Twist reflector design using E-type and H-type modes

Abstract

A complete solution of plane wave scattering from a twist reflector of infinite extent for arbitrary incidence is presented. The solution is accomplished through the use of an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> -and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> -type modal representation of the fields in the twister and free space regions. The equivalent circuits for strip and parallel plate twister gratings are derived by transforming <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> mode results [5] to appropriate type mode parameters. The modal reflection coefficients <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Gamma'</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Gamma''</tex> are determined from these equivalent circuit parameters and together with the use of a type mode description of the incident and reflected fields lead to two simple conditions for an optimum design; one geometric, namely <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\tan \phi = \sec \theta</tex> and one electrical, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Gamma"/\Gamma' = - 1</tex> . The computed performance of this optimum twist reflector in terms of a cross-polarized suppression ratio versus incidence angle for various planes of incidence represents the best that can be done with any physical structure. A design procedure including design formulas and curves is given from which twist reflector dimensions can be determined. Experimental verification for two specific implementations, parallel plates and parallel strips twist reflectors, is described.