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

In an absorbing or an active host medium characterized by a complex refractive index n 2 = n 2 ′ +i n 2 ′′ , our previously developed modified dipole long-wave approximation (MLWA) is shown to essentially overlie with the exact Mie theory results for localized surface plasmon resonance of spherical nanoparticles with radius a ≲25nm ( a ≲20nm) 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 ∼50nm ( a ∼40nm), and can be used, at least qualitatively, up to a ∼70nm ( a ∼50nm) correspondingly. A first order analytic perturbation theory (PT) in a normalized extinction coefficient, κ ¯= 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 isolate and capture the effect of host absorption or host gain on the overall extinction efficiency of various plasmonic nanoparticles.