Multifrequency spatial filtering: a general property of two-dimensional photonic crystals

Abstract

Spatial filtering, an analog of frequency-domain filtering that can be obtained in the incidence angle domain at a fixed frequency is studied in the transmission mode for slabs of two-dimensional rod-type photonic crystals. In the present paper, the emphasis is put on the demonstration of the possibility to obtain various regimes of spatial filtering, i.e., band-stop, band-pass, and low-pass filtering in different frequency ranges in one simple configuration. The operation is based on the use of several Floquet-Bloch modes with appropriate dispersion properties, so that such one or two co-existing mode(s) contribute to the forming of a proper filter characteristic within each specific frequency range. It is shown that high-efficiency transmission and steep switching between pass and stop bands can be obtained in the angle domain for wide ranges of variation of the problem parameters. In particular, by varying the rod-diameter-to-lattice-constant ratio, one attains lots of freedom in the engineering of spatial filters with desired transmission characteristics.