A fast coupled-integral-equation (CIE) technique is developed to compute the plane-TE-wave scattering by a wide class of periodic 2D inhomogeneous structures with curvilinear boundaries, which includes finite-thickness relief and rod gratings made of homogeneous material as special cases. The CIEs in the spectral domain are derived from the standard volume electric field integral equation. The kernel of the CIEs is of Picard type and offers therefore the possibility of deriving recursions, which allow the computation of the convolution integrals occurring in the CIEs with linear amounts of arithmetic complexity and memory. To utilize this advantage, the CIEs are solved iteratively. We apply the biconjugate gradient stabilized method. To make the iterative solution process faster, an efficient preconditioning operator (PO) is proposed that is based on a formal analytical inversion of the CIEs. The application of the PO also takes only linear complexity and memory. Numerical studies are carried out to demonstrate the potential and flexibility of the CIE technique proposed. Though the best efficiency and accuracy are observed at either low permittivity contrast or high conductivity, the technique can be used in a wide range of variation of material parameters of the structures including when they contain components made of both dielectrics with high permittivity and typical metals.

Cataloged from PDF version of article.Strongly asymmetric Fabry-Perot-type transmission arising at the two-way coupling has been studied in the case of normal incidence for slabs of two-dimensional photonic crystals (PCs) with one-sided corrugations that are made of linear isotropic materials. Comparing to the scenario of unidirectional transmission known for the structures with broken spatial inversion symmetry that requires zero order being uncoupled, in the studied mechanism zero order is either the sole order or one of the orders that may be coupled to a Floquet-Bloch mode. Contrary to the earlier studies of asymmetric transmission at the coupled zero order, structures with nondeep corrugations are considered, which allow one to combine Fabry-Perot-type total-transmission maxima with diffractions in a desired way. At a proper choice of PC lattice and corrugation parameters, higher orders can dominate in Fabry-Perot-type transmission at the noncorrugated-side illumination and also at the total-transmission maxima, whereas only zero order contributes to the transmission at the corrugated-side illumination. As a result, strong asymmetry can be obtained without uncoupling of zero order but it invokes the unidirectional contribution of higher orders. The presented results show that the entire structure can be approximately decomposed into the two independent, regular and grating (nonregular), parts whose contributions to the transmission are additive. Multiple asymmetric transmission maxima can coexist with a rather high equivalent group index of refraction. Possible applications of the studied transmission mechanism are discussed

Finite-thickness photonic crystals (PC's) with periodically corrugated interfaces are suggested to realize some unusual features in the behavior of transmitted Bragg beams (diffraction orders). The scattering of s -polarized plane waves by such structures is studied. It follows from the numerical results that rather thin corrugated PC's borrow their basic properties from both conventional PC's and gratings, leading to some new effects. In particular, a shift of the actual cutoff frequencies towards larger values than those of the Rayleigh cutoff frequencies can be obtained due to the ordinary opaque range in transmission, within which all propagative orders vanish. This effect can even be enhanced due to the nonordinary behavior arising at the edges of the ordinary opaque range, which manifests itself in that some but not all propagative orders in transmission are suppressed. Hence the opaque ranges for individual orders are wider than the corresponding ordinary range. Besides, frequency ranges exist which are not connected with the edge of the ordinary opaque range, where a similar nonordinary effect does appear. As a result, each propagative order in transmission generally has its own set of opaque ranges. Only a single order can be contributive while several others are formally propagative, too. The corrugations have to be located at the upper interface in order to realize these nonordinary effects. Moving the corrugation from the upper to the lower interface leads to a disappearance of the observed effects, so that their nature cannot be explained exclusively in terms of matching the wave vectors of the diffraction orders and the Floquet-Bloch waves. The conventional sequence of cutoffs for different diffraction orders with respect to each other can be changed for certain structures if the rods of a PC are made of Drude metal. Hence, transmission regimes can be realized which are beyond the classical theory of gratings. Several effects arising when varying the angle of incidence are demonstrated and briefly discussed. The detected effects can be used for controlling the number of actually contributive beams and for obtaining alternating ranges of single-beam and multibeam operation, which should lead to extending the potentials of optical and microwave technologies based on the use of single-beam and multibeam regimes.

Considered is the beam wave guidance and scattering by 2D quasi-optical reflectors modeling the components of beam waveguides. The incident field is taken as the complex-source-point field to simulate a finite-width beam generated by a small-aperture source. A numerical solution is obtained from the coupled singular integral equations (SIEs) for the surface currents on reflectors, discretized by using the recently introduced Nystrom-type quadrature formulas. This analysis is applied to study what effect the edge illumination has on the performance of a chain of confocal elliptic reflectors. We also develop a semianalytical approach for shaped reflector synthesis after a prescribed near-field pattern. Here a new point is the use of auxiliary SIEs of the same type as in the scattering analysis problem, however, for the gradient of the objective function. Sample results are presented for the synthesis of a reflector-type beam splitter.

Scattering of s-polarized plane waves by finite-thickness periodic structures is studied, which contain components made of ultralow-permittivity metamaterial ͑ULPM͒, and therefore exhibit intermediate properties between those made of pure metals and of pure dielectrics. The numerical results presented demonstrate basic frequency-and angular-selectivity-concerned effects arising in the structures with sinusoidal corrugations, which are made of ULPM, and for a stack of two such periodic structures, in which one of them is made of ULPM and the other one of a dielectric. The results presented are mostly related to the zero-permittivity case, when there is no wave propagating in the transverse direction within the metamaterial. The field inside ULPM is either close to or exactly the static one. For the structures of the first type, this can lead to a straightening of the field lines at the lower ͑noncorrugated͒ interface and, in turn, to a suppressing of higher modes ͑Bragg beams͒ in the transmitted field, which are allowed to propagate. The known property of a zero-permittivity noncorrugated slab, i.e., the cutoff-type frequency dependence of the transmittance, appears also for corrugated periodic structures studied in both single-and multimode regimes. In our study, a similar behavior vs the angle of incidence is demonstrated and a condition for its appearance is given. For the structures of the second type, it is shown that these effects can be combined with those, which are typical for dielectric gratings and usually associated with bulk and surface modes. Stacking ULPM and dielectric layers can also lead to an enhancement of some effects, which are inherent to each of the layers, as well as to several abnormal effects. The effects found promise to be useful for controlling and, in particular, for splitting/combining of light and microwave radiation.