Heat Generation Using Lorentzian Nanoparticles. The Full Maxwell System

TL;DR

This paper analyzes heat generation near dispersive Lorentzian nanoparticles excited by electromagnetic waves, extending previous 2D results to the full Maxwell system, with implications for medical and material applications.

Contribution

It extends prior 2D analyses to the full Maxwell system, providing a comprehensive mathematical model for heat generation near nanoparticles under electromagnetic excitation.

Findings

Heat can be controlled by tuning incident frequencies near resonances.

Heat concentration is highest close to the nanoparticle and decreases with distance.

The model applies to plasmonic and dielectric nanoparticles in various applications.

Abstract

We analyse and quantify the amount of heat generated by a nanoparticle, injected in a background medium, while excited by incident electromagnetic waves. These nanoparticles are dispersive with electric permittivity following the Lorentz model. The purpose is to determine the quantity of heat generated extremely close to the nanoparticle (at a distance proportional to the radius of the nanoparticle). This study extends our previous results, derived in the 2D TM and TE regimes, to the full Maxwell system. We show that by exciting the medium with incident frequencies close to the Plasmonic or Dielectric resonant frequencies, we can generate any desired amount of heat close to the injected nanoparticle while the amount of heat decreases away from it. These results offer a wide range of potential applications in the areas of photo-thermal therapy, drug delivery, and material science, to cite a few. To do so, we employ time-domain integral equations and asymptotic analysis techniques to study the corresponding mathematical model for heat generation. This model is given by the heat equation where the body source term comes from the modulus of the electric field generated by the used incident electromagnetic field. Therefore, we first analyse the dominant term of this electric field by studying the full Maxwell scattering problem in the presence of Plasmonic or All-dielectric nanoparticles. As a second step, we analyse the propagation of this dominant electric field in the estimation of the heat potential. For both the electromagnetic and parabolic models, the presence of the nanoparticles is translated into the appearance of large scales in the contrasts for the heat-conductivity (for the parabolic model) and the permittivity (for the full Maxwell system) between the nanoparticle and its surrounding.