Analysis of Post-Wall Waveguides and Circuits Using a Model of Two-Dimensional Photonic Crystals

Abstract

A semi-analytical method to analyze post-wall waveguides and circuits based on the model of two-dimensional photonic crystals formed by layered periodic arrays of circular cylinders is presented. The propagation constant of the fundamental TE mode, the attenuation constant due to the leakage loss and the effective width of an equivalent rectangular waveguide are calculated. Using the concept of the effective width, the original structure is replaced by an equivalent rectangular structure. When additional metallic posts are loaded in the rectangular waveguide, functional post-wall waveguide-based passive circuits are formed. The S-parameters of the post-wall circuits, which act as bandpass filters, are calculated using the image theory combined with the lattice sums technique.

1-D Periodic Lattice Sums for Complex and Leaky Waves in 2-D Structures Using Higher Order Ewald Formulation

“…where γ is the Euler constant [59]. Then, expressing the integral in (42) through the exponential integral ( ) q E z [13]: (44) and using the approximation of the exponential integral for small arguments [59]:…”

“…Also, modes in stopband regions are characterized by complex wavenumbers. The knowledge of the modal complex propagation wavenumber is of significant importance for the investigation of the leakage phenomena and the analysis of the radiation features in EBG waveguides and antennas [39], [40], for the design and fabrication of novel leaky-wave antennas [41], [42], and for the studies of a wide class of waveguide-based passive filters with dielectric and ohmic losses [43], [44]. We finally note that complex wavenumbers are also needed if the LSs are used in full-wave procedures to calculate the near field excited by a non-periodic line source on infinite 1-D periodic 2-D gratings [45]- [47].…”

Efficient Analysis of Electromagnetic Scattering in Post-Wall Waveguides and Its Application to Optimization of Millimeter Wave Filters

“…The accuracy of our formalism has been validated based on a comparison with the boundary integralresonant mode expansion (BI-RME) method [4] and a hybridization of method of moments with a cylindrical eigenfunction expansion [11]. Excellent agreement has been observed for several configurations within the entire frequency range [5], [6]. The method is briefly discussed in Section II.…”

“…In our recent works, we have proposed a self-contained, rigorous and numerically fast full-wave formalism, which can efficiently analyze the spectral responses of PWWs (both the real and complex solutions) and waveguide-based passive circuits (i.e. filters) relying on the model of 2-D electromagnetic crystals [5], [6]. Such PWW-based filters are studied utilizing the lattice sums technique presenting a highly efficient computational scheme not only for the analysis of electromagnetic scattering in PWWs but also it is perfectly suitable for the optimization of a wide class of mm-wave filters [7].…”

“…in dense integrated optics [8]. The proposed optimization scheme is easily applicable to design of PWW-based filter structure, as the forward solver [5] is computationally efficient. In contrast to deterministic optimizers, which usually require an initial starting…”