## 1. Introduction

[2] With recent improvements of a surface/volume integral equation approach [*Vaupel and Hansen*, 2000a, 2000b] a much faster analysis of complex coplanar/microstrip structures could be achieved with increased accuracy especially when applied to structures with negligible dielectric losses. These improvements are now utilized within a detailed radiation efficiency analysis concept particularly well suited for a special class of reflector backed slot antenna receivers for the submillimeter-wave region [*Aroudaki et al.*, 1994]. These receivers are based on the concepts in *Zmuidzinas and LeDuc* [1992] and *Chattopadhyay et al.* [2000]. First realizations with measurements are presented by *Schäfer et al.* [1995, 1997] but without the possibility of a detailed efficiency consideration. The basic concept of such receivers comprises the utilization of a quartz lens with doubleslot or strip dipole antenna as lens feeding structures. Using a quartz lens, a lens matching layer is not absolutely necessary, but the low permittivity of quartz causes a large backward radiation into the air region below the lens. In order to diminish these radiation losses, an additional reflector was attached below the lens. Numerical simulations in *Aroudaki et al.* [1994] have shown furthermore, that an effective tuning of the antenna resonance frequency can be performed by adjusting the distance of this reflector. Nevertheless, a parallel plate medium is formed by this additional reflector and thus the possible excitation of parasitic parallel plate modes may lead to radiation losses as well. For the detailed analysis of all radiation effects, we have improved the spectral domain integration technique of our surface/volume integral equation approach in *Vaupel and Hansen* [2000a, 2000b]. Since the parallel plate poles of the corresponding Green's function cause large variations of the integrands, we have consequently used an integration path deformation for both the *k*_{x} and *k*_{y} wavenumbers similar as in *Yang et al.* [1990] and *Garino et al.* [2000] together with an integration area reduction to the first quadrant of the *k*_{x}-*k*_{y} plane. Due to the smooth integrand behavior achieved by these measures, we apply a piecewise uniform integrand sampling by an appropriate subdivision of the *k*_{x}-*k*_{y} plane. The optimized row and column arrangement of the sampling points allows the setup of a very efficient database for the basis functions leading to a drastic reduction of computational and storage requirements compared with the hitherto evaluation in polar coordinates [*Vaupel and Hansen*, 1999a, 1999b; *Horng et al.*, 1992]. The integration path deformation also allows the computation of structures with negligible dielectric losses, a prerequisite for a detailed radiation efficiency analysis. For this analysis, we extract the parallel plate wave contributions using the corresponding scalar Green's functions for the symmetric Sommerfeld integrals, the modified saddle point method and the residue theorem. The space wave power is determined with the standard saddle point method. The reliability of the combined application of the various methods is tested by checking the overall power balance of the structure.