Discrete dipole approximation with surface interation (DDA-SI) kullanarak nano parçacıklarının dielectiric üzerindeki yüzey plazmon rezonansının modellenmesi

Analysis of surface plasmon resonance of arbitrary shape nano-particles on a substrate is important for many engineering applications. The strong optical absorption of noble metal nano-particles is due to the localized surface plasmon, which enables the development of novel applications such as surface enhanced Raman spectroscopy based biological sensing, optical transparency based sensors, and uni-directional nanoantennas. Size, shape, and distance between nano-particles on a surface are the key factors in the design of these structure. Usually, these systems utilize noble material such as gold which is deposited on a dielectric surface. Tuning the structures of the noble metals increases the local absorption e ciency of light within speci c frequency ranges, depending rely on the nal design of the system. Understanding the physics of plasmon phenomena and its relation with these parameters should be studied in depth. This thesis provides a theoretical study and a numerical validation of the coupled phenomena that occurs between gold nano-particles on a dielectric substrate where the nano-particles have di erent shapes and separation distances. Numerical study of nano-particles on a substrate is carried out using Discrete Dipole Approximation with Surface Interaction (DDA-SI) approach. The DDA-SI is based on the discretization of the nano-particles to dipoles for solving volume integral of Maxwell s equations and Green s dyadic tensor of electric eld within the dipoles to calculate the optical properties of arbitrarily shaped, non-homogeneous, anisotropic objects. There are some renowned open sources packages for DDAs. These packages are mostly used for calculating the interaction of particles in a free space with direct wave propagating. However, in order to calculate the light scattering from objects placed on a substrate, the substrate itself also is required to be approximated by the dipoles which increase the computational time remarkably. In this study, we used the Discrete Dipole Approximation with Surface Interaction (DDA-SI) which is an open source MATLAB based software package for calculation of optical properties of nano-particles (extinction, absorption and scattering) on a substrate. It can be used to investigate both the near- and far- eld e ects and accounts for the coupling between di erent particles on the surface. This study focuses on speci c geometries such as cube, spheroid and triangular geometries, each of varying sizes and separation distances from each other. Apart from studying the plasmon resonance of individual nano-particle on a dielectric substrate, a system with more nano-particles is scrutinized. It is found out that as the distance between particles decreases, the plasmon resonance frequency is pushed into the infrared region due to the inter-particle coupling, and the redshift becomes dominant. Furthermore, we found out that the coupling e ect becomes negligible if the ratio of their distance between nano-particles to the radius, c = d=a, is greater than three. During this study, the main DDA-SI toolbox is further developed, vecrorized and optimized numerically which named DDA-SI-3 in order to calculate the optical properties of noble metals. The imaginary component of refractive index for noble metals for larger wavelengths is large and make the calculation challenging. Therefore, we applied the new numerical method to calculate the linear system of DDA-SI in order to achieve more precise, faster and stable calculations. The structure of interaction matrix is studied and for this, speci c preconditioning matrices are extracted. It is also found out that the use of the least square method, with the proper preconditioning matrices for iteratively solving the linear system, yields results to achieve more accurate and relatively faster calculation.