Document Type



Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence


Electrical and electronic engineering

Publication Details

International Journal of Applied Mathematics, forthcoming 2013, p.1-15,


Simulating the electromagnetic field patterns generated by integrated antennas uses in mobile phones, for example, is fundamental to understanding their transmission characteristics and thereby engineering designs that optimize the directional properties of electromagnetic propagation. Modern integrated antennas have complex three-dimensional geometry designed to optimize their performance in terms of their multi-band and multi -modal attributes. This geometry, coupled with their close proximity to other component of the device (such as the battery and Printed Circuit Board, for example) produce complex field patterns due to the scattering of the electric (and magnetic) field within a spatial domain that is the same order of scale as the wavelength. Simulating this interaction therefore requires models that are generalized and not specific to an idealized antenna geometry. In this paper, we present a three-dimensional model for simulating the interaction of an electromagnetic field generated by antennas whose geometry is arbitrary with complex dielectric components in the near-field, in particular, the Fresnel zone. The resulting field pattern is then taken to a secondary source, whose far-field intensity map is computed by application of a Fourier transform. The material properties of the dielectric are taken to include variations in the relative permittivity and conductivity which are assumed to be isotropic. The evaluation of the scattered electromagnetic field is undertaken using a new approach based on a free space Green's function to the Poisson equation whose properties are compared to the conventional Green's function solution to the inhomogeneous Helmholtz equation. Some example simulations are provided to illustrate the approach used which include fractal antennas based on self-similar patterns.