Scattering by many small particles and creating materials with a desired refraction coefficient

Andriychuk

2012

Optics Communications

Self Cite

Electromagnetic (EM) wave scattering by many parallel infinite cylinders is studied asymptotically as a → 0, where a is the radius of the cylinders. It is assumed that the centers of the cylindersx m are distributed so that, where N (∆) is the number of pointŝin an arbitrary open subset of the plane xOy, the axes of cylinders are parallel to z-axis. The function N(x) ≥ 0 is a given continuous function. An equation for the self-consistent (limiting) field is derived as a → 0. The cylinders are assumed perfectly conducting. Formula for the effective refraction coefficient of the new medium, obtained by embedding many thin cylinders into a given region, is derived. The numerical results presented demonstrate the validity of the proposed approach and its efficiency for solving the many-body scattering problems, as well as the possibility to create media with negative refraction coefficients.

“…This work continues the earlier investigations in [10]- [21], and the numerical modeling presented in [1]- [3].…”

supporting

confidence: 84%

“…On the basis of this theory a recipe for creating a material with a desired refraction coefficient was formulated. This recipe was verified numerically in [2].…”

Section: Numerical Resultsmentioning

confidence: 82%

Section: Numerical Resultsmentioning

confidence: 99%

“…The distribution of the pointsx m in a bounded domain Ω on the plane P = xOy is given by formula (2). The incident field is u 0 (x) := e ikx 2 , and…”

Section: Asymptotic Formulas For the Effective Fieldmentioning

confidence: 99%

Section: The Relative Error For the Solution To Las (31)mentioning

confidence: 99%

See 3 more Smart Citations

Scattering of electromagnetic waves by many thin cylinders: Theory and computational modeling

Andriychuk

2012

Optics Communications

Self Cite

Many-body wave scattering problems in the case of small scatterers

2012

J. Appl. Math. Comput.

Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The case of transmission (interface) boundary conditions is also studied in detail. The limiting case is considered, when the size a of small particles tends to zero while their number tends to infinity at a suitable rate. Equations for the limiting effective (self-consistent) field in the medium are derived. The theory is based on a study of integral equations and asymptotics of their solutions as a → 0. The case of wave scattering by many small particles embedded in an inhomogeneous medium is also studied.

Application of the asymptotic solution to EM field scattering problem for creation of media with prescribed permeability

Andriychuk

2013

J. Appl. Math. Comput.

Scattering of electromagnetic (EM) waves by many small impedance particles (bodies), embedded in a homogeneous medium, is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for the effective EM field in the limiting medium, in the limit a → 0, where a is the characteristic size of a particle and the number M (a) of the particles tends to infinity at a suitable rate. The proposed theory allows one to create a medium with a desirable spatially inhomogeneous permeability. The main new physical result is the explicit analytical formula for the permeability µ(x) of the limiting medium. The computational results confirm a possibility to create the media with various distributions of µ(x).