Light-matter interactions with Flying Doughnuts

Abstract

The field of toroidal electrodynamics has gained attention following the detection of toroidal dipole excitations in metamaterials in 2010. Distinct from electric and magnetic dipoles, a toroidal dipole is a localised electromagnetic excitation that corresponds to currents flowing on the surface of a torus. The electromagnetic radiation from toroidal dipole excitations can destructively interfere with the radiation from other modes of excitation, providing a new mechanism of induced transparency and scattering suppression. Toroidal electrodynamics expands with the observation of toroidal light pulses, also known as Flying Doughnuts (FD), which propagate in free space at the speed of light. FDs are solutions to Maxwell’s equations introduced by Hellwarth and Nouchi in 1996, which possess toroidal topology and exist only as short bursts of electromagnetic energy. However, it is little known about how these toroidal pulses interact with matter. This thesis reports on the interaction of toroidal light pulses with matter, focusing on toroidal excitations and non-radiating modes.

I have numerically demonstrated supertoroidal anapoles, which are non-radiating charge current configurations that involve supertoroidal currents. Supertoroidal currents are fractal current configurations where each iteration replaces the previous one with a toroidal current loop, accompanied by a toroidal solenoidal current forming the smallest loop. Unlike conventional anapoles formed by the destructive interference of electric and toroidal dipoles, supertoroidal anapoles consist of the interference of a toroidal dipole, the first-order mean square radius of the toroidal dipole, and an electric dipole. I also observed (numerically) the higher-order anapoles formed from quadrupoles and octupoles of electric and toroidal type. I show numerically that under illumination with an FD pulse, scattering from a dielectric torus is substantially suppressed by supertoroidal anapoles by more than 72%. Further, I studied supertoroidal anapoles’

dependence on the torus’s geometric parameters. I discovered that a dielectric torus with the largest major radius R and the smallest minor radius r is the best strategy to support supertoroidal anapoles, where R ≫ r and R+r < λ. Moreover, I show that, in contrast to plane wave illumination, FD illumination suppresses scattering by an order of magnitude due to supertoroidal anapoles.

I demonstrated that by carefully tuning the geometric parameters of a dielectric disc, it is possible to engineer anapole modes (scattering suppression) over a broad bandwidth of 315nm within the wavelength range from 665nm to 980nm with the maximum suppression at 780nm, when transverse magnetic (TM) FD is an illuminating source and a disc-shaped particle is the scatterer. Further, I show that the disc radius defines the anapole excitation wavelength, and the disc height defines the bandwidth of the anapole; the taller the disc (h < λ), the broader the anapole. Additionally, I show the electric and toroidal dipoles and the anapole mode in the transient regime. I also demonstrate that even though the duration of the incident pulse is ≈ 4 fs, the excitations take up to 15 fs to dissipate their energy through electromagnetic radiation. Further, I investigated the effect of material loss on scattering suppression and observed broadly similar behaviour to lossless material, supporting broad and strong anapole modes. Moreover, unlike plane wave illumination, I report that FD illumination suppresses scattering by an order of magnitude due to the conventional anapole modes.

I also investigated the interaction of FD with films and curved interfaces. I demonstrated that the reflection of transverse electric (TE) FD on dielectric film and plasmonic films is 20% and 15% stronger, respectively, compared to TM FD illumination. Moreover, the multipole expansion of displacement current within a high-index dispersive film reveals that the scattering is mediated by the combination of electric and toroidal dipoles (however, their contributions cannot be distinguished with the exact multipole expressions). Investigating FD interactions with curved interfaces shows that the radial spectra distribution of FD does not change upon reflection from the curved interface, which ensures that FD survives after interacting with a curved interface. The findings of FD interactions with curved interfaces are crucial for the experimental realisation of FD-matter interaction, as such experiments involve curved optical components such as parabolic mirrors for the tight focusing of FD.

The findings outlined in this thesis contribute to the expanding field of toroidal electrodynamics, firmly establishing its potential for diverse applications, including sensing and spectroscopy using toroidal light sources, anapole nanolasers, anapole-assisted absorption engineering applications, and beyond.

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Identifiers

ORCID for Resmi Ravi Kumar: orcid.org/0000-0002-1551-2792

ORCID for Nikitas Papasimakis: orcid.org/0000-0002-6347-6466

ORCID for Nikolay Zheludev: orcid.org/0000-0002-1013-6636

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