Semi-analytic approach for electromagnetic problems of large arrays structures

Abstract

There are limited electromagnetic problems which have closed form analytic solutions. Most of the real-world electromagnetic problems like electromagnetic scattering, electromagnetic radiation, waveguide modeling, etc., are not analytically calculable, because of the multitude of irregular geometries found in actual devices. Numerical computational techniques can be used as alternative method to overcome the inability of deriving closed form solutions of Maxwell's equations under various constitutive relations of media, and boundary conditions. This makes computational electromagnetics important in microwave, RF and photonic areas. Care must be taken into choosing the right method; otherwise the wrong method can either yield incorrect results, or results which take excessively long or demand great computational resources. Moreover, there are important electromagnetic problems for which numerical method solutions are challenging, if not impossible. Large non-periodic array of dipoles and multilayer spheres are examples of those problems. Some of these problems, because of their specific geometries and characteristics, can be modeled accurately and efficiently by applying Discrete Dipole Approximation (DDA), multipole expansion and translation addition theorem. The usual solution approach is to model the electromagnetic fields, or other unknowns, using multipole expansions, truncate appropriately the infinite summations, apply the boundary conditions, and then solve the resulting matrix problem by numerical methods. Because the approach contains both of analytic methods and numerical matrix solvers, it can be considered as a semi-analytic approach.