special frequencies related to the surface plasmon resonances of the composite film. Furthermore, the frequencies of peak transmission are found to be substantially split when the dielectric in the holes is anisotropic. For typical NLC parameters, the splitting is of order 5-10% of the metal plasma frequency. Thus, the extraordinary transmission can be controlled by a static magnetic or electric field whose direction can be rotated to orient the director of the NLC. Finally, as a practical means of producing the NLC-filled holes, we consider the case where the entire perforated metal film is dipped into a pool of NLC, so that all the holes are filled with the NLC, and there are also homogeneous slabs of NLC on both sides of the film. The transmission in this geometry is shown to have similar characteristics to that in which the NLC-filled screen is placed in air.