Generalized superradiant assembly for nanophotonic thermal emitters

Sudaraka Mallawaarachchi, Sarath D. Gunapala, Mark I. Stockman, and Malin Premaratne

Phys. Rev. B 97, 125406 – Published 8 March 2018

Abstract

Superradiance explains the collective enhancement of emission, observed when nanophotonic emitters are arranged within subwavelength proximity and perfect symmetry. Thermal superradiant emitter assemblies with variable photon far-field coupling rates are known to be capable of outperforming their conventional, nonsuperradiant counterparts. However, due to the inability to account for assemblies comprising emitters with various materials and dimensional configurations, existing thermal superradiant models are inadequate and incongruent. In this paper, a generalized thermal superradiant assembly for nanophotonic emitters is developed from first principles. Spectral analysis shows that not only does the proposed model outperform existing models in power delivery, but also portrays unforeseen and startling characteristics during emission. These electromagnetically induced transparency like (EIT-like) and superscattering-like characteristics are reported here for a superradiant assembly, and the effects escalate as the emitters become increasingly disparate. The fact that the EIT-like characteristics are in close agreement with a recent experimental observation involving the superradiant decay of qubits strongly bolsters the validity of the proposed model.

Received 16 October 2017
Revised 28 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.125406

Physics Subject Headings (PhySH)

Nanophotonics Superradiance & subradiance

Condensed Matter, Materials & Applied PhysicsInterdisciplinary PhysicsAtomic, Molecular & OpticalGeneral PhysicsParticles & Fields

Authors & Affiliations

Sudaraka Mallawaarachchi^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

^*sudaraka@ieee.org
^†malin.premaratne@monash.edu

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Issue

Vol. 97, Iss. 12 — 15 March 2018

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Images

Figure 1
The configuration shown comprises many nanophotonic thermal emitters engulfed in a spherical, near-PEC body. Each emitter can be uniquely characterized using a specific absorptive material and dimensions, thus giving the ability to uniquely define ( $γ_{a}$ ) and ( $γ_{c}$ ) for each emitter. The cross section shown in the inset shows how the emitters unevenly penetrate towards the center of the sphere, thus capturing the dimensional variability between the emitters. It is noted that the emitters are arranged symmetrically on the surface of the sphere such that a given emitter always forms a part of a hypothetical ring that spans the surface of the sphere. Symmetry akin to this nature is vital to attain the effects of superradiance when nonidentical emitters are used.
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Figure 2
A singular emitter is highlighted to show the operation parameters of the assembly. The photons emanating from the emitter are coupled to the far field at a rate of $γ_{c}$ and the photons engulfed within the emitter are absorbed at a rate of $γ_{a}$ . Note that each emitter has a unique configuration of $γ_{a}$ and $γ_{c}$ , which leads to myriads of interference configurations, resulting in the observed startling phenomena.
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Figure 3
Diagram illustrating the vertical distribution of normalized and orthogonal radiation channels. The $k th$ emitter is located at the midpoint betwixt the periodic boundaries located a distance of $L$ apart. The infinite reality of free space is achieved by considering $L \to \infty$ .
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Figure 4
Simplified configuration shown comprises only two thermal emitters, each with a unique material and a dimensional configuration. This emitter assembly is best realized using PEC deep subwavelength slits. The emitters have unique absorption rates ( $γ_{a_{1}}$ and $γ_{a_{2}}$ ) and far-field coupling rates ( $γ_{c_{1}}$ and $γ_{c_{2}}$ ). The various dimensions aid in retaining a unique resonance frequency across the emitters. The emission cross section for this assembly is analytically derived in Eq. (23).
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Figure 5
Numerically obtained emission spectra by solving Eq. (1), together with Eq. (21) for different assemblies comprising 5 emitters in each. Primary emitter parameters used for the simulation are $γ_{a} = 10^{12} s^{- 1}$ and $γ_{c} = 10^{13} s^{- 1}$ . (a) The uniform emitter assembly case depicts the expected anomalous power scaling discussed elsewhere [15]. Each emitter within this assembly uses the parameters $γ_{a}$ and $2 γ_{c}$ . (b) The material varied emitter configuration shows a higher power emission at resonance. All emitters have the same $γ_{c}$ parameter and the photon absorption rate parameters are $[1.7 γ_{a}, 1.6 γ_{a}, γ_{a}, 1.6 γ_{a}, 1.7 γ_{a}]$ . (c) The dimensionally varied emitter configuration achieves a similar power emission at resonance. All emitters have the same $γ_{a}$ value and the photon far-field coupling rate parameters are $[0.5 γ_{c}, 0.7 γ_{c}, γ_{c}, 0.7 γ_{c}, 0.5 γ_{c}]$ . (d) The final assembly is completely generalized using emitter parameters for photon absorption rates from (b) and photon far-field coupling rates from (c). The energy values computed at the point of resonance are [1.051, 3.043, 2.975, and 4.155] $\times$ $10^{- 23}$ J, respectively.
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Figure 6
Analytically obtained emission spectra by solving Eq. (1), together with Eq. (23) for different assemblies comprising 2 emitters in each. Primary emitter parameters used for the computation are $γ_{a} = 10^{12} s^{- 1}, γ_{c} = 10^{13} s^{- 1}$ . The left emitter in each assembly has the parameters $γ_{a}$ and $0.1 γ_{c}$ . (a) Superscattering-like emission phenomenon observed when the right emitter has parameters $[1.5 γ_{a}, 0.5 γ_{c}]$ . (b) Superscattering-like emission phenomenon observed with a higher disparity when the right emitter has parameters $[15 γ_{a}, 0.15 γ_{c}]$ . (c) EIT-like emission phenomenon observed when the right emitter has parameters $[30 γ_{a}, 4 γ_{c}]$ . (d) EIT-like emission phenomenon observed with a higher disparity when the right emitter has parameters $[250 γ_{a}, 70 γ_{c}]$ . The energy values computed at the point of resonance are [1.633, 2.673, 2.545, 2.063] $\times$ $10^{- 22}$ J, respectively.
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