Synthesis of Nano-Antennas for Desired Far-Field Radiation Patterns Using Vector Spherical Harmonics

A theoretical method is proposed and applied to design a nano-antenna consisting of a number of dielectric spherical nano-particles to scatter the incident plane-wave in an arbitrary pattern. Two known pencil-beam and end-fire radiation patterns are considered as desired patterns. Also, a radiation pattern suitable for solar cell applications is synthesized. The permittivity and electrical size of spheres are chosen to be similar for all spheres. An electromagnetic plane wave is impinged on spheres. Multiple scattering occurs between spheres. Finally, total scattering is calculated using boundary conditions. All calculations are based on the expansion of all electromagnetic waves into vector spherical wave functions. As the method of analyzing the scattering of small dielectric spheres is proposed, the particle swarm optimization tool is implemented to find the positions of spheres optimally. The optimization tool is applied to have an approximately desired scattering pattern. It is observed that an increased number of iterations of optimization tools increases the accuracy of the scattering pattern of spheres.