Numerical analysis and synthesis of 2D quasi-optical reflectors and beam waveguides based on an integral-equation approach with Nystrom's discretization

Considered is the beam wave guidance and scattering by 2D quasi-optical reflectors modeling the components of beam waveguides. The incident field is taken as the complex-source-point field to simulate a finite-width beam generated by a small-aperture source. A numerical solution is obtained from the coupled singular integral equations (SIEs) for the surface currents on reflectors, discretized by using the recently introduced Nystrom-type quadrature formulas. This analysis is applied to study what effect the edge illumination has on the performance of a chain of confocal elliptic reflectors. We also develop a semianalytical approach for shaped reflector synthesis after a prescribed near-field pattern. Here a new point is the use of auxiliary SIEs of the same type as in the scattering analysis problem, however, for the gradient of the objective function. Sample results are presented for the synthesis of a reflector-type beam splitter.     

DESIGN OF 2-D QUASI-OPTICAL BEAM SPLITTERS USING ANALYTICAL GRADIENTS

Quasi-optical systems comprised of diffractive phase elements (DPEs) are designed as beam splitters. The design tasks are reformulated as optimization problems in which target functionals are defined. Analytical gradients are derived to those functionals, which can be passed to gradient methods to efficiently determine the DPEs. Rayleigh-Sommerfeld diffraction integrals are applied to compute the wave propagation in free-space between parallel planes in the quasi-optical systems. Numerical results for several beam splitters are depicted. Furthermore a procedure is proposed, how the phase functions of the DPEs could be smoothed out.     

A two-dimensional quasi-optical power combining oscillator array with external injection locking

A quasi-optical power combiner for a 4/spl times/4 IMPATT oscillator array has been designed and experimentally investigated. The combiner consists of a bi-periodic dielectric phase grating which transforms the near field of a rectangular horn array into a pseudoplane wave. The horn array is excited by oscillators which operate uniformly in both amplitude and phase. A parabolic mirror with a superimposed surface relief couples the pseudoplane wave into a rectangular output horn antenna. In principle, the combiner has no restriction in inter-element spacing and is hence scalable up to submillimeter wavelengths without degradation of power combining efficiency. The quasi-optical design has been verified by scalar field measurements in several planes. The oscillator matrix is injection-locked by a master oscillator from the output port. A continuous wave output power of 1.3 W with an overall power combining efficiency of 70% has been measured at 65 GHz.     

Fast iterative, coupled-integral-equation technique for inhomogeneous profiled and periodic slabs

A fast coupled-integral-equation (CIE) technique is developed to compute the plane-TE-wave scattering by a wide class of periodic 2D inhomogeneous structures with curvilinear boundaries, which includes finite-thickness relief and rod gratings made of homogeneous material as special cases. The CIEs in the spectral domain are derived from the standard volume electric field integral equation. The kernel of the CIEs is of Picard type and offers therefore the possibility of deriving recursions, which allow the computation of the convolution integrals occurring in the CIEs with linear amounts of arithmetic complexity and memory. To utilize this advantage, the CIEs are solved iteratively. We apply the biconjugate gradient stabilized method. To make the iterative solution process faster, an efficient preconditioning operator (PO) is proposed that is based on a formal analytical inversion of the CIEs. The application of the PO also takes only linear complexity and memory. Numerical studies are carried out to demonstrate the potential and flexibility of the CIE technique proposed. Though the best efficiency and accuracy are observed at either low permittivity contrast or high conductivity, the technique can be used in a wide range of variation of material parameters of the structures including when they contain components made of both dielectrics with high permittivity and typical metals.     

Diffraction synthesis and experimental verification of a quasi-optical power splitter at 150 GHz

A general and flexible synthesis method based on the physical optics approximation is proposed for computing smooth-surface reliefs of reflectors. As a design example, the method has been applied to a quasi-optical power splitter consisting of two reflectors in a dual-offset configuration that couples a launched beam from a pyramidal horn antenna into a 2/spl times/4 horn antenna array. The two reflectors were treated as diffractive phase elements so that the proposed synthesis method allows reflector designs for many applications. The quasi-optical design has been confirmed at 150 GHz utilizing a vector field measurement system. The measured field distribution in the receiving antenna array plane is compared with the simulated one and shows a very good agreement.