Mathematical modeling of the photoacoustic effect generated by the heating of metallic nanoparticles

Triki, Faouzi; Vauthrin, Margaux

doi:10.1090/qam/1502

Authors: Faouzi Triki and Margaux Vauthrin
Journal: Quart. Appl. Math. 76 (2018), 673-698
MSC (2010): Primary 35B30, 35R30
DOI: https://doi.org/10.1090/qam/1502
Published electronically: February 22, 2018
MathSciNet review: 3855826
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Abstract: This paper is devoted to the modeling of the photoacoustic effect generated by the electromagnetic heating of metallic nanoparticles embedded in a biological tissue. We first derive an asymptotic model for the plasmonic resonances and the electromagnetic fields. We then describe the acoustic generation created by the electromagnetic heating of the nanoparticle. Precisely, we derive the model equations that describe the coupling between the temperature rise in the medium and the acoustic wave generation. We obtain a direct relation between the acoustic waves and the electromagnetic external sources. Finally, we solve the multiwave inverse problem that consists in the recovery of the electric permittivity of the biological tissue from the measurements of the generated acoustic waves on the boundary of the sample.

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