Self and Mutual Admittance of Slot Antennas on a Dielectric Half-space

In this paper, an efficient implementation of the spectral domain moment technique is presented for computing the self and mutual coupling between slot antennas on a dielectric half-space. It is demonstrated that by the proper selection of the weighting functions in the method of moments, the analytic evaluation or simplification of the transverse moment integrals is enabled. This results into a significant reduction of the required computational labor. The method is then utilized in order to provide design data for the self and mutual admittances between two slot antennas on a dielectric substrate lens in the case of fused quartz (e, = 3.80), crystal quartz (e, = 4.53), silicon (e, = 11.9) and GaAs (e, = 12.8). The presented technique and associated results are useful when designing twin slot quasi-optical receivers, imaging arrays, phased arrays or power-combining arrays of slot elements at millimeter-wave frequencies. 1925 0195-9271/93/1000-1925507.00/0 © 1993 Plenum Publishing Corporation 1926 Eleftheriades and Rebeiz I. I N T R O D U C T I O N A popular and effective technique for avoiding surface-waves in millimeterwave printed circuit antennas is by the use of a substrate lens, first proposed by Rutledge et al. [1]. The substrate lens, which is in practice electrically large, makes the printed antennas behave as if they are residing on an infinite dielectric half-space. An increasingly popular antenna to use with the substrate lens is the slot antenna. The main virtues of the slot antenna are that first, it radiates ~/~ of its power into the dielectric lens and therefore does not need a backing cavity when placed on high dielectric constant substrates [3]. Furthermore, the ground-plane of the slot antenna isolates the back-side of the wafer and allows the easy integration of active devices [2]. Kerr et al. [4] first proposed the use of a twin-slot antenna configuration to achieve highly symmetric patterns and low cross-polarization levels. Rogers and Neikirk also used a twin slot antenna on a layered dielectric substrate to reduce the power lost to the TM0 mode and increase the directivity of the patterns [5, 6]. A twin-slot antenna on a dielectric lens has been recently utilized by Zmuidzinas et al. [7] and Gauthier et al. [8] for the efficient coupling of the incoming radiation in monolithic SIS and Schottky receivers, respectively. Also, Filipovic and Rebeiz have calculated (and measured) the antenna patterns of a twin slot antenna on an extended substrate lens using a ray-optics approach and determined that its fundamental Gaussian coupling efficiency is between 80% and 90% for a silicon lens with a matching-cap layer [9]. A rigorous analysis of a slot (and dipole) antenna at the interface of an air-dielectric half-space was performed by Kominami et al., using Galerkin's technique in the spectral domain [2]. Subsequently, Zmuidzinas et al. [7] reported a direct extension to Kominami's technique for the computation of the mutual coupling between twin slot antennas on a quartz substrate; However, these authors did not provide any specific design data. Furthermore, Elliott presented variational expressions for the mutual coupling between slot antennas on a dielectric half-space, derived with the aid of Lorentz's reciprocity theorem [10]. The purpose of this paper is to introduce an efficient implementation of the spectral domain moment method for calculating the mutual coupling between slots on a substrate lens and to provide corresponding computational data. This will facilitate the design of twin slot antenna systems as well as imaging-arrays, phased-arrays or power-combining arrays of slot elements. Specifically, it is demonstrated that by the proper selection of the weighting functions in the method of moments the analytic evaluation or simplification of the transverse moment integrals is enabled. This results into a significant reduction of the required computational labor. The de-