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About this book

This book provides an overview of the use of toroidal moments. This includes methods of excitation, numerical analysis, and experimental measurements of associating structures. Special emphasis is placed on understanding the fundamental physics, characteristics, and real-world applications of toroidal multipoles.

This book also covers a variety of both planar and 3D meta-atom and metamolecule schemes capable to sustain toroidal moments across a wide range of spectrum. It discusses the implementation of innovative approaches, for exploring the spectral features and excitation methodologies, predicting the properties of the correlating metasystems in their excited states.

An applicable text for undergraduate, graduate, and postgraduate students, this book is also of interest to researchers, theorizers, and experimentalists working in optical physics, photonics, and nanotechnology.

Table of Contents

Frontmatter

Chapter 1. Introduction and Overview

Abstract
Pioneering efforts in understanding the light-matter interactions at subwavelength scales date back to nineteenth and twentieth centuries with the demonstration of electromagnetic wave propagation by breaking the diffraction limit and enhancing near-field effects for light localization. Studies showed that judicious interaction between light and matter leads to the emergence of resonant properties, which encompass an immense domain of physical insights from classical to advanced quantum electrodynamics. While light and matter are different entities, they possess significant influence on each other through some sort of intermediary doer. This has previously been demonstrated by Albert Einstein’s well-known equation, E = mc2, in which both photon energy and matter are the main indicators of the identical entity that are related to each other by the square of the speed of light in vacuum. However, the inherent characteristics of light and matter reveal the difference between these entities, which make the interaction between them consequential. In this limit, the wavelength (λ) of light and geometry of the matter have the key role in defining the properties of these interactions.
Arash Ahmadivand, Burak Gerislioglu, Zeinab Ramezani

Chapter 2. Classical Electrodynamics

Abstract
Classical electrodynamics primarily deals with electromagnetic fields and their interactions caused by macroscopic distributions of charges and currents. In a specific mathematical process, this implies that the charge and current distributions can be confined in infinitesimally small volumes of space. In this Chapter, we firstly introduce the static electric and magnetic fields, and demonstrate how the conservation of electric charge and its relation to electric current leads to the dynamic connection between electricity and magnetism. Then, we discuss how these two were judiciously combined under classical electrodynamics, described by couple of dynamic field equations—the Maxwell equations.
Arash Ahmadivand, Burak Gerislioglu, Zeinab Ramezani

Chapter 3. Expansion of Electromagnetic Multipoles

Abstract
This Chapter presents a complete electromagnetic multipole expansion, effective for all point sources in space, including the presence of toroidal moments. To that end, in light of the provided information in Chap. 2, we utilized the solution of inhomogeneous Helmholtz equations to evaluate the electromagnetic field due to alternating poloidal currents in a toroidal solenoid. This solution was obtained through the use of Green’s functions and Debye potentials for point sources and fields. The achieved results enabled us to show the physical meaning of unconventional toroidal moments, in comparison to the classical electric and magnetic moments. Besides, the analysis in the long wavelength limit clearly demonstrates that the toroidal moments were neglected previously in the multipole expansion.
Arash Ahmadivand, Burak Gerislioglu, Zeinab Ramezani

Chapter 4. Physical Mechanism Behind the Toroidal Multipoles

Abstract
In this chapter, we presented a set of calculations for the radiation intensity, angular momentum loss, and recoil force of the most general type of source, in terms of electric, magnetic, and toroidal multipole moments. In these calculations, we considered a set of studies based on radii of any multipolarity and an arbitrary time dependence. The results are articulated in terms of time derivatives of the multipole moments and mean radii of the associated distributions. To that end, we recalled the equations for the description of electromagnetic multipoles as well as dynamic toroidal moments from Chap. 2. Besides, we employed the classical electrodynamics framework to obtain the rate of angular momentum loss of a time-dependent toroidal dipole, which was derived by Radescu and Vlad (Phys Rev E 57(5):6030, 1998); Radescu and Vaman (Phys Rev E 65:046609, 2002), in connection with a forced precession of the toroidal dipole around a particular axis.
Arash Ahmadivand, Burak Gerislioglu, Zeinab Ramezani

Chapter 5. Toroidal Excitations in Metamaterials

Abstract
Thus far, we showed that toroidal excitations exist in free space as spatially and temporally confined electromagnetic pulses propagating at the velocity of light and interacting with matter. In this Chapter, we presented an exhaustive study on the theoretical and experimental observation of toroidal excitations in both bulk and quasi-infinite artificially structured media, also known as metamaterials. Using the established framework to analyze the toroidal electrodynamics, we discussed the strategies that have been utilized to efficiently excite toroidal modes in well-engineered subwavelength architectures. We initially argued the formation of the toroidal resonances in 3D metamaterials, and later, we revealed that how the flatland metaphotonics successfully addressed the fabrication, simulation, and inherent losses in bulk metastructures.
Arash Ahmadivand, Burak Gerislioglu, Zeinab Ramezani

Chapter 6. Toroidal Metadevices

Abstract
Toroidal excitations in well-engineered media have recently considered as a promising way that feature futuristic optical technologies through controlling radiative losses in both plasmonic and photonic systems. As mentioned in previous Chapters, within the past decade, there has been extensive research over the excitation principles of toroidal multipoles, specifically toroidal dipole, in flatland and 3D metasystems. In this Chapter, we focus on revolutionary devices that have been put in practice based on this notion, including infrared photodetectors, deep ultraviolet (DUV) beam sources, and immunobiosensors. Besides, we argue the vacuum Rabi oscillations through strong plexciton dynamics in this context.
Arash Ahmadivand, Burak Gerislioglu, Zeinab Ramezani
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