We present resonance-free solutions of scattering problems involving closed conductors using the magnetic field integral equation (MFIE). In the literature, MFIE is often combined with the electric-field integral equation (EFIE) to avoid internal resonances that can significantly contaminate solutions especially when scatterers become electrically large. The resulting combined-field integral equation (CFIE), however, possesses the disadvantages of EFIE, e.g., ill-conditioning for dense discretizations. We show that placing an interacting inner surface inside the given object and enforcing internal fields to be zero can mitigate internal resonances, making MFIE resonance-free without employing EFIE. Using an arbitrary inner surface can significantly suppress internal fields; but, as also shown in this contribution, the size of the inner surface, i.e., the distance between inner and outer surfaces, can be critical to obtain accurate results that are comparable to those obtained with the conventional CFIE.

Numerical solutions of electromagnetic problems involving nanostructures at terahertz (THz)frequencies are considered. We particularly focus on nanoparticles that are made of typical metals at the lower THz frequencies. Even though the frequency is relatively low, we show that penetrable models are needed for accurately representing electromagnetic characteristics, especially to predict penetrating magnetic fields inside small particles. Due to large permittivity values with negative real parts, stable formulations are needed to obtain equivalent currents and secondary fields. It is shown that the modified combined tangential formulation, which was proposed for plasmonic simulations in wide frequency ranges, provides accurate solutions that are consistent with analytical results for spherical nanoparticles.

In this paper, we present design and numerical simulations of nano-cavities for free-space matching in solar cells at optical frequencies. The cavity designs are inspired by the well-known antenna geometries that are commonly used at radio and microwave frequencies. Using such designs that have not been explored before in the context of solar cells, the electromagnetic mismatch between solar-cell surfaces and vacuum is significantly reduced, in comparison to planar interfaces and those with the conventional corrugations. This way, using the designed optimal cavities, the efficiency of solar cells can be increased without employing any matching layer that complicates the fabrication processes. All simulations and comparisons are performed in highly accurate in-house implementations of surface integral equations accelerated with the multilevel fast multipole algorithm.

We present a new method to mitigate internal resonances of the magnetic-field integral equation (MFIE) for closed conductors, without combining this equation with the electric-field integral equation (EFIE) that is commonly practiced in the literature. For a given object and its surface, a smaller closed surface is placed inside to create a double layer. This way, the magnetic field intensity is enforced to zero on the inner surface, making the overall solution unique at all frequencies. By eliminating the need for EFIE, the resulting implementation is purely based on MFIE interactions. In addition to its formulation, the initial numerical results of the proposed method on canonical problems are presented.

The conventional combined-field integral equation (CFIE)using a Galerkin scheme suffers from inaccuracy issues due to the incorrect testing of the identity operator in the magnetic-field integral equation (MFIE). In this contribution, a mixed discretization scheme is used for correct testing of MFIE in the context of CFIE. The projection of testing spaces of EFIE and MFIE onto each other is required while solving CFIE numerically with the mixed discretization scheme. For this purpose, computations of the Gram matrix inversions are required to perform the projection operations. Such an operation can easily become computationally expensive, especially when solving large-scale problems using accelerated algorithms, such as the multilevel fast multipole algorithm (MLFMA). In this work, matrix decomposition methods and iterative solvers are used to solve Gram systems while solving CFIE with the mixed discretization scheme in the framework of MLFMA. The accuracy and efficiency of the results are compared, in the context of large-scale problems.

We present computational analysis of optical nanostructures, including but not limited to frequency-selective surfaces, metamaterials, nanoantennas, nanowires, and photonic crystals. A rigorous implementation based on surface integral equations and the multilevel fast multipole algorithm is developed for the analysis of such three-dimensional complex structures, without resorting to infinity, self-similarity, periodicity or homogeneity assumptions. The developed simulation environment provides accurate analysis of nanooptical structures to expand our knowledge on these important components of the state-of-the-art technology.

We present a new method for the reconfiguration of inkjet-printed antennas to make them operate at different frequencies while matching to different impedances other than originally designed. Suitable antennas are modified by replacing conventional ground planes with patterned structures involving optimal arrangements of hexagonal cells. The cells are switched on or off, while the optimal distributions are found via genetic algorithms to reach desired characteristics. A full-wave solver is used for the required analysis in the optimization trials without sacrificing the accuracy. The antennas are fabricated by using a low-cost inkjet-printing setup to demonstrate the effectiveness of the approach, particularly in the context of radio-frequency-identification applications.

We present the design and investigation of plasmonic lenses to achieve maximum power focusing for imaging applications. As opposed to commonly used slits opened on metallic structures, the designs are based on different arrangements of holes on metallic slabs. The structures are obtained via an optimization environment based on a three-dimensional numerical solver using an efficient implementation of the multilevel fast multipole algorithm (MLFMA) and optimization modules using genetic algorithm. We demonstrate the effectiveness of the designs via sample structures involving hexagonal holes on silver slabs.

We present a new type of pixel antennas involving hexagonal unit cells that are suitable for fabrication in low-cost inkjet-printing setups. Antennas are optimized in a rigorous simulation environment based on the multilevel fast multipole algorithm integrated into genetic algorithms. Hexagonal cells are suitable for both the optimization environment and fabrication setup. Optimizations are performed particularly to design radio-frequency-identification tags, by removing pixels from a given template to achieve the best performance, e.g., minimum reflection coefficient values and maximum reading ranges. The overall design, optimization, and fabrication procedure has a fast demand response, requiring only one day from a request to the prototype stage.

An infinitely smooth parametrical representation with derivatives of all orders is used, resulting into exponentially converging solutions of hyper-singular electric field integral equation (EFIE) in 2D. A version of superformula tailored for this purpose has been subject to optimization of its parameters via genetic algorithms to provide smooth parameterization for a desired boundary in two-dimensional problems. The organization of the hyper-singular kernel and convergence of the solution for EFIE assuming TE polarization will be presented.

We present computational analysis of optical chiral metamaterials that consist of helical metallic elements. At optical frequencies, metals are modeled as penetrable objects with plasmonic properties. A rigorous implementation based on boundary element methods and the multilevel fast multipole algorithm is used for efficient and accurate analysis of three-dimensional structures. Numerical results demonstrate interesting polarization-rotating characteristics of such arrays with helical elements, as well as their complex responses depending on geometric parameters.

We present a novel type of pixel antennas that are suitable for fabrication in low-cost setups based on commercial inkjet printers. The proposed antennas involve hexagonal cells that can be removed in accordance with rigorous optimizations via genetic algorithms that are supported by fullwave solutions with the multilevel fast multipole algorithm. Optimal pixel configurations are determined precisely for desired electrical characteristics, such as low power-reflection values at required frequencies. Measurements on fabricated samples demonstrate the effectiveness of the optimizations, as well as the favorable characteristics of the hexagonal-cell pixel antennas that fully benefit from the advantages of low-cost inkjet printing.

It is known that solutions of the integral equations converge at the smoothness rate of the parametrical function representing the boundary contour. Thus using an infinitely smooth parametrical representation with derivatives of all orders results into exponentially converging solutions. A version of superformula tailored for this purpose is exposed to optimization of its parameters via genetic algorithms to obtain smooth parameterization for desired boundaries in two dimensional problems. The convergence of the resulting solutions of the electric-field integral equation will be presented.

We present an electromagnetic optimization environment based on full-wave solutions via surface integral equations and the multilevel fast multipole algorithm (MLFMA). Optimizations are performed by using genetic algorithms, while the required trials are performed accurately via MLFMA. The developed mechanism can handle many different operations, such as portion moving/removing, rotation, and gap opening, that have different effects in the constructed matrix equations but that can efficiently be executed in numerical simulations. The effectiveness of the optimization environment is demonstrated on alternative problems, such as the design of pixel antennas and corrugated sheets for optimal electromagnetic responses.