Hybrid potential-field formulation (HPFF) is proposed for broadband electromagnetic solutions of composite problems involving open and closed conducting surfaces. HPFF provides a well-balanced combination of potential and field formulations for electrically large structures with small-scale features, being free of internal-resonance problems and dense-discretization breakdowns.

This paper presents accurate and efficient analyses of transparent antennas near platforms. Various numerical electromagnetic simulation tools are investigated during analyses of antennas mounted on platforms. The simulation environment developed in this work utilizes the equivalent source (ES) representations, and employs surface integral equation-based solutions accelerated by multilevel fast multipole algorithm to model interactions between antennas and vehicles, focusing on the impact of placements. The tool demonstrates remarkable performance compared to commercial tools and enables realistic simulations of transparent antennas on actual vehicle wind-shields. This facilitates more effective performance assessments and optimizations of antenna orientations and placements.

We present design and simulation of three-dimensional (3D) shell structures, which generate directional radiation patterns from isotropic sources thanks to their near-zero-index (NZI) characteristics, as well as realizations of these shells via low-cost 3D printing. Throughout the design process of NZI beam generators, both homogenized structures, for which near-zero relative permittivity and/or permeability values are enforced, and actual models involving periodic arrangements of dielectric rods are considered. Solutions of the electromagnetic problems are obtained by using rigorous implementations of the state-of-the-art surface-integral-equation (SIE) formulations in frequency domain. Iterative solutions of matrix equations derived from SIEs are accelerated by different forms of the multilevel fast multipole algorithm (MLFMA) and suitable preconditioners, when necessary. In the design process of NZI shells, alternative strategies are employed to obtain customized radiation patterns. In this context, various cavities with strong resonance behaviors are designed as source regions. At the same time, outer surfaces are modified to either enhance or suppress outgoing electromagnetic fields. In addition to comprehensive simulations and analyses of NZI beam generators, their capabilities are verified by measurements, specifically at 10.3 GHz, on different prototypes fabricated via 3D printing. Measurements of diverse NZI shell structures are presented to demonstrate that NZI properties can successfully be achieved by well-designed arrangements of dielectric rods with proper materials. The results demonstrate the feasibility of efficient, effective, low-cost, and reconfigurable NZI shells to generate alternative beam configurations that can be useful in a plethora of microwave applications.

This paper examines accurate and efficient analyses of densely discretized composite conductors consisting of open and closed surfaces. A novel surface-integral-equation formulation, namely the hybrid potential-field formulation (HPFF), is proposed by appropriately employing field and potential formulations on composite problems. HPFF is not susceptible to both low-frequency breakdowns and internal-resonance problems. Numerical examples show the superior performance of HPFF compared to other available formulations, specifically for densely discretized structures with both open and closed surfaces.

This paper presents an efficient combination of genetic algorithms and machine-learning techniques to optimize scattering properties of 3D dielectric (PLA) slabs with surface deformations. The top and bottom surfaces of slabs are optimized to obtain the desired electromagnetic properties while they are represented by Bezier functions so that final designs can be fabricated via 3D printers. The numerical results demonstrate the superiority of the developed optimization environment to reach the desired scattering characteristics.

We propose and demonstrate a multiple-precision arithmetic framework applied to the inherent hierarchical tree structure of the multilevel fast multipole algorithm (MLFMA), dubbed the multiple-precision arithmetic MLFMA (MPA-MLFMA) that provides an unconventional but elegant treatment to both the low-frequency breakdown and the efficiency limitations of MLFMA for electrically large problems with fine geometrical details. We show that a distinct machine precision can be assigned to each level of the tree structure of MPA-MLFMA, which in turn enables controlled accuracy and efficiency over arbitrarily large frequency bandwidths. We present the capabilities of MPA-MLFMA over a wide range of broadband and multi-scale scattering problems. We also discuss the implications of a multiple-precision framework implemented in software and hardware platforms.

We present design and simulations of electromagnetic beam splitters that are based on near-zero-index (NZI) materials. NZI structures are metamaterials that possess near-zero relative permittivity and/or permeability values, which can be realized by periodically arranging unit cells. Due to their exotic properties, they may be used to forward beams in desired directions when their geometries are properly designed. We consider homogenized models, where relative permittivity and permeability values are assumed to be small, in an efficient and accurate simulation environment. The results show that relatively simple geometries can be used to re-direct beams, whereas receiving incoming fields with minimum reflection seems to be a major challenge.

