Variations of focal regions versus numbers and positions of sources in two-dimensional media

Abstract

This paper explores the behaviour of the primary and secondary hot spots in homogeneous and two-dimensional inhomogeneous medium. Circular arrays are considered with a radius of up to five wavelengths. The number of sources and their positions in the array are varied, and the influence of these variations on the primary and secondary hot spots is observed. It is found that the primary hot spot reaches its final shape with the addition of a very small number of sources to the array. An increase in the number of sources results in a reduction of the normalized magnitude of the secondary hot spots, but the size of the normalized primary hot spot remains the same. An upper limit of sources in the array exists after which no further reduction of the secondary hot spots is observed. The finite-difference time-domain method (FDTD) is used to obtain the electric-field distribution in the inhomogeneous medium. A genetic algorithm is then applied to find the optimal positions of the antennae in the array.