Multipolar, time-dynamical model for the loss compensation and lasing of a spherical plasmonic nanoparticle spaser immersed in an active gain medium

Abstract

The plasmonic response of a metal nanoparticle in the presence of surrounding gain elements is studied, using a space and time-dependent model, which integrates a quantum formalism to describe the gain and a classical treatment for the metal. Our model fully takes into account the influence of the system geometry (nanosphere) and offers for the first time, the possibility to describe the temporal evolution of the fields and the coupling among the multipolar modes of the particle. We calculate the lasing threshold value for all multipoles of the spaser, and demonstrate that the dipolar one is lowest. The onset of the lasing instability, in the linear regime, is then studied both with and without external field forcing. We also study the behaviour of the system below the lasing threshold, with the external field, demonstrating the existence of an amplification regime where the nanoparticle’s plasmon is strongly enhanced as the threshold is approached. Finally, a qualitative discussion is provided on later, non-linear stages of the dynamics and the approach to the steady-state of the spaser; in particular, it is shown that, for the considered geometry, the spasing is necessarily multi-modal and multipolar modes are always activated.

Active Nanophotonics

“…When the plasmonic nanoparticle is larger, the resonant higher-order modes can appear in the radiation spectrum, and they can also operate in the lasing regime. However, as expected, in [337] a rigorous theoretical analysis of the lasing threshold for all multipoles of the spaser demonstrated that the dipolar one is the lowest. Various approaches to reducing the laser-threshold in such plasmonic nanoparticle-based spasers have been proposed, including inverted structures 29 with dielectric gain as a core surrounded plasmonic shell [338], increase of the background permittivity [339], the use of low-loss materials (e.g., Ag instead of Au) [106], exotic shapes [153], [340], [341] and electric pumping [297], [342].…”

Nanolasers Enabled by Metallic Nanoparticles: From Spasers to Random Lasers

“…Larger mode volume may allow larger number of plasmons in a spasing mode. Exploring this concept with a time‐domain model of a metallic particle immersed in an active medium, Veltri et al . showed that the optical response of the plasmonic resonator is always both multi‐modal and multipolar.…”

“…Larger mode volume may allow larger number of plasmons in a spasing mode. Exploring this concept with a time-domain model of a metallic particle immersed in an active medium, Veltri et al [67] showed that the optical response of the plasmonic resonator is always both multi-modal and multipolar. Their model indicated that a spaser inevitably generates "dark modes" due to a cascade of non-linear coupled fields that always launches and activates higher-order, multipolar modes, which do not depend on the ratio of the particle size vs. the excitation wavelength.…”

Spaser Based on Graphene Tube

“…and imaginary parts of both sides, assuming γ ω (which is valid for the frequency range which will be used), the Quality factor of SP modes is derived by using the definition Q = ω/2γ, Figure 4 shows the Quality factor of SP modes as a function of plasmon wavenumber and energy for different values of E F using Eq. (18). If Drude conductivity is inserted into Eq.…”