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. (A.E. Serebryannikov). θ. Spatial filters are also considered from the spatialfrequency filtering perspective [1]. For example, such filters were employed in the analysis of the spatial spectrum, enhancement of the antenna directivity, radar data processing, aerial imaging, and sorting the incoming radiation according to the source location. The known theoretical and experimental performances of the spatial filters include those based on anisotropic (anti-cutoff) media [2], multilayer stacks combined with a prism [3], resonant grating systems [4], metallic grids over a ground plane [5], interference patterns [1], and axisymmetric microstructures [6]. Various photonic crystal (PhC) http://dx.

Single–Band and Multiband Angular Filtering Using Two–Dimensional Photonic Crystals and One–Layer Gratings

“…23.3a and b that illustrate behavior of transmittance related to the second, third, and fourth lowest FloquetBloch modes (regions of T > 0 indicated by the numbers 2, 3, and 4, respectively). The features observed here are very general and can be obtained for various sets of PhC parameters [8,11].…”

“…The distribution of the Floquet-Bloch modes in the entire wavevector space (k-space) determines the type(s) of angular filtering, which can be realized for a chosen set of structural parameters and frequency [11]. It is known that electromagnetic waves follow in PhC Bloch's theorem as electrons in a crystal, so the distribution of the modes in k-space or its two-dimensional analog, i.e., the (k x ,k y )-plane, can be reconstructed from the distribution of the modes in the first Brillouin Zone (BZ).…”

“…To time, both transmission-mode and reflection-mode angular filters have been proposed. The coexistence of spatial (angular) and frequency-domain filtering is an important theoretical and practical extension [4,11]. Another aspect is related to angle-tolerant frequency-domain filtering [15,16].…”

“…While the principal possibility of rather strong sensitivity of transmission and reflection to incidence angle variations is quite evident, the main problem is how to fulfill the general requirements regarding sharpness of the band boundaries and constant efficiency within a band, e.g., see Refs. [8,11,15,16]. Indeed, any structure or medium with dispersion properties different from the host medium (usually air) is sensitive to variations in incident angle, so transmission and/or reflection is modulated.…”

“…From this perspective, PhCs represent simple and very suitable platform for angular filtering, because of suggesting a rich variety of dispersion types usable for angular filtering. Similarly to our earlier studies [8,11,17], the structures considered here are assumed to be made of conventional isotropic, passive dielectric materials and, thus, are easily realizable. For the sake of completeness, we also consider reflection-mode angular filtering in reflector-backed single-layer gratings, which is inspired by reflection mode of PhC gratings.…”