EM Wave Scattering by Many Small Impedance Particles and Applica- tions to Materials Science

An explicit formula is derived for the electromagnetic (EM) field scattered by one small impedance particle of an arbitrary shape. If is the characteristic size of the particle, is the wavelength, and is the boundary impedance of , on , where is the surface of the particle, is the unit outer normal to , and , is the EM field, then the scattered field is . Here , is the wave number, is an arbitrary point, and , where is the incident field, is the area of , is the frequency, is the magnetic permeability of the space exterior to , and is a tensor which is calculated explicitly. The scattered field is as when is fixed and does not depend on . Thus, is much larger than the classical value for the field scattered by a small particle. It is proved that the effective field in the medium, in which many small particles are embedded, has a limit as and the number of the particles tends to at a suitable rate. This limit solves a linear integral equation. The refraction coefficient of the limiting medium is calculated analytically. This yields a recipe for creating materials with a desired refraction coefficient.