Amplified and directional spontaneous emission from arbitrary composite bodies: A self-consistent treatment of Purcell effect below threshold

Abstract

We study amplified spontaneous emission (ASE) from wavelength-scale composite bodies-complicated arrangements of active and passive media-demonstrating highly directional and tunable radiation patterns, depending strongly on pump conditions, materials, and object shapes. For instance, we show that under large enough gain, PT symmetric dielectric spheres radiate mostly along either active or passive regions, depending on the gain distribution. Our predictions are based on a recently proposed fluctuating volume-current (FVC) formulation of electromagnetic radiation that can handle inhomogeneities in the dielectric and fluctuation statistics of active media, e.g. arising from the presence of non-uniform pump or material properties, which we exploit to demonstrate an approach to modelling ASE in regimes where Purcell effect (PE) has a significant impact on the gain, leading to spatial dispersion and/or changes in power requirements. The nonlinear feedback of PE on the active medium, captured by the Maxwell-Bloch equations but often ignored in linear formulations of ASE, is introduced into our linear framework by a self-consistent renormalization of the (dressed) gain parameters, requiring the solution of a large system of nonlinear equations involving many linear scattering calculations.Noise in structures comprising passive and active materials can lead to important radiative effects, 1 e.g. spontaneous emission (SE), 2 superluminescence, 3 and fluorescence. 4 Although large-etalon gain amplifiers and related devices have been studied for decades, [5][6][7][8] there is increased interest in the design of wavelength-scale composites for tunable sources of scattering and incoherent emission, 9,10 or which serve as perfect absorbers 11 at mid-infrared and visible wavelengths. In this paper, we extend a recently developed fluctuatingvolume current (FVC) formulation of electromagnetic (EM) fluctuations [12][13][14][15] to the problem of modeling spontaneous emission and scattering from composite, wavelength-scale structures, e.g. metal-dielectric spasers, [16][17][18] subject to inhomogeneities in both material and noise properties. We begin by studying amplified spontaneous emission (ASE) from piecewise-constant composite bodies, showing that their emissivity can exhibit a high degree of directionality, depending sensitively on the gain profile and shape of the objects. For instance, we find that under large enough gain, the directivity of parity-time (PT ) symmetric spheres can be designed to lie primarily along active or passive regions, depending on the presence or absence of centrosymmetry, respectively. Such composite micron-scale emitters act as tunable sources of incoherent radiation, forming a special class of infrared/visible antennas exhibiting polarization-and direction-sensitive absorption and emission properties. An important ingredient for the design of directional emission is the ability to tune the gain profile of the objects, which can be far from homogeneous in realistic settings. Here, we consider tw...

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