Lens or resonator? Electromagnetic behavior of an extended hemielliptic lens for a sub‐millimeter‐wave receiver

Abstract

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.

Layer-to-layer ceramic stereolithography for the design of extended hemispherical lenses at 60 GHz

“…First, manufacturing such ILAs is challenging and costly when starting from bulk materials, especially at millimeter waves for which smooth and accurate surface finish is required. Secondly, the radiation characteristics of these lenses are substantially distorted because the strong dielectric contrast at the lens / air interface favors excitation of multiple internal reflections and whispering gallery modes [2]. These effects could be reduced using quarter wavelength matching layers or caps with a suitable thickness and permittivity.…”

Physical optics modeling of 2D dielectric lenses

“…In the meantime, an exact solution for electromagnetic scattering by a dielectric body is a complicated problem when the body is of a large electrical size. There are various approaches to the problem ranging from the finite difference, finite elements, and similar methods [9] to sophisticated formulations based on the integral equations [10,11] combined with regularization techniques [12][13][14]. Exact methods are usually limited to systems of small size, often less than ten wavelengths in diameter even in those cases when advanced solvers are available (e.g., ANSOFT HFSS software).…”

“…A rigorous regularization method [13,14] is proposed for the body of special geometry considered as a resonator. A promising hybrid technique is developed for diffractive microlenses [5], where the finite difference method solves the problem in the near field and the partial plane wave (PW) propagation is used to transform the solution to the far field.…”

Asymptotic wave-like modeling of dielectric lenses

“…There are various approaches to numerical solution of dielectric scattering problems ranging from the finite difference, finite elements and similar methods [4] to special sophisticated formulations based on the integral equations [5,6] combined with regularization techniques of their solution [7][8][9]. Exact methods are usually limited to systems of small size, often less than ten wavelengths in diameter even in those cases when advanced solvers are available (e.g., Ansoft HFSS software).…”

“…A rigorous solution based on regularization technique is presented in [8,9] for a special class of small-size twodimensional problems of relatively complicated geometry. A promising hybrid method is proposed for diffractive micro-lenses in [11] where the finite difference method solves the problem in the near field of the lens and the partial plane wave propagation is used to transform the solution to the far-field domain.…”