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arXiv:0709.1442

Light-matter interaction in Mie nanolasers

Claudio Conti, Andrea Fratalocchi, Giancarlo Ruocco

Published Sep 10, 2007• 0 citations
arXivHTMLPDF

Abstract

By deriving a three dimensional vector set of Maxwell-Bloch equations, we report on an ab-initio investigation of a spherical Mie nanolaser. Parallel numerical simulations predict a rich physical scenario, ranging from a nontrivial vectorial energy-matter interplay in the initial stage of evolution to mode competition and dynamical frequency pulling effects. Application of these effects could favor the realization of nonlinearly-controlled largely-tunable nanolaser devices.

DOI
10.48550/arxiv.0709.1442

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Nanoplasmonic metamaterials are an exciting new class of engineered media that promise a range of important applications, such as subwavelength focusing, cloaking, and slowing/stopping of light. At optical frequencies, using gain to overcome potentially not insignificant losses has recently emerged as a viable solution to ultra-low-loss operation that may lead to next-generation active metamaterials. Maxwell-Bloch models for active nanoplasmonic metamaterials are able to describe the coherent spatiotemporal and nonlinear gain-plasmon dynamics. Here, we extend the Maxwell-Bloch theory to a Maxwell-Bloch Langevin approach-a spatially resolved model that describes the light field and noise dynamics in gain-enhanced nanoplasmonic structures. Using the example of an optically pumped nanofishnet metamaterial with an embedded laser dye (four-level) medium exhibiting a negative refractive index, we demonstrate the transition from loss-compensation to amplification and to nanolasing. We observe ultrafast relaxation oscillations of the bright negative-index mode with frequencies just below the THz regime. The influence of noise on mode competition and the onset and magnitude of the relaxation oscillations is elucidated, and the dynamics and spectra of the emitted light indicate that coherent amplification and lasing are maintained even in the presence of noise and amplified spontaneous emission.
An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations,which describe the optical pulse propagation and interaction with homogeneously broadened two-level medium.The convergence and stability of this numerical method are also proved by comparing with the analytic solutions derived under special condition,and the method maintains its erroneous exponents and is applicable.Simulations of arbitrary conditions are discussed by employing this new method,and the evolutions of pulse and Bloch vectors for different detunings,relaxation times and initial input pulse power are analyzed.The established numerical method can be used to solve the Maxwell-Bloch equations and their corrections.
We present a theory to describe the transient and steady state behaviors of the active modes of a photonic crystal with active constituents (active photonic crystal). Using a couple mode model, we showed that the full vectorial Maxwell-Bloch equations describing the physics of light matter interaction in the active photonic crystal can be written as a system of integro-difierential equations. Using the method of moments and the mean value theorem, we showed that the system of integro-difierential equations can be transformed to a set of difierential equations in slow time and slow spatial scales. The slow time (spatial) scale refers to a duration (distance) that is much longer than the optical time period (lattice constant of the photonic crystal). In the steady state, the slow scale equations reduce to a nonlinear matrix eigenvalue problem, from which the nonlinear Bloch modes can be obtained by an iterative method. For cases, where the coupling between the modes are negligible, we describe the transient behavior as an one-dimensional problem in the spatial coordinate, and the steady behaviors are expressed using simple analytical expressions.