Selective and Collaborative Optimization Methods for Plasmonics: A Comparison

In this paper, we optimize the size parameters of hollow nanospheres and nanoshells used in cancer photothermal therapy and we focus on two practical therapy cases: the visible range for shallow cancer and the near infrared for deep cancer. For this, we consider analytical models: the Mie theory for coated spheres. The investigated optimization methods are the Evolutionary Method (EM) and the Particle Swarm Optimization (PSO) which are based on competitiveness and collaborative algorithms, respectively. A comparative study is achieved by checking the e-ciency of the optimization methods, to improve the nanoparticles e-ciency. The biomedical application of plasmonic resonances of metal nanostructures, taking advantage of the acute interaction, between light and metallic objects, remains an open domain even if some recent experimental studies have been already devoted to applications. For instance, the flrst suc- cesses of cancer treatment using nanoparticle-based photothermal therapy (PTT) are encouraging for more investigation in this fleld to ensure strong and tunable surface plasmon resonance (SPR) for e-cient heat conversion. Nevertheless, at our knowledge, up to now, no optimization method has been developed to improve the e-ciency of these plasmonic structures, through the mastering of the nanoparticles shape and size. The nanoshells and the hollow nanospheres are among the most commonly used nanoparticles for PTT. The nanoshells are made of a silica core coated with a thin gold shell while the hollow nanospheres look like a gold bubble. For PTT applications, the illumination of the nanostructure induces an elevation of temperature which is used to burn the cancer cells. The absorption band of these particles can be tuned by adjusting the thickness of the gold shell and the inner radius and thus would enable both strong scattering and absorption e-ciency (1). Therefore, they can be used as contrast agents with dual functions for imaging as well as therapy. In this study, the target is to maximize the electromagnetic absorption of either the nanoshell, or of the hollow nanosphere, computed using the Mie theory (coated sphere) (2), responsible for heating process in PTT. For this, two optimization methods are investigated. The meta-heuristics used in this study are the Evolutionary Method (EM) which is based on competitiveness and the Particle Swarm Optimization (PSO) which is based on a collaborative search algorithm. Some modiflcations of these conventional methods were proposed (3,4) to get faster convergence in the optimization of planar biosensor. The optimization of nanoparticles difiers from the one of planar biosensor in terms of the mathematical properties of the model (difierent topology) | even if the best parameters should correspond in both cases to a plasmon resonance | and the target of the optimization (the maximum of absorbed intensity in the metal instead of the maximum of the re∞ected intensity). It should be mentioned that a problem of optimization in plasmonics is based on a complex model of interaction between light and matter, depending on many material and geometrical parameters, and therefore requires always the use of rapid optimization method. This paper is organized as follows: the second section presents the PTT using gold nanoshell, hollow nanosphere and other nanoparticles. In the third section, the optimization methods used in this study are brie∞y described. In the fourth section, simulation results in some commonly used experimental conditions are presented and discussed before concluding.