Nano‐antenna synthesis for end‐fire and pencil‐beam far‐field radiation patterns using vector spherical wave functions

Abstract

Two sets of irregularly placed dielectric nano-spheres are synthesised as two nano-antennas. One of them has an end-fire and the other has a pencil-beam far-field radiation pattern. The electrical sizes (radiuses) and relative permittivities of all spheres are chosen to be 0.1 and 4, respectively. An incident plane-wave is illuminated on spheres. The aim is to find the optimal positions of spheres to scatter the incident wave similar to the end-fire and pencil beam radiation patterns. At first, the numbers of spheres of the nano-antennas are determined. Next, a random three-dimensional distribution of spheres is considered. Desired pencil-beam and end-fire patterns besides all scattered and incident waves are expanded to vector spherical wave functions. Therefore, the analysis is performed in the spectral domain of the spherical harmonics. The multiple scattering between spheres is considered. Coefficients of scattered waves are calculated by applying boundary conditions on the surface of all spheres. The aggregate difference of coefficients of total far-field scattering waves and coefficients of the desired far-field pattern is considered as a cost-function for an optimisation method. Particle swarm optimisation tool is used to optimise the positions of spheres to decrease the cost value. This process is done in several iterations. It is shown that by increasing the number of iterations, the value of cost function is decreased. So, this is an efficient method to design antennas including nano-antennas for any arbitrary radiation pattern and polarisation.