From Mie to Fresnel through effective medium approximation with multipole contributions

Abstract

The Mie theory gives the exact solution to scattering from spherical particles while the Fresnel theory provides the solution to optical behavior of multilayer thin film structures. Often, the bridge between the two theories to explain the behavior of materials such as nanoparticles in a host dielectric matrix, is done by effective medium approximation (EMA) models which exclusively rely on the dipolar response of the scattering objects. Here, we present a way to capture multipole effects using EMA. The effective complex dielectric function of the composite is derived using the Clausius–Mossotti relation and the multipole coefficients of the approximate Mie theory. The optical density (OD) of the dielectric slab is then calculated using the Fresnel approach. We have applied the resulting equation to predict the particle size dependent dipole and quadrupole behavior for spherical Ag nanoparticles embedded in glass matrix. This dielectric function contains the relevant properties of EMA and at the same time predicts the multipole contributions present in the single particle Mie model.

PAME: Plasmonic Assay Modeling Environment

“…Even if exotic nanoparticle are incorporated into PAME, they would still need to be homogenized through an effective mixing theory to fit the TMM multilayer model. While classical EMTs can account for non-spherical inclusions through a dipole polarizability parameter (Garcıa et al, 1999;Quinten, 2011), modern two-material EMTs derived from spectral density theory (Bergman, 1978;Sancho-Parramon, 2011;Lans, 2013), N-material generalized tensor formulations (Habashy and Abubakar, 2007;Zhdanov, 2008), and multipole treatments (Malasi et al, 2014) give better descriptions of real films topologies, and will be incorporated into PAME in the near future.…”

PAME: Plasmonic Assay Modeling Environment

“…liquid mixing rules. These are hardly exhaustive, and new methods are continually appearing (Amendola and Meneghetti, 2009;Battie et al, 2014;Malasi et al, 2014). Adding EMTs to PAME is straightforward, and more will be added in upcoming releases.…”

“…While classical EMTs can account for non-spherical inclusions through a dipole polarizability parameter (Garcıa et al, 1999;Quinten, 2011), modern two-material EMTs derived from spectral density theory (Bergman, 1978;Sancho-Parramon, 2011;Lans, 2013), N-material generalized tensor formulations (Habashy and Abubakar, 2007;Zhdanov, 2008), and multipole treatments (Malasi et al, 2014) give better descriptions of real films topologies, and will be incorporated into PAME in the near future.…”

Peer Review #1 of "PAME: plasmonic assay modeling environment (v0.1)"

“…At present, PAME includes MG, with and without Garcia's extension, the Bruggeman equation (Bruggeman, 1935), the quasicrystalline approximation with coherent potential (Liu et al, 2011;Tsang et al, 1985), and various binary liquid mixing rules. These are hardly exhaustive, and new methods are continually appearing (Amendola and Meneghetti, 2009;Battie et al, 2014;Malasi et al, 2014). Adding EMTs to PAME is straightforward, and more will be added in upcoming releases.…”

“…Even if exotic nanoparticle are incorporated into PAME, they would still need to be homogenized through an effective mixing theory to fit the TMM multilayer model. While classical EMTs can account for non-spherical inclusions through a dipole polarizability parameter (Garcıa et al, 1999;Quinten, 2011), modern two-material EMTs derived from spectral density theory (Bergman, 1978;Sancho-Parramon, 2011;Lans, 2013), N-material generalized tensor formulations (Habashy and Abubakar, 2007;Zhdanov, 2008), and multipole treatments (Malasi et al, 2014) give better descriptions of real films topologies, and will be incorporated into PAME in the near future.…”