Equivalence between the Hamiltonian and Langevin noise descriptions of plasmon polaritons in a dispersive and lossy inhomogeneous medium

Drezet, Aurélien

doi:10.1103/physreva.96.033849

Cited by 20 publications

(20 citation statements)

References 82 publications

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“…In addition we consider it possible to extend our approach to disordered systems, for instance crystals subject to substitutional site disorder, thus enabling a theory of the dielectric tensor for disordered systems within the frame of the coherent potential approximation (CPA). An extension of our work to include finite temperature requires a quantized formalism for photons and phonons that should treat the lattice vibrations and the photons on equal footing, for a recent discussion of this problem see [70].…”

Section: Discussionmentioning

confidence: 99%

On the theory of light propagation in crystalline dielectrics

Dommermuth

Schopohl

2018

J. Phys. Commun.

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A synoptic view on the long-established theory of light propagation in crystalline dielectrics is presented, where charges, tightly bound to atoms (molecules, ions) interact with the microscopic local electromagnetic field. Applying the Helmholtz-Hodge decomposition to the current density in Maxwell's equations, two decoupled sets of equations result determining separately the divergencefree (transversal) and curl-free (longitudinal) parts of the electromagnetic field, thus facilitating the restatement of Maxwell's equations as equivalent field-integral equations. Employing a suitably chosen basis system of Bloch functions we present for dielectric crystals an exact solution to the inhomogenous field-integral equations determining the local electromagnetic field that polarizes individual atoms or ionic subunits in reaction to an external electromagnetic wave. From the solvability condition of the associated homogenous integral equation then the propagating modes and the photonic bandstructure q OPEN ACCESS

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Section: Discussionmentioning

confidence: 99%

On the theory of light propagation in crystalline dielectrics

Dommermuth

Schopohl

2018

J. Phys. Commun.

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“…where k 0 = ω/c, and (r, ω) = R (r, ω) + i I (r, ω) is the dielectric permittivity. The noise current densityĵ N (r, ω) = ω √h 0 I (r, ω)/π b(r, ω) counteracts the dissipation, such that the commutation relations between the electromagnetic field operators are spatially preserved for the dissipative materials [42,54,55] as well as nondissipative dielectrics [56,57]. A formal solution of Eq.…”

Section: A Green's Function Quantization Approachmentioning

confidence: 99%

Quantized quasinormal-mode description of nonlinear cavity-QED effects from coupled resonators with a Fano-like resonance

Franke

Richter

Ren

et al. 2020

Phys. Rev. Research

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We employ a recently developed quantization scheme for quasinormal modes (QNMs) to study a nonperturbative open cavity-QED system consisting of a hybrid metal-dielectric resonator coupled to a quantum emitter. This hybrid cavity system allows one to explore the complex coupling between a low-Q (quality factor) resonance and a high-Q resonance, manifesting in a striking Fano resonance, an effect that is not captured by traditional quantization schemes using normal modes or a Jaynes-Cummings (JC)-type model. The QNM quantization approach rigorously includes dissipative coupling between the QNMs and is supplemented with generalized input-output relations for the output electric field operator for multiple modes in the system and correlation functions outside the system. The role of the dissipation-induced mode coupling is explored in the strong coupling regime between the photons and emitter beyond the first rung of the JC dressed-state ladder. Important differences in the quantum master equation and input-output relations between the QNM quantum model and phenomenological dissipative JC models are found. For the hybridized high-Q cavity mode, we show how the dissipation-induced coupling causes a significant reduction in the cavity-emitter coupling rate, and the cavity decay rate, compared to a simpler JC model. In a second step, numerical results for the Fock distributions and system as well as output correlation functions obtained from the quantized QNM model for the hybrid structure are compared with results from a phenomenological approach. We demonstrate explicitly how the quantized QNM model manifests in multiphoton quantum correlations beyond what is predicted by the usual JC models.

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“…Note that with respect to the phenomenological quantization approach, other models have also adopted the approach of leaving a small imaginary part of the permittivity until the very end of the calculations [32,42]; below we will present a more detailed mathematical treatment, and one which can easily be applied to quantized mode theories (using QNMs) in a rigorous and intuitive way.…”

Section: B Green Function Quantization Approach With Permittivity Sementioning

confidence: 99%

“…[15,28] is proportional to the imaginary part of the dielectric permittivity which, at first sight, seems to vanish in the case of nonabsorbing media, and would be inconsistent with the limiting case of quantization in free space. While it was shown explicitly