# Field Quantization for Radiative Decay of Plasmons in Finite and Infinite Geometries

## TL;DR

This paper develops a quantum field theory framework for plasmons in nanostructures, enabling calculation of their radiative decay rates across various geometries relevant to nanotechnology and quantum sensing.

## Contribution

It introduces a quasistatic quantization method for plasmons in complex geometries and derives analytical expressions for their radiative decay rates.

## Key findings

- Quantized plasmon fields are obtained for multiple geometries.
- Analytical decay rate formulas are derived using perturbation theory.
- The approach applies to both finite and infinite nanostructures.

## Abstract

We investigate field quantization in high-curvature geometries. The models and calculations can help with 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. Quasistatic formulation, leading to nonretarded quantities, is employed and justified on the basis of the nanoscale, here subwavelength, dimensions of the considered domains of interest. Within the quasistatic framework, we represent the nanostructure material domains with frequency-dependent dielectric functions. Quantities associated with the normal modes of the electronic systems, the nonretarded plasmon dispersion relations, eigenmodes, and fields are then calculated for several geometric entities of use in nanoscience and nanotechnology. From the classical energy of the charge density oscillations in the modeled nanoparticle, we then derive the Hamiltonian of the system, which is used for quantization. The quantized plasmon field is obtained and, employing an interaction Hamiltonian derived from the first-order perturbation theory within the hydrodynamic model of the electron gas, we obtain an analytical expression for the radiative decay rate of the plasmons. The established treatment is applied to multiple geometries to investigate the quantized charge density oscillations on their bounding surfaces. Specifically, using one sheet of a two-sheeted hyperboloid of revolution, paraboloid of revolution, and cylindrical domains, all with one infinite dimension, and the finite spheroidal and toroidal domains are treated. ...