Gratings with Preselected Plane-Wave Propagation Directions
Abstract
A generalized Poisson summation formula produces exact expressions for the locations and strengths of line currents that radiate preselected plane waves. The line currents can be in free space or placed above a perfectly conducting ground plane. Closed-form expressions are obtained for the line current locations and amplitudes when the plane-wave parameters have periodic amplitudes and propagation vectors. A corresponding wire-impedance solution employs thin-wire approximations and takes into account all multiple interactions between wires. For general non-periodic plane-wave parameters, the line-source locations and amplitudes can be determined from an FFT approach involving a complex contour integral and the corresponding wire impedances can be computed numerically. These results generalize to 2D arrays of electric and magnetic dipoles characterized by polarizability dyads. Specifically, the plane-wave parameters for the 2D array are selected in accordance with two independent periodic constructs, and the dipole strengths and polarizability dyads are expressed as the product of two functions, each of which has the form of the line-source solutions. With this technique, the number of degrees of freedom for planar gratings has been increased significantly to allow for the creation of a wide range of plane-wave fields.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 15, 2022
- Accession Number
- AD1231231
Entities
People
- Thorkild B. Hansen