We present design and optimization of three-dimensional dielectric structures that provide efficient backscattering reduction (BSR). Although BSR is a subject involved in a plethora of applications and is studied intensively in the literature, the complexity of the designed structures often leads to challenges in fabrication and production phases. In this study, very effective BSR is achieved with relatively simple dielectric geometries using only a single material and air-filled holes. Moreover, with the designed structures, BSR can be achieved not only in a single frequency range but also in two frequency bands. All structures are solved and analyzed by the multilevel fast multipole algorithm (MLFMA) and optimizations are successfully performed by combining this method with genetic algorithms (GAs). By optimizing the size, arrangement, and depth of holes on dielectric structures, backscattering from a metal plate can be reduced by as much as 37 dB.

Well-designed arrangements of arrays of circular lossy dielectric rods with finite lengths have been exploited to obtain proper radiation patterns for microwave applications. Accelerated three-dimensional (3D) numerical modeling of such radiation mechanisms via the multilevel fast multipole algorithm (MLFMA) is suitable for well-matched results with real-life experiments. Enabling rigorous and accurate analyses of the corresponding problems, MLFMA, has been observed to provide quasi-optimal designs within a reasonable period of time, when this algorithm is efficiently combined with genetic algorithms (GAs). However, as shown in this contribution, the corresponding two-dimensional (2D) multiple scattering modeling via a well-conditioned version of the T-matrix method provides a much faster tool for GAs to optimize radiation patterns for a goal set on the central cross section plane of the rod arrays. Optimized geometries obtained using a combination of the 2D solver and GAs have been validated by using a 3D solver based on MLFMA to demonstrate the feasibility of the approach.

We present efficient and accurate optimizations of three-dimensional dielectric slabs for desired scattering properties. Optimizations are performed by using an effective combination of genetic algorithms and the multilevel fast multi-pole algorithm. A multigrid approach with Bezier surfaces is employed to obtain superior designs that can be fabricated via 3D printers. By simultaneously optimizing top and bottom surfaces, scattering properties can be designed in accordance with the given constraints. Numerical results show that slabs with interesting scattering characteristics can be obtained via the developed optimization environment.

We present a novel measurement approach to electromagnetic characterization of 3D printing filaments via Nicholson-Ross-Weir (NRW) method. In particular, we measure reflection and transmission coefficients of 3D-printed samples by placing them into 3D-printed sample holder waveguides and using a vector network analyzer. Then constitutive parameters are found by using these coefficients. NRW method produces inaccurate results when sample thicknesses are greater than half of the guided wavelength. In addition, measured dielectric and magnetic loss values are highly sensitive to phase data of reflection and transmission coefficients. We show that stable and accurate results can be obtained via 3D-printed sample holder waveguides with proper thicknesses.

This chapter has focused on MLFMA as a representative kernel-based fast factorization technique. To construct a basis for further discussion, we first considered the conventional MLFMA, which is based on the plane-wave expansion of electromagnetic waves, at a formulation level. To solve multi-scale problems involving dense (uniform or non-uniform) discretizations of electrically large objects, alternative MLFMA versions are needed since the conventional MLFMA suffers from a low-frequency breakdown. We listed a variety of ways to implement low-frequency-stable MLFMAs, such as based on multipoles, inhomogeneous plane waves, coordinate shifts, and approximation techniques. We showed how MLFMA implementations can be used to solve extremely large problems via parallelization, while they can be applied to complex structures with different material properties, including plasmonic and NZI objects. Examples were given for solutions of densely discretized objects to demonstrate how MLFMA can handle such complicated problems that possess modeling challenges. Finally, problems with non-uniform discretizations that naturally arise in multi-scale simulations were considered. A rigorous implementation for stable, accurate, and efficient solutions of these problems requires a well-designed combination of a suitable formulation/discretization, an effective solution algorithm (MLFMA version), and a carefully designed clustering mechanism.

Computational design and analyses of nanoantennas obtained via surface shape optimization are presented. Starting with a kernel geometry, free deformations are applied on selected surfaces to reach optimal designs that can provide improved power enhancement capabilities at desired frequencies. An in-house implementation of genetic algorithms is efficiently combined with the multilevel fast multipole algorithm developed for accurate solutions of plasmonic problems to construct the effective optimization environment. The geometries obtained via optimization do not only represent optimal shapes within the allowed deformation limits but also reveal certain types of modifications on kernel geometries to improve their performances. (c) 2023 Society of Photo-Optical Instrumentation Engineers (SPIE)

We present computational design and analysis of near-zero-index (NZI) shell structures with elliptical cavities, which can provide directional radiation characteristics when excited by isotropic sources. Alternative strategies, such as geometric shaping of internal cavities, using pyramidal textures, and selecting suitable material properties, are employed to create symmetric and asymmetric beams.

Fast, accurate, and stable solutions to composite objects involving open and closed perfectly conducting surfaces are considered. A novel formulation, called the hybrid potential-field formulation (HPFF), is developed by using potential and field formulations simultaneously. Closed surfaces are formulated with the recently developed combined potential-field formulation, whereas open surfaces are formulated with potential integral equations. The developed formulation does not suffer from low-frequency (dense-discretization) breakdowns or internal-resonance problems. Superior performances of HPFF are demonstrated on canonical problems.

During the optimization by means of genetic algorithms of the three-dimensional rod arrays consisting of finite-length cylinders, commonly used in the design of high-frequency resonance scattering, three-dimensional solvers, such as the multilevel fast multipole algorithm, perform the analyses with a time bottleneck. Simulation results seem independent of longitudinal dimensions in many applications. Therefore, the exploitation of the well-conditioned solvers in two dimensions appears to be worthy, and it is aimed to cast further comparisons between the two types of solvers in this contribution.

We consider accurate and iteratively efficient solutions of electromagnetic problems involving homogenized near-zero-index (NZI) bodies using surface-integral-equation formulations in the frequency domain. NZI structures can be practically useful in a plethora of optical applications, as they possess near-zero permittivity and/or permeability values that cannot be found in nature. Hence, numerical simulations are of the utmost importance for rigorous design and analysis of NZI structures. Unfortunately, small values of electromagnetic parameters bring computational challenges in numerical solutions of homogeneous models. Conventional formulations available in the literature encounter stability issues that make them inaccurate and/or inefficient as permittivity and/or permeability approach zero. We propose a novel formulation that involves a well-balanced combination of operators and that can provide both accurate and efficient solutions for all NZI cases. Numerical results are presented to demonstrate the superior properties of the developed formulation in comparison to the conventional ones.

Design and optimization of efficient and compact nano-optical isolators based on irregular arrays of dielectric rods are presented. These designs allow electromagnetic waves to propagate in single direction and prevent them from propagating in the opposite direction. This way, high forward transmission is achieved, while the main source is protected from reflected waves. Effective optimization algorithms are integrated with the multilevel fast multipole algorithm (MLFMA), a fast and accurate full-wave numerical solver, to design efficient isolators composed of different arrangements of dielectric elements with controlled forward and backward transmissions.

We present a novel surface-integral-equation formulation that provides broadband solutions of electromagnetic problems involving perfectly conducting objects. The formulation, namely the combined potential-field formulation (CPFF), is based on a well-balanced combination of the conventional potential integral equations (PIEs), the magnetic-field integral equation (MFIE), and an additional PIE involving magnetic vector potential. In addition to being stable for dense discretizations, CPFF is free of internal resonances, and it enables accurate and efficient solutions of large-scale closed conductors using conventional basis and testing functions. Numerical results demonstrate that CPFF clearly outperforms other formulations, including the popular combined-field integral equation (CFIE), for densely discretized objects comparable to or larger than wavelength.

This study presents design and optimization of compact and efficient nanooptical couplers involving photonic crystals. Nanooptical couplers that have single and double input ports are designed to obtain efficient transmission of electromagnetic waves in desired directions. In addition, these nanooptical couplers are cascaded by adding one after another to realize electromagnetic transmission systems. In the design and optimization of all these nanooptical couplers, the multilevel fast multipole algorithm, which is an efficient full-wave solution method, is used to perform electromagnetic analyses and simulations. A heuristic optimization method based on genetic algorithms is employed to obtain effective designs that provide the highest efficiency values. Two types of optimization strategies are applied using nanorods with a fixed length and using nanorods with varying lengths. This way, photonic crystals consisting of irregular arrays of both identical and nonidentical dielectric elements are designed for the realization of nanooptical couplers. The designs and their numerical results show that it is possible to design and further improve efficient nanooptical couplers with simple and compact geometries based on the principles of photonic crystals. Using relatively simple geometries and a single material, the designed nanooptical couplers are more preferable than the available designs in the literature.