Purcell factor of spherical Mie resonators

Zambrana‐Puyalto, Xavier; Bonod, Nicolas

doi:10.1103/physrevb.91.195422

Cited by 139 publications

(120 citation statements)

References 53 publications

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“…Equation (1) is similar to the standard laser condition [19] that determines the threshold value of N 21 , but with the cavity mode quality factor and volume replaced by their plasmon counterparts in metaldielectric system characterized by dispersive dielectric function ε(ω, r). While the plasmon quality factor Q is well-defined in terms of the metal dielectric function ε(ω) = ε ′ (ω) + iε ′′ (ω), there is an active debate on mode volume definition in plasmonic systems [25][26][27][28][29][30][31][32][33][34][35]. Since QEs are usually distributed outside the plasmonic structure, the standard expression for cavity mode volume, dV ε(r)|E(r)| 2 /max[ε(r)|E(r)| 2 ], where E(r) is the mode electric field, is ill-defined for open systems [27,28,31].…”

Section: Introductionmentioning

confidence: 99%

Mode Volume, Energy Transfer, and Spaser Threshold in Plasmonic Systems with Gain

Shahbazyan

2017

ACS Photonics

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We present a unified approach to describe spasing in plasmonic systems modeled by quantum emitters interacting with resonant plasmon mode. We show that spaser threshold implies detailed energy transfer balance between the gain and plasmon mode and derive explicit spaser condition valid for arbitrary plasmonic systems. By defining carefully the plasmon mode volume relative to the gain region, we show that the spaser condition represents, in fact, the standard laser threshold condition extended to plasmonic systems with dispersive dielectric function. For extended gain region, the saturated mode volume depends solely on the system parameters that determine the lower bound of threshold population inversion.

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Section: Introductionmentioning

confidence: 99%

Mode Volume, Energy Transfer, and Spaser Threshold in Plasmonic Systems with Gain

Shahbazyan

2017

ACS Photonics

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“…Plasmonic or highindex dielectric nanoparticles are frequently used for this purpose 1,2 . The multipole expansion provides insight into several optical phenomena, such as Fano resonances 3,4 , electromagnetically-induced-transparency 5 , directional light emission [6][7][8][9] , manipulating and controlling spontaneous emission [10][11][12] , light perfect absorption [13][14][15] , electromagnetic cloaking 16,17 , and optical (pulling, pushing, and lateral) forces [18][19][20][21][22] . In all these cases, an external field induces displacement or conductive currents into the samples.…”

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confidence: 99%

An electromagnetic multipole expansion beyond the long-wavelength approximation

Alaee

Rockstuhl

Fernandez‐Corbaton

2018

Optics Communications

375

313

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The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The multipole moments of the source. These numbers are frequently computed with expressions obtained after the long-wavelength approximation. Here, we derive exact expressions for the multipole moments of dynamic sources that resemble in their simplicity their approximate counterparts. We validate our new expressions against analytical results for a spherical source, and then use them to calculate the induced moments for some selected sources with a nontrivial shape. The comparison of the results to those obtained with approximate expressions shows a considerable disagreement even for sources of subwavelength size. Our expressions are relevant for any scientific area dealing with the interaction between the electromagnetic field and material systems.PACS numbers: 78.67. Pt, 13.40.Em,78.67.Bf, 03.50.De The multipolar decomposition of a given chargecurrent distribution is taught in every undergraduate course in physics. The resulting set of numbers are called the multipolar moments. They are classified according to their order, i.e. dipoles, quadrupoles etc... For each order, there are electric and magnetic multipolar moments. Each multipolar moment is uniquely connected to a corresponding multipolar field. Their importance stems from the fact that the multipolar moments of a charge-current distribution completely characterize both the radiation of electromagnetic fields by the source, and the coupling of external fields onto it. The multipolar decomposition is important in any scientific area dealing with the interaction between the electromagnetic field and material systems. In particle physics, the multipole moments of the nuclei provide information on the distribution of charges inside the nucleus. In chemistry, the dipole and quadrupolar polarizabilities of a molecule determine most of its properties. In electrical engineering, the multipole expansion is used to quantify the radiation from antennas. And the list goes on.In this Letter, we present new exact expressions for the multipolar decomposition of an electric charge-current distribution. They provide a straightforward path for upgrading analytical and numerical models currently using the long-wavelength approximation. After the upgrade, the models become exact. The expressions that we provide are directly applicable to the many areas where the multipole decomposition of electrical current density distributions is used. For the sake of concreteness, in this article we apply them to a specific field: Nanophotonics.In nanophotonics, one purpose is to control and manipulate light on the nanoscale. Plasmonic or highindex dielectric nanoparticles are frequently used for this purpose 1,2 . The multipole expansion provides insight into several optical phenomena, such as Fano resonances 3,4 , electromagnetically-induced-transparen...

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“…14) and reconciles the Purcell factor with the energy-like confinement definition of the mode volume [165,166]. Similar definitions should work for the effective mode area or length.…”

Section: Retarded Regimementioning

confidence: 92%

Plasmonic Purcell factor and coupling efficiency to surface plasmons. Implications for addressing and controlling optical nanosources

Francs

Barthès

Bouhélier

et al. 2016

J. Opt.

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Abstract. The Purcell factor Fp is a key quantity in cavity quantum electrodynamics (cQED) that quantifies the coupling rate between a dipolar emitter and a cavity mode. Its simple form Fp ∝ Q/V unravels the possible strategies to enhance and control light-matter interaction. Practically, efficient light-matter interaction is achieved thanks to either i) high quality factor Q at the basis of cQED or ii) low modal volume V at the basis of nanophotonics and plasmonics. In the last decade, strong efforts have been done to derive a plasmonic Purcell factor in order to transpose cQED concepts to the nanocale, in a scale-law approach. In this work, we discuss the plasmonic Purcell factor for both delocalized (SPP) and localized (LSP) surface-plasmon-polaritons and briefly summarize the expected applications for nanophotonics. On the basis of the SPP resonance shape (Lorentzian or Fano profile), we derive closed form expression for the coupling rate to delocalized plasmons. The quality factor factor and modal confinement of both SPP and LSP are quantified, demonstrating their strongly subwavelength behaviour.

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Purcell factor of spherical Mie resonators

Cited by 139 publications

References 53 publications

Mode Volume, Energy Transfer, and Spaser Threshold in Plasmonic Systems with Gain

Mode Volume, Energy Transfer, and Spaser Threshold in Plasmonic Systems with Gain

An electromagnetic multipole expansion beyond the long-wavelength approximation

Plasmonic Purcell factor and coupling efficiency to surface plasmons. Implications for addressing and controlling optical nanosources

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