Efficient Tracking of Dispersion Surfaces for Printed Structures using the Method of Moments

TL;DR

This paper presents an efficient, non-approximate method for computing dispersion surfaces of printed periodic structures using an accelerated periodic Method of Moments, enabling rapid analysis of lossless and lossy media over broad frequency ranges.

Contribution

The paper introduces a novel tracking algorithm combined with interpolation and Macro basis functions to significantly reduce computational effort in dispersion surface analysis.

Findings

Only 12 impedance matrices needed for broad frequency and phase shift coverage

Method validated on lossless metasurfaces with commercial software

Applicable to lossy structures and leaky waves without approximation

Abstract

The dispersion surfaces of printed periodic structures in layered media are efficiently computed using a full-wave method based on the periodic Method of Moments (MoM). The geometry of the dispersion surface is estimated after mapping the determinant of the periodic MoM impedance matrix over a range of frequencies and impressed phase shifts. For lossless periodic structures in the long-wavelength regime, such as lossless metasurfaces, a tracking algorithm is proposed to represent the dispersion surface as a superposition of parameterized iso-frequency curves. The mapping process of the determinant is accelerated using a specialized interpolation technique with respect to the frequency and impressed phase shifts. The algorithm combines a fast evaluation of the rapidly varying part of the periodic impedance matrix and the interpolation of the computationally intensive but slowly varying remainder. The mapping is further accelerated through the use of Macro basis functions (MBFs). The method has been first tested on lossless metasurface-type structures and validated using the commercial software CST. The specialized technique enables a drastic reduction of the number of periodic impedance matrices that needs to be explicitly computed. In the two examples considered, only 12 matrices are required to cover any phase shift and a frequency band larger than one octave. An important advantage of the proposed method is that it does not entail any approximation, so that it can be used for lossy structure and leaky waves, as demonstrated through two additional examples.