Multipolar Analysis of Ordered and Disordered Metasurfaces

Optical metasurfaces are 2D arrangements of nanoparticles that enable abrupt modulation of an impinging light wavefront within an ultra-thin surface. They are promising candidates to replace bulky conventional optical components such as mirrors, lenses, diffusers, etc. The rapid growth of nanofabrication and a constantly increasing demand for miniaturization have made metasurface’s design with desired optical functionalities an ever-growing necessity. Analytical tools that can provide physical insights and improved design capabilities are crucial for that aim, and are the center of attention in this thesis. Based on a local-coordinate transition matrix (T-matrix) method, we aim at providing analytical insights to both ordered and disordered metasurfaces. The local-coordinate T-matrix method provides a comprehensive analytical tool to monitor the changes in the effective response of the nanoparticles inside a lattice.


For periodic metasurface made from identical nanoparticles, despite their abundance and importance, closed-form analytical expressions describing their optical response have not been reported, and most attempts have been predominantly approximations. ... mehrIn this thesis, we provide a comprehensive and unifying multipolar theory for periodic metasurfaces that describes the scattering analytically and enables the derivation of a closed-form expression for the optical response. Our analytical expressions are valid for diffraction orders under oblique and normal incidences up to an octupolar order. In this formalism, we link the macroscopic optical response of the metasurface to the optical response of the individual nanoparticles (via their T or polarizability matrix) and the lattice coupling matrix. Furthermore, we extensively explore the symmetries of the optical response of the nanoparticles inside and outside different lattices. Moreover, we propose several designs based on the insights from these expressions throughout the thesis.

In particular, we study Huygens’ metasurfaces and their limits and capabilities. They are made from non-absorbing and equally induced electric and magnetic moments and are reflection-less. The reflection suppression enables efficient modulation of an optical wavefront without absorption losses.


To investigate disordered metasurfaces, we have resorted to statistical measures such as configurational entropy, structure factor, and pair correlation function. We introduce multiple disordered point configurations in metasurfaces, and study the optical response in correlation to their statistical measures. In particular, we have identified critical disorder regimes where the zeroth-order transmission and reflection go to zero, and the light is diffused to all non-specular directions. Driven from the insights, we have investigated metasurface-based optical diffusers.

The thesis follows a systematic and step-by-step approach. It seeks to provide a solid and comprehensive reference for future research on the topic.