Fast iterative, coupled-integral-equation technique for inhomogeneous profiled and periodic slabs

Abstract

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.

One-way absorption of terahertz waves in rod-type and multilayer structures containing polar dielectrics

“…Perfect one-way absorption may appear in a wide range of variation of the incidence angle. The presented results are obtained by using the coupled integral equation technique, an efficient iterative solver with preconditioning that has controllable convergence and accuracy and is quite flexible regarding geometrical and material parameters of the studied structures [40]. Transmittance (T ) and reflectance (R) are directly obtained from this technique, and then absorption is obtained from A = 1 − T − R.…”

Multichannel optical diode with unidirectional diffraction relevant total transmission

“…The diffraction angles, n φ → and n φ ← , are measured in the counterclockwise direction with respect to the normal to the incidence side for the reflected waves, and in the clockwise direction with respect to the normal to the exit side for the transmitted waves. Diffraction results have been obtained by using Coupled Integral Equation Technique [25]. CST Microwave Studio [26] has been used for the calculations of the dispersion of FB waves.…”

Unidirectional transmission in non-symmetric gratings containing metallic layers

“…Several performances of epsilon-near-zero and matched-impedance zero-index metamaterials have been suggested in [11,19,20]. The presented transmission and reflection results are obtained by using an original computer code, which is based on the fast coupled-integral-equations technique [21].…”