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. In 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

Fundamental Limits of Optical Force and Torque

Optical force and torque provide unprecedented control on the spatial motion of small particles. A valid scientific question, that has many practical implications, concerns the existence of fundamental upper bounds for the achievable force and torque exerted by a plane wave illumination with a given intensity. Here, while studying isotropic particles, we show that different light-matter interaction channels contribute to the exerted force and torque; and analytically derive upper bounds for each of the contributions. Specific examples for particles that achieve those upper bounds are provided. We study how and to which extent different contributions can add up to result in the maximum optical force and torque. Our insights are important for applications ranging from molecular sorting, particle manipulation, nanorobotics up to ambitious projects such as laser-propelled spaceships.Comment: 5 pages, 5 figures, 2 tables, Supplemental Material (27 pages, 6 figures

Self-stabilizing curved metasurfaces as a sail for light-propelled spacecrafts

Laser-driven spacecrafts are promising candidates for explorations to outer space. These spacecrafts should accelerate to a fraction of the speed of light upon illumination with earth-based laser systems. There are several challenges for such an ambitious mission that needs to be addressed yet. A matter of utmost importance is the stability of the spacecraft during the acceleration. Furthermore, the spacecraft sails should effectively reflect the light without absorptive-overheating. To address these requirements, we propose the design of a lightweight, low-absorbing, high-reflective, and self-stabilizing curved metasurface made from c-Si nanoparticles. A method to determine the stability is presented and, based on the multipole expansion method, the rotational stability of the curved metasurfaces is examined and the optimal operating regime is identified. The curvature is shown to be beneficial for the overall stability of the metasurface. The validity of the method is verified through numerical simulations of the time evolution of the trajectory of an identified metasurface. The results show that curved metasurfaces are a promising candidate for laser-driven spacecrafts

Optical Force and Torque on Dipolar Dual Chiral Particles

On the one hand, electromagnetic dual particles preserve the helicity of light upon interaction. On the other hand, chiral particles respond differently to light of opposite helicity. These two properties on their own constitute a source of fascination. Their combined action, however, is less explored. Here, we study on analytical grounds the force and torque as well as the optical cross sections of dual chiral particles in the dipolar approximation exerted by a particular wave of well-defined helicity: A circularly polarized plane wave. We put emphasis on particles that possess a maximally electromagnetic chiral and hence dual response. Besides the analytical insights, we also investigate the exerted optical force and torque on a real particle at the example of a metallic helix that is designed to approach the maximal electromagnetic chirality condition. Various applications in the context of optical sorting but also nanorobotics can be foreseen considering the particles studied in this contribution.Comment: 7 pages, 5 figure

All-dielectric reciprocal bianisotropic nanoparticles

The study of high-index dielectric nanoparticles currently attracts a lot of attention. They do not suffer from absorption but promise to provide control on the properties of light comparable to plasmonic nanoparticles. To further advance the field, it is important to identify versatile dielectric nanoparticles with unconventional properties. Here, we show that breaking the symmetry of an all-dielectric nanoparticle leads to a geometrically tunable magneto-electric coupling, i.e. an omega-type bianisotropy. The suggested nanoparticle exhibits different backscatterings and, as an interesting consequence, different optical scattering forces for opposite illumination directions. An array of such nanoparticles provides different reflection phases when illuminated from opposite directions. With a proper geometrical tuning, this bianisotropic nanoparticle is capable of providing a $2\pi$ phase change in the reflection spectrum while possessing a rather large and constant amplitude. This allows creating reflectarrays with near-perfect transmission out of the resonance band due to the absence of an usually employed metallic screen.Comment: 7 pages, 6 figure

Colossal enhancement of the magnetic dipole moment by exploiting lattice coupling in metasurfaces

An artificial magnetic response is not only intellectually intriguing but also key to multiple applications. While previously suitably structured metallic particles and high-permittivity dielectric particles have been used for this purpose, here, we highlight the possibility of exploiting lattice effects to significantly enhance an intrinsically weak magnetic dipole moment of a periodically arranged scatterer. We identify the effective magnetic dipole moment as it is modulated by the lattice and coupled to other electromagnetic multipole moments the scatterer can sustain. Besides a more abstract consideration on the base of parametrized Mie coefficients to study the theoretical upper limit, we present an actual particle that shows an enhancement of the magnetic dipole moment by 100 with respect to what is attainable as a maximal value for an isolated particle