T-matrix modelling of plasmonic nanoparticle arrays

Active nanoparticle arrays are an attractive platform for manipulating light-matter interactions on the nanoscale. The multiscale character of the optical response of those systems gives rise to exciting physical phenomena, but also makes precise numerical modelling challenging, as it encompasses the interplay of mid-to-long-range periodicity, response of the individual nanoparticles with spatial features much smaller than the wavelength, and possibly nonlinear dynamics of the active medium. This thesis focuses on the development of the multiple-scattering T-matrix method (MSTMM; also known as the superposition T-matrix method) and its applications in modelling the optical properties of plasmonic nanoparticle arrays. MSTMM is a linear model that combines a computationally efficient (due to a dramatic reduction of the degrees of freedom) yet precise description of the optical interactions between the nanoparticles with a faithful model of linear optical response of the individual nanoparticles. Chapter 1 reviews some of the commonly used approaches to the numerical simulations, compares their theoretical modelling capabilities and practical scalability with regards to nanoparticle arrays, and provides a motivation for employing the multiple-scattering T-matrix approach. Chapter 2 is dedicated to the theory of MSTMM and its developments aimed to broaden its applicability to a larger class of physical systems. Its first sections provide a brief guide through the basic concepts of vector spherical wavefunctions, T-matrix and translation operators that make the theoretical backbone of MSTMM in finite systems. The method is then expanded in two main directions: (1) Using exponentially convergent lattice summation, MSTMM is extended to infinite periodic arrays. This enables fast computation of transmission and (employing nonlinear eigensolvers) photonic band structure. (2) The computational efficiency of the method is enhanced by taking into consideration the symmetries of the arrays, which considerably improves the array sizes the method can handle in practice. The group theoretical considerations also find their use in lattice mode analysis. Chapter 3 showcases MSTMM on several examples, including analysis of some real-world lasing experiments with plasmonic nanoarrays, where the method was used for explaining the observed lasing modes. Chapter 4 discusses possible utilisation of MSTMM in nonclassical context, mainly in the framework of macroscopic quantum electrodynamics