Arbitrary Beam Shaping Using 1-D Impedance Surfaces Supporting Leaky Waves

Abstract

A technique for generating an arbitrary, prescribed radiation pattern from a 1-D leaky-wave antenna is presented. The technique is applied to leaky-wave impedance surfaces. A homogenized model for an impedance surface is used so that the work is not limited to particular geometries. The model consists of a grounded, uniaxial dielectric substrate topped by a reactance sheet. To synthesize prescribed aperture fields, the leakage constant α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> and phase constant β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> along the antenna are tailored. The aperture field is determined by adapting the Orchard-Elliott method used in array synthesis to continuous line sources. The aperture field is related to α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> and β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> using a well-known approach, then the transverse resonance technique is employed to analytically relate α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> and β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> to the electrical parameters of the impedance surface. Specifically, the extraordinary index and sheet reactance are used to control α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> and β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> . The designs presented demonstrate the synthesis of a variety of far-field patterns. Full-wave simulations show an improvement over previous beam synthesis techniques based on geometrical optics. Moreover, the numerical techniques demonstrate an efficient, gradient search method as an alternative to the iterative FFT methods explored previously, which have not generated radiation patterns with such high accuracy.