Optical theorem for electromagnetic field scattering by dielectric structures and energy emission from the evanescent wave

Abstract

We present an optical theorem for evanescent (near field) electromagnetic wave scattering by a dielectric structure. The derivation is based on the formalism of angular spectrum wave amplitudes and block scattering matrix. The optical theorem shows that an energy flux is emitted in the direction of the evanescent wave decay upon scattering. The energy emission effect from an evanescent wave is illustrated in two examples of evanescent wave scattering, first, by the electrical dipole and, second, one-dimensional grating with line-like rulings. Within the latter example, we show that an emitted energy flux upon evanescent wave scattering can travel through a dielectric structure even if the structure has a forbidden gap in the transmission spectrum of incident propagating waves.

Energy Emission from Evanescent Wave and Interference of Opposite Wave Streams: Near Field Coherent Scattering by Random Medium

“…This identity is written in terms of a scalar product for vector functions of k ⊥ and coincides with the projection of extended optical theorem [2] onto evanescent waves. The "dagger" superscript in (6) denotes a complex conjugate transpose of a tensor operator and the symbol means an imaginary part of the quantity.…”

“…Following [2], we consider a dielectric medium with scalar dielectric permittivity ( r) occupying a region between the planes z = 0 and z = L of the Cartesian coordinate system x, y, z. The electric field E 0 α ( r) of a monochromatic electromagnetic wave with frequency ω incident onto the left boundary plane z = 0 is written as (2π…”

“…are renormalized angular spectrum amplitudes of incident waves going forward and backward, respectively. In Equation 2 Note that a solution to the boundary problem (2) and (3) can give not only the angular spectrum amplitudes of local fields waves inside the medium but also the S-matrix of the whole medium slab [2] as well, according to the limit relations…”

“…The limit relations (4) give the following expressions for the energy fluxes (5) on the left (8πω/c 2 )P z (0) = −(Ã † H prÃf ,f ) and the right (8πω/c 2 )P z (L) = −2 H evBf ,f + (B † H prBf ,f ) boundary planes. The first of these expressions actually represents the energy emission effect [2] from an evanescent wave. In a lossless dielectric medium, both expressions are equal to each other and so…”

“…Evanescent waves occur in different physical phenomena and suitable for several applications [1]. Recently an optical theorem for evanescent (near field) electromagnetic wave scattering by a dielectric structure was peseneted [2]. This optical theorem shows that an energy flux is emitted in the direction of the evanescent wave decay at mentioned scaattering.…”