Intuitive understanding of extinction of small particles in absorbing and active host media within the MLWA

TL;DR

This paper evaluates the accuracy of a modified dipole long-wave approximation (MLWA) against exact Mie theory for small spherical nanoparticles in absorbing or active media, and develops a perturbation theory to analyze host effects.

Contribution

It demonstrates the validity range of MLWA compared to Mie theory and introduces a perturbation approach to understand host medium effects on nanoparticle extinction.

Findings

MLWA agrees well with Mie theory for particles up to 25-50 nm depending on material.

The perturbation theory reliably captures host absorption effects within certain parameters.

Agreement extends qualitatively up to larger particle sizes, around 70 nm for some materials.

Abstract

In an absorbing or an active host medium characterized by a complex refractive index $n_2=n_2'+{\rm i}n_2''$, our previously developed modified dipole long-wave approximation (MLWA) is shown to essentially overly with the exact Mie theory results for spherical nanoparticle with radius $a\lesssim 25$ nm ($a\lesssim 20$ nm) in the case of Ag and Au (Al and Mg) nanoparticles. The agreement for Au and Ag (Al and Mg) nanoparticles, slightly better in the case of Au than Ag, continues to be acceptable up to $a\sim 50$ nm ($a\sim 40$ nm), and can be used, at least qualitatively, up to $a\sim 70$~nm ($a\sim 50$ nm) correspondingly. A first order analytic perturbation theory (PT) in a normalized extinction coefficient, $\bar\kappa=n_2''/n_2'$, around a nonabsorbing host is developed within the dipole MLWA and its properties are investigated. It is shown that, in a suitable parameter range, the PT can reliably capture the effect of host absorption or gain on the extinction efficiency of various plasmonic nanoparticles.