Heat Generation using Lorentzian Nanoparticles: Estimation via Time-Domain Techniques

TL;DR

This paper develops a time-domain integral equation method to estimate heat generation in Lorentzian nanoparticles, highlighting how different incident frequencies influence their plasmonic or dielectric behavior and resulting heat.

Contribution

It introduces a novel time-domain approach to analyze heat generation in nanoparticles modeled by the Lorentzian framework, avoiding Fourier transforms and explicitly linking heat to electromagnetic properties.

Findings

Heat is primarily determined by the electric field and material properties.

Different incident frequencies lead to plasmonic or dielectric behaviors.

The method provides explicit heat estimates based on eigenvalues and eigenfunctions.

Abstract

We analyze the mathematical model that describes the heat generated by electromagnetic nanoparticles. We use the known optical properties of the nanoparticles to control the support and amount of the heat needed around a nanoparticle. Precisely, we show that the dominant part of the heat around the nanoparticle is the electric field multiplied by a constant dependent, explicitly and only, on the permittivity and quantities related to the eigenvalues and eigenfunctions of the Magnetization (or the Newtonian) operator, defined on the nanoparticle, and inversely proportional to the distance to the nanoparticle. The nanoparticles are described via the Lorentz model. If the used incident frequency is chosen related to the plasmonic frequency $\omega_p$ (via the Magnetization operator) then the nanoparticle behaves as a plasmonic one while if it is chosen related to the undamped resonance frequency $\omega_0$ (via the Newtonian operator), then it behaves as a dielectric one. The two regimes exhibit different optical behaviors. In both cases, we estimate the generated heat and discuss advantages of each incident frequency regime. The analysis is based on time-domain integral equation techniques avoiding the use of (formal) Fourier type transformations.