Scattering by periodic surfaces

Abstract

Reflection behavior is examined for an interface having periodic height variation. Upon employing the Bloch theorem, in conjunction with the extended boundary condition, exact matrix equations are obtained for surface fields, as well as transmitted and reflected wave amplitudes. Tunneling considerations then lead to new energy constraints for problems of this type, in which propagating waves are coupled with evanescent modes. In the limit of surface corrugations shallow compared with impinging wavelength, analytic results are obtained confirming both the energy constraints and early computations by Rayleigh. Numerical results demonstrate the efficiency of the method. Subject Classification: 20.30.

Transfer Relations for Electromagnetic Wave Scattering from Periodic Dielectric One-Dimensional Interface: TE Polarization Lines

“…In detail, equations (37) and (38) are obtained by excluding the operator A m|m+1 from relations (30) and (31), as well as equations (39) and (40) are obtained by excluding the operatorà m|m+1 from relations (34) and (35).…”

“…The operator amplitudes of waves in splits between layers of the stack layers may be excluded from the transfer relations (29)(30)(31)(32)(33)(34)(35)(36)) that leads to the following separate system of recurrent equations with a layer attachment…”

“…First the transfer relations (29)(30)(31)(32)(33)(34)(35)(36) were obtained by Gazaryan [1] in the case of one-dimensional scattering medium using the field superposition principle. For the case of three-dimensional scattering medium the transfer relations (29)(30)(31)(32)(33)(34)(35)(36) were derived in [54] on base of the Watson composition rule (15)(16)(17)(18). All transfer relations are derived by the same way which becomes clear from derivation of equation (29) (see Appendix).…”

“…It is worth noting for us paper [28] where the Wood anomalies [29], discovered by light diffraction from a grating, are studied by light diffraction on a rough surface. The problem of wave scattering from periodic dielectric interface are considered using the Waterman [30] extended boundary condition approach in papers [31][32][33][34][35], for the case of one-dimensional interface, and in [36] for the case of two-dimensional interface.…”

Scattering and Thermal Emission from a Two Dimensional Periodic Surface

“…Scattering from a one dimensional periodic surface has been studied extensively with a large number of techniques, including both approximate [1][2][3], and numerically exact [4][5][6][7][8][9][10][11] methods. Models for one dimensional periodic surface scattering have found application in a wide range of areas, ranging from optical grating design [8] to the prediction of wave propagation over the ocean [10].…”