The behavior of a 2-D model of an extended hemielliptic silicon lens of a size typical for THz applications is accurately studied for the case of a plane E-wave illumination. The full-wave analysis of the scattering problem is based on the Muller's boundary integral-equations (MBIE) that are uniquely solvable. A Galerkin discretization scheme with a trigonometric basis leads to a very efficient numerical algorithm. Numerical results related to the focusability of the lens versus its rear-side extension and the angle of the plane-wave incidence, as well as near-field profiles, demonstrate strong resonances. Such effects can change the principles of optimal design of lens-based receivers.
The objective of the paper is the assessment of the accuracy of a conventional FDTD code in the computation of the near and far-field scattering characteristics of a circular dielectric cylinder. We excite the cylinder with an electric or magnetic line current and demonstrate the failure of the two-dimensional (2-D) FDTD algorithm to characterize accurately the emission rate and the field patterns near high-Q whispering-gallerymode resonances. This is proven by comparison with the exact series solutions. The computational errors in the emission rate are then studied at the resonances still detectable with FDTD, i.e. having Q-factors up to 10 3 .
We assess the accuracy and relevance of the numerical algorithms based on the principles of Geometrical Optics (GO) and Physical Optics (PO) in the analysis of reduced-size homogeneous dielectric lenses prone to behave as open resonators. As a benchmark solution, we use the Muller boundary integral equations (IEs) discretized with trigonometric Galerkin scheme that has guaranteed and fast convergence as well as controllable accuracy. The lens cross-section is chosen typical for practical applications, namely an extended hemiellipse whose eccentricity satisfies the GO focusing condition. The analysis concerns homogeneous lenses made of rexolite, fused quartz, and silicon with the size varying between 3 and 20 wavelengths in free space. We consider the 2-D case with both Eand Hpolarized plane waves under normal and oblique incidence, and compare characteristics of the near fields.Index Terms-Dielectric lens antennas, boundary integral equations, geometrical optics, physical optics.
The objective of the paper is to assess the accuracy of a standard FDTD code in the analysis of the near and far-field characteristics of two-dimensional (2-D) models of small-size dielectric lens antennas made of low or high-index materials and fed by the line sources. We consider extended hemielliptic lenses and use the Muller boundary integral equations (MBIE) method as a suitable reference solution. Inaccuracies of FDTD near socalled half-bowtie resonances are detected. Denser meshing reduces the error of FDTD only to a certain level determined by the type of absorbing boundary conditions used and other fine details of the code. Out of these resonances, FDTD code is demonstrated as capable of providing sufficient accuracy in the near and far-field analysis of small-size hemielliptic lenses typical for the millimeter-wave (mm-wave) applications. Index Terms-hemielliptic dielectric lens antenna, FDTD, Muller boundary integral equations, resonances.
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