It is shown that far- and near-field effects, which are similar to those arising in transmission through finite-thickness photonic crystals (PCs) with structural defects, can be obtained in the conventional defect-free dielectric square-lattice PCs. Multiple narrow peaks of total transmission can appear within a frequency range, where the noncircular isofrequency dispersion contours of one type are quickly transformed for a higher-order Floquet-Bloch wave to the noncircular contours of the other type, leading to a frequency-domain passband being very narrow within a certain range of variation of the angles of incidence. In this regime, the mirror reflectance of the equivalent Fabry-Pérot resonator takes rather large values, which correspond to large values of Q factor and group index of refraction, strong field localization, and good isolation of the transmission peaks from each other. In some examples presented, Q factor exceeds 104. © 2010 The American Physical Society

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.

a b s t r a c tThe potential of one-dimensional, periodic, graded-index, isotropic dielectric lattices with defects in multiband spatial and spatial-frequency filtering is studied. It is shown that both narrow-and wide-bandpass filters can be obtained at a proper choice of the number, location, and parameters of the defects placed inside the relatively thin slabs. The peculiarities of achieving multibandness for narrow-and wide-bandpass filters are discussed. Multiband narrow-bandpass filtering is closely related to the transmission features that are associated with Fabry-Pérot resonators with semitransparent planar mirrors. Correspondingly, the observed transmission can be interpreted in terms of the equivalent parameters of such resonators. In particular, it is shown that the resonators filled with an ultralow-index medium can be mimicked, so that defect-mode angle-domain spectrum can be rarefied at large angles of incidence. The obtained results are also expected to be applicable for prediction of the angle-domain behavior of transmission in case of piecewise-homogeneous multilayers.