Significance of the nonlocal optical response of metal nanoparticles in describing the operation of plasmonic lasers

Dasuni Lelwala Gamacharige, Sarath D. Gunapala, Mark I. Stockman, and Malin Premaratne

Phys. Rev. B 99, 115405 – Published 6 March 2019

Abstract

A metal nanoparticle (MNP) coupled to a quantum emitter (QE) is a versatile composite nanostructure with unique chemical and physical properties which has been studied intensively, owing to its vast range of promising applications in nanoscience and nanotechnology. When pumped into a higher gain level, an MNP-QE composite nanostructure functions as a nanoplasmonic counterpart of a conventional laser, which is capable of operating at subwavelengths. The theory of plasmonic lasers is hitherto developed on the local optical response of the MNP, disregarding the nanoscale effects of its free electrons. In this paper, we perform a comprehensive quantum mechanical analysis of a complex MNP-QE composite nanostructure, capturing the size-dependent nonclassical effects through the nonlocal optical response of the MNP. Our study reveals that the nonlocal correction introduces significant deviations to the plasmon statistics of the hybrid particle suggested by the local calculations, becoming more prominent when the number of QEs coupled to the MNP increases. Furthermore, for the typical material parameter values used in the literature, we observed the initiation of quenching effects at lower pumping rates than suggested by the local response formalism. In essence, nonlocally assessed plasmon statistics of MNP-QE composite nanostructures demand the concerted coupling of an even higher number of QEs to compensate the deterioration in coherence and to sustain lasing.

Received 17 December 2018
Revised 14 February 2019

DOI:https://doi.org/10.1103/PhysRevB.99.115405

Physics Subject Headings (PhySH)

Hybrid quantum systems Plasmonics

Nanoparticles

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Dasuni Lelwala Gamacharige^1,*, Sarath D. Gunapala², Mark I. Stockman³, and Malin Premaratne^1,†

¹Advanced Computing and Simulation Laboratory (AχL), Department of Electrical and Computer Systems Engineering, Monash University, Clayton, Victoria 3800, Australia
²Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA
³Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303 USA

^*dasuni.lelwalagamacharige@monash.edu
^†malin.premaratne@monash.edu

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Issue

Vol. 99, Iss. 11 — 15 March 2019

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Images

Figure 1
Schematic of a spherical MNP coated with identical QEs placed around its equatorial orbit of radius $R$ in $x - y$ plane. The dielectric function of the plasmonic metal is given by $ε_{m}$ and the entire composite nanostructure is immersed in a homogeneous bath with a real positive relative permittivity $ε_{b}$ . Dipole moment of the MNP $(d_{m})$ as well as that of all the QEs $(d_{qe})$ are aligned along the $z$ axis.
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Figure 2
Significance of nonlocal effects at different numbers of coupled QEs. QEs placed in a $R =$ 12.5 nm equatorial orbital of a silver MNP of $r_{m} =$ 10 nm, immersed in a bath of $ε_{b} = 3$ . Solid and dashed curves denote results for GNOR and LRA formalisms, respectively. (a) Plasmon state distribution. (b) Mean plasmon number against pumping rate. (c) Second-order coherence function against pumping rate. (d) Variation of $F_{1} (M_{max})$ (blue) and $F_{2}^{p} (N_{pl})$ (red) with the number of QEs (arrows point the curves toward their respective axes).
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Figure 3
Local and nonlocal evaluation of maximum pump rate before the plasmon state population switches from a Poisson to a thermal distribution. (a) Variation of maximum pump rate with MNP radius at different bath permittivities. Solid and dashed curves denote results for GNOR and LRA formalisms, respectively. (b) Variation of $F_{1} (p_{max})$ with the number of QEs at different MNP radii and bath permittivities.
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Figure 4
Deviation of local and nonlocal dynamics of MNP-QE composite nanostructure at different MNP radii and bath permittivities. Subfigures (a), (b), and (c) are evaluated at $ε_{b} = 3$ , whereas (d), (e), and (f) are evaluated at $r_{m} = 7 nm$ . (a), (d) Mean plasmon number against pumping rate, with $N_{qe}^{max}$ . Solid and dashed curves denote results for GNOR and LRA formalisms, respectively. (b), (e) Variation of $F_{1} (M_{max})$ with the number of QEs. (c), (f) Variation of $F_{2}^{p} (N_{pl})$ with the number of QEs.
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Figure 5
Comparison of mean plasmon number variation with properties of the quantum emitters and their separation from the MNP surface at different MNP radii. Solid and dashed curves denote results for GNOR and LRA formalisms, respectively. (a) Mean plasmon number against MNP-QE resonance detuning. (b) Mean plasmon number against QE dipole moment. (c) Mean plasmon number against MNP-QE surface separation distance.
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Figure 6
An alternative arrangement of QEs around a spherical MNP. QEs are randomly placed in a concentric spherical shell with inner radius $r_{1}$ and outer radius $r_{2}$ .
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