Quantization of surface charge density on hyperboloidal and paraboloidal domains with application to plasmon decay rate on nanoprobes

Abstract

Field quantization in high curvature geometries help understanding the elastic and inelastic scattering of photons and electrons in nanostructures and probe-like metallic domains. The results find important applications in high-resolution photonic and electronic modalities of scanning probe microscopy, nano-optics, plasmonics, and quantum sensing. We present a calculation of relevant photon interactions in both hyperboloidal and paraboloidal material domains. The two morphologies are compared for their plasmon dispersion properties, field distributions, and radiative decay rates, which are shown to be consistent with the corresponding quantities for the finite prolate spheroidal domains. The results are relevant to other material domains that model a nanostructure such as a probe tip, quantum dot, or nanoantenna.

Surface plasmon enhanced fast electron emission from metallised fibre optic nanotips

“…Plasmon bands in other nanostructures of similar size and curvature also yield a spectral peak associated with excitation of specific normal modes of the surface charge density in the gold thin film of a given curvature [24,25]. From the presented analytical calculations of the nonretarded plasmon dispersion relations for a gold-coated dielectric probe, the availability of several symmetric and anti-symmetric modes for the charge density oscillations can be observed.…”

“…To model the observed photonic signal, in principle the quasistatic formulation discussed earlier can be used to obtain the near-field distribution corresponding to a given set of eigenvalues (m,q); the higher the plasmon momentum q, the higher the charge density oscillation along the hyperboloidal surface. However, to avoid further analytical complexities [25], in order to investigate whether the experimentally observed photonic spectral peak can be predicted theoretically on the basis of plasmon excitation near the tip apex, we further employed the FDTD technique to numerically compute the fields. Within the FDTD computational domain, a 2 μm long probe with an apex radius of curvature of 50 nm was created for a silica core and a 50 nm thin film of gold.…”

“…By coupling a laser beam of suitable wavelength into the fibre, plasmons are excited in the curved metallic film at the tapered end. Theoretical studies [24,25] of surface plasmons excited at the metal-dielectric interface suggest the corresponding modes undergo a curvature-induced dispersion modification. As a result, useful resonant modes can be extended to the visible wavelength range in order to attain field enhancement at the apex of the probe.…”

Electromagnetic-field imbalance in surface plasmon polariton and its role in slow propagation and field-matter interaction

“…SPP modes in a metal sphere have small radiative decay rates [32]. Only low energy dipole or quadrupole modes contribute to the far field radiation in the SPP excited around a metal nanotip [42]. We expect the small energy flux induced by the reduced magnetic field to be related to such small radiative decay rates.…”

General Approach to Study Geometric Effects on Classical & Quantum Fields & Eigenmodes of Particles with Finite & Infinite Extend for Applications in Plasmonics & Scanning Probe Microscopy

“…In the next chapter, we apply the whole procedure given in the current chapter to two infinite geometries as solid paraboloid and hyperboloid and one finite geometry, prolate spheroid. The results for these two cases have been provided in [1].…”