TEMPORAL AND SPECTRAL ANALYSIS OF GAIN ASSISTED DIPOLAR LOCALIZED SURFACE PLASMONS

Abstract

The thesis titled “TEMPORAL AND SPECTRAL ANALYSIS OF GAIN ASSISTED DIPOLAR LOCALIZED SURFACE PLASMONS” explores the dynamics of coherent localized surface plasmons (LSPs), commonly known as spasers, under continuous and pulsed pumping scenarios. The thesis mainly focuses on the temporal and spectral profiles of spaser which largely depends on the gain media modulated by the pump source. The spaser system under consideration consists of a metal nanoparticle, gain medium and pump source. We consider a 40 nm silver nanoparticle which supports LSP dipolar mode, with 2.50 eV frequency and high dissipation rate of ~1014 s−1. The nanoparticle is surrounded by a gain medium comprising of an ensemble of quantum dots (QDs), which can be modelled as two-level, three-level, or four-level systems depending on the gain medium spectrum. Each quantum dot couples identically with the LSPs with a coupling strength of ~1012 s−1. The resonance frequency of QDs is slightly detuned from LSP frequency but their spectral overlap is significant enough to facilitate their interaction. The decay rate of the population from the excited state to the ground state in the quantum dots is of the order of ~1012 s−1. Using the aforementioned spaser system, we conduct a series of analyses focusing on the dynamics of LSPs while modulating the pump either as a continuous wave (CW) or a Gaussian pulse source. The CW source can be either a coherent or an incoherent source. Our findings reveal that for a spaser-type system, an incoherent pump source is more effective than a coherent one in sustaining the LSPs. In subsequent analyses, we examine the effects of pumping a Λ-type gain medium with a Gaussian pulse. Our results demonstrate that achieving intense and Gaussian-shaped LSPs requires careful tuning of the pump pulse amplitude and its temporal width. In practical scenarios, there often exists a detuning between the pump pulse frequency and the transition frequency of the quantum dots. We report that a chirped Gaussian pump pulse can significantly enhance the number of LSPs produced. We delve into the specifics by introducing V-shaped and Λ-shaped chirps and study their impact on the LSP dynamics. Additionally, we address the influence of noise, considering a time-harmonic detuning term in our analysis. In another work, we study the impact of electron-phonon interaction on the dynamics of LSPs. We explore two types of interaction potentials- linear and quadratic. The linear interaction potential leads to a periodic steady-state solution for the LSPs. The quadratic interaction, on the other hand, has been explored phenomenologically by increasing the decay rates in a three-level system. This approach not only increases the number of LSPs but also broadens the LSP spectrum. In our last work, we demonstrate the effect of inhomogeneously broadened gain medium on the spaser. The inhomogeneities sets in as different set of atoms has distinct spectral responses. The incorporation of the inhomogeneously broadened gain medium increases the threshold pump rate and decreases the number of LSP. In summary, this thesis provides a comprehensive examination of the dynamics of dipolar localized surface plasmons in spaser systems under various pumping conditions, highlighting the configuration of gain medium as two, three and four level systems.