Full-wave optimization of three-dimensional photonic-crystal structures involving dielectric rods.

We present rigorous optimization and design of three-dimensional photonic-crystal (PhC) structures involving finite dielectric rods. These types of PhCs are known to be useful in diverse applications, such as imaging, power focusing, filtering, and pattern shaping at optical frequencies. Without resorting to their two-dimensional models, which are commonly used in the literature, we consider PhCs as three-dimensional structures, whose electromagnetic characteristics are optimized via genetic algorithms integrated with an efficient and accurate solver based on the multilevel fast multipole algorithm. In addition to the designs of PhCs that can provide desired output patterns, we present sensitivity tests to understand the critical geometric parameters, as well as to test and evaluate the tolerance of the proposed designs to possible fabrication errors.

Publisher Correction: Full-Wave Electromagnetic Optimisation of Corrugated Metallic Reflectors Using a Multigrid Approach.

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has been fixed in the paper.

Full-Wave Electromagnetic Optimisation of Corrugated Metallic Reectors Using a Multigrid Approach.

A multigrid optimisation strategy is introduced to design passive metallic reflectors with corrugated shapes. The strategy is based on using genetic algorithms at multiple grids and shaping the metal sheets, starting from coarse details to fine tunings. This corresponds to a systematic expansion of the related optimisation space, which is explored more efficiently in comparison to a brute-force optimisation without using grid. By employing the multilevel fast multipole algorithm to analyse the electromagnetic problems corresponding to optimisation trials, we obtain accurately designed reflectors that provide focussing abilities with very high performances at single and multiple locations. The designed reflectors are also resistant to fabrication errors with less complex corrugations and simplified reflection mechanisms compared to those found by no-grid optimisation trials.

Computational electromagnetic analysis of deformed nanowires using the multilevel fast multipole algorithm.

We consider computational analysis of deformed nanowires and their arrays using a full-wave simulation environment based on integral-equation formulations and the multilevel fast multipole algorithm (MLFMA). Without requiring any periodicity assumptions, MLFMA allows for fast and accurate simulations of complex nanowire structures with three-dimensional geometries and random deformations. We present the results of hundreds of simulations, where deformed nanowires are considered as isolated, as well as in array configurations, and their scattering characteristics are compared to those of non-deformed ones. Based on the simulation results, we rigorously investigate common effects of deformations on scattering properties of nanowires and identify strong field enhancements in forward-scattering directions.

Fast and accurate analysis of large-scale composite structures with the parallel multilevel fast multipole algorithm.

Accurate electromagnetic modeling of complicated optical structures poses several challenges. Optical metamaterial and plasmonic structures are composed of multiple coexisting dielectric and/or conducting parts. Such composite structures may possess diverse values of conductivities and dielectric constants, including negative permittivity and permeability. Further challenges are the large sizes of the structures with respect to wavelength and the complexities of the geometries. In order to overcome these challenges and to achieve rigorous and efficient electromagnetic modeling of three-dimensional optical composite structures, we have developed a parallel implementation of the multilevel fast multipole algorithm (MLFMA). Precise formulation of composite structures is achieved with the so-called "electric and magnetic current combined-field integral equation." Surface integral equations are carefully discretized with piecewise linear basis functions, and the ensuing dense matrix equations are solved iteratively with parallel MLFMA. The hierarchical strategy is used for the efficient parallelization of MLFMA on distributed-memory architectures. In this paper, fast and accurate solutions of large-scale canonical and complicated real-life problems, such as optical metamaterials, discretized with tens of millions of unknowns are presented in order to demonstrate the capabilities of the proposed electromagnetic solver.

Solutions of large-scale electromagnetics problems involving dielectric objects with the parallel multilevel fast multipole algorithm.

Fast and accurate solutions of large-scale electromagnetics problems involving homogeneous dielectric objects are considered. Problems are formulated with the electric and magnetic current combined-field integral equation and discretized with the Rao-Wilton-Glisson functions. Solutions are performed iteratively by using the multilevel fast multipole algorithm (MLFMA). For the solution of large-scale problems discretized with millions of unknowns, MLFMA is parallelized on distributed-memory architectures using a rigorous technique, namely, the hierarchical partitioning strategy. Efficiency and accuracy of the developed implementation are demonstrated on very large problems involving as many as 100 million unknowns.

Computational study of scattering from healthy and diseased red blood cells.

We present a comparative study of scattering from healthy red blood cells (RBCs) and diseased RBCs with deformed shapes. Scattering problems involving three-dimensional RBCs are formulated accurately with the electric and magnetic current combined-field integral equation and solved efficiently by the multilevel fast multipole algorithm. We compare scattering cross section values obtained for different RBC shapes and different orientations. In this way, we determine strict guidelines to distinguish deformed RBCs from healthy RBCs and to diagnose various diseases using scattering cross section values. The results may be useful for designing new and improved flow cytometry procedures.