Scattering and Absorption of Waves by Flat Material Strips Analyzed Using Generalized Boundary Conditions and Nystrom-Type Algorithm

Abstract

The scattering of the H-and E-polarized plane waves by a thin flat homogeneous magneto-dielectric strip is considered. Assuming the strip to be thinner than the wavelength, we shrink its cross-section to the median line where the generalized boundary conditions are imposed. The numerical solution is built on two singular integral equations discretized using Nystrom-type numerical algorithm. The obtained results demonstrate fast convergence and good agreement with data known for the limiting values of the strip parameters. This opens a way to the accurate numerical analysis of various striplike configurations simulating natural objects and electromagnetic circuit components, both in traditional microwave applications and nanophotonics.Index Terms-Discrete mathematical model, generalized two-side boundary conditions, scattering cross-sections, singular and hyper-singular integral equations, strip scatterer.

Test of accuracy of the generalized boundary conditions in the scattering by thin dielectric strips

“…Note that these quantities are computed from the far-field data [13]. They are not sensitive to the field behavior at the strip edges because the condition of local power finiteness tells that "the edges do not radiate."…”

“…Further we discretize SIEs (6) and (7) using a Nystrom-type method, i.e. approximating the unknowns by polynomials and using two quadrature rules of interpolation type of the order N [13]. The theorems on quadratures ensure convergence of such numerical scheme with the rate of at least 1/N if .…”

“…It has been applied to study the scattering by thin half-planes and strips in [9][10][11][12][13][14][15][16][17]. In the early works, it had been established that the effective electric and magnetic currents were decoupled and satisfied independent IEs.…”

Grating and plasmon resonances in the scattering of light by finite silver nanostrip gratings

“…In view of the limited space, we omit the details and refer to [ 8 -6 ]. Thereby, applying the above mentioned quadrature formulas, we arrive at two independent sets of matrix equations of the orders , although the actual rate is always higher [6,7]. The empiric rule to achieve 4-digit accuracy in the analysis of surface currents is to take 5…”

“…As a reliable instrument, we use the developed earlier by us median-line integral equation method based on the two-side generalized boundary conditions (GBCs) [5] and Nystrom-type discretization of the interpolation type [6,7].…”