Scattering of an obliquely incident plane wave by a general-shaped groove engraved on a perfectly conducting plane is rigorously solved. The scattered field is represented by a Fourier-integral representation. To analytically represent the fields in a general-shaped groove, the groove is divided into L number of layers. Fields are then expressed in each layer as summations of 2D spatial harmonic fields with unknown coefficients. Matching the boundary conditions between layers provides a linear set of equations connecting all the unknown harmonic coefficients. Judicious use of Fourier transform on the equations resulting from matching boundary conditions at the groove aperture provides a series representation of the scattered field in the spectral domain with unknown harmonic coefficients of the first layer in the groove. A stable solution is obtained by solving the complete system of equations with an adaptive choice for the number of modes in each layer.
© 2007 Optical Society of America
Diffraction and Gratings
Original Manuscript: July 24, 2006
Revised Manuscript: December 13, 2006
Manuscript Accepted: December 14, 2006
Published: May 9, 2007
Mohamed A. Basha, Sujeet K. Chaudhuri, Safieddin Safavi-Naeini, and H. J. Eom, "Rigorous formulation for electromagnetic plane-wave scattering from a general-shaped groove in a perfectly conducting plane," J. Opt. Soc. Am. A 24, 1647-1655 (2007)