Ternary optimization for designing metasurfaces

Azin Hojjati,Mohammad Soleimani,Vahid Nayyeri,Omar M Ramahi

doi:10.1038/s41598-021-96564-5

Azin Hojjati, Mohammad Soleimani + Show 2 more

Open Access

https://doi.org/10.1038/s41598-021-96564-5

Copy DOI

Abstract

A fully automated approach for designing metasurfaces whose unit cell may include metallic vias is proposed. Towards this aim, a ternary version of the particle swarm optimization (PSO) algorithm is employed in order to find the optimal metallic pattern and via-hole positions simultaneously. In the proposed design method, the upper surface of the unit cell is first pixelated. One of the possible three states of a metallic covered pixel, an uncovered etched pixel and a pixel containing a centered metalized via-hole is assigned to each pixel. The optimal state of each pixel is then determined by utilizing a ternary PSO algorithm to achieve favorable design goals. This method can be used for designing various metasurfaces as well as other via-assisted electromagnetic structures. As a proof of concept, the proposed method was applied to design two surfaces: a frequency selective surface with a minimum resonance frequency, and a linear-to-circular polarization converter with a maximum polarization conversion bandwidth. Comparison of the results with previous works confirms the efficiency and capability of the proposed method to design diverse metasurfaces in an automated fashion without the need for any theoretical or physical model.

Highlights

A fully automated approach for designing metasurfaces whose unit cell may include metallic vias is proposed
In order to decrease the number of independent pixels which leads to an increase in the convergence rate and to reduce the frequency selective surfaces (FSS) sensitivity to the polarization of the incident wave, an eight-reflection symmetry was applied to the unit cell
This strong similarity indicates the strong capability of our design procedure, despite random initialization, which resulted in a unit cell topology highly similar to a unit cell obtained by a physical model

Summary

Design method development

A periodic array of a unit cell located on a dielectric substrate is considered as a metasurface with an arbitrary function. In order to decrease the number of independent pixels, and to increase the convergence rate, different types of symmetry can be applied to the unit cell topology. For an optimization problem with N optimization parameters, as well as the traditional PSO algorithm, a number of candidate solutions (particles) composing the population (swarm), explore the N-dimensional search space by moving around it. Unlike the traditional PSO algorithm in which the particle position vector elements can possess continuous values, in this algorithm, only one of the three basic phasor values of 1∠ − 120◦ , 1∠0◦ or 1∠120◦ can be assigned to these elements. GN ] are the best experiences of the mth particle and the swarm, respectively, c1 and c2 are positive constants, and e1 and e2 are vectors with random elements between 0 and 1 to guarantee the random behavior of the optimization algorithm. To ensure the applicability of this algorithm in finding the global optimum and its appropriate convergence, and in order to find a proper range for the swarm population as well as the maximum iteration number, this algorithm was examined using several standard benchmark functions (see the “Appendix”)

Design examples

Conclusion