Nanoparticles optimal shape designing in the cylindrical coordinate to use for optical devices

Abstract

Nanoparticles have unique optical properties that can enhance the performance of optical devices. In this regard size and shape of nanoparticles are very important factors that influence these properties. Although there are many different sample shapes of nanoparticles but researchers have not yet identified the best shape to use, especially in general. This article presents a mathematical model to determine the optimal shape of nanoparticles for use in various optical devices. We use the shape-measure method in cylindrical coordinates to solve this problem. This method has many advantages like it is independent of the initial shape and transforming the optimal shape design problem into a simple optimization one, even in strongly nonlinear cases. The use of cylindrical coordinates also makes calculations faster and more straightforward. First the optical properties of nanoparticles is described by using the discrete dipole method; then, simultaneously the optimal surface and image for the optimal shape and size of the nanoparticles are determined. Numerical simulations are also provided to demonstrate the effectiveness and benefits of the new approach.