Optimization of polarizers and metasurfaces using evolutionary algorithms
Modern satellite communication on-the-move (SOTM) system demands multifunctional devices with enhanced capabilities, optimum performance, and strict compliance with various regulatory standards. Designing these complex structures with conventional parametric analysis is economically and computationally infeasible. Evolutionary optimization algorithms are reliable and robust computational design methodologies and are intelligent choices for such complex problems where the traditional parametric analysis is cost prohibitive. The objective of this thesis is to optimize the electromagnetic (EM) structures using sophisticated state-of-the-art optimization methods. An extensive study is conducted to understand the specifics of EM design problems and to judiciously implement a suitable evolutionary algorithm (EA) for optimization.
In this thesis, some vital components of SOTM systems, for instance, waveguide polarizers, phase-gradient metasurfaces (PGMs), and 2D beam-steering antenna systems, have been optimized using state-of-the-art EAs. Full-wave commercial solver CST Microwave Studio (MWS) is used to perform simulations of all EM designs considered in this thesis. For seamless automation of design optimization, the field solvers are interfaced with optimization algorithms coded in MATLAB using macro programming. The cross-entropy (CE) method and particle swarm optimization (PSO) method are the two EAs used in this thesis.
The first part of this dissertation investigates the CE method framework to address waveguide polarizer design problem. A dielectrically loaded waveguide polarizer design is first treated as a continuous optimization problem and addressed using the classical version of the CE method for continuous parameters. To overcome the limitations of commercially available dielectrics, the modified version of the CE method for mixed parameters is later implemented to address the polarizer design as a combinatorial optimization problem. A compact wideband polarizer with significantly improved axial ratio bandwidth is obtained with the second optimization approach. A reasonably constant differential phase-shift of (90 ± 0:3) degrees is achieved for the frequency range from 10.5 to 14.5 GHz. The axial ratio within this range is below 0.13.
A simple generalized version of the CE method is proposed for the optimization of electrically large, computationally expensive, and memory hungry EM structures with a large number of design parameters. The proposed approach is implemented to design a PGM-based 1D beam-steering antenna system that has all the side-lobe levels (SLLs) below the Federal Communications Commission (FCC) mask (25.209) for Ka-band. First, it is used to optimize the design variables in a PGM that offsets the beam from broadside to 20° elevation tilt angle. The optimization reduces the SLLs considerably with a few peaks slightly above the FCC mask. Later, the same algorithm is implemented to optimize the amplitude of the feed array in a beam-steering PGM. This approach successfully brings all the SLLs below the FCC mask.
The second part of the dissertation focuses on optimizing the performance of a Near-Field Meta-Steering system and suppressing the undesired sidelobes and grating lobes that appear in the far-field pattern while steering the beam away from the broadside. The periodic nature of PGMs is exploited to our advantage to make the optimization process cheaper and faster. The design and optimization challenges in a PGM-based 2D beam-steering antenna are addressed in two steps. First, the strength of "offending" grating lobes is reduced efficiently by optimizing a supercell using Floquet analysis and multi-objective particle swarm optimization. Second, the effects of the transmission phase gradient of PGMs on radiation-pattern quality are investigated. It is shown that the number of unwanted dominant lobes in a 2D beam-steering antenna system and their levels can be reduced substantially by increasing the transmission phase gradient of the PGMs. This method reduces all grating lobes to a level below −20 dB for all beam directions, without applying any amplitude tapering to the aperture field in a 2D beam-steering systems.
Floquet analysis based approach is followed to optimize the upper PGM for oblique incidence. The optimization successfully suppressed all the grating lobes below −30 dB for the broadside pattern in a Near-field Meta-steering (NFMS) system. A low-cost, compact NFMS system is designed by placing a pair of optimized PGMs close to and above the aperture of a medium-gain truncated resonant cavity antenna (RCA). The maximum directivity of the steering system is 17.8 dBi and it can steer the beam in a conical volume with an apex angle of 35° within a 3 dB reduction in peak directivity.
Several 4th order (90°) rotationally symmetric phase-transforming cells (PTCs) are investigated to design upper PGM in the NFMS systems. A comprehensive study on the behaviour of various PTCs and supercells when a plane wave is obliquely incident on them and rotated, is presented. The supercell with the best performance as a function of obliquely incident wave rotation is optimized using PSO, and a pair of full metasurfaces are designed. The steering performance of the optimized PGM-pair excited with a dipole antenna array is also presented. The outcome of this investigation will help the engineers to make an educated decision when designing an NFMS system.
The EM structures in this thesis are designed using an automated optimization process and exhibit enhanced capabilities and improved performance parameters compared to initial designs or pre-existing solutions. The methodologies provided in this thesis are relevant to the real-world EM engineering optimization problems. They are readily applicable to any other EM problem with similar design requirements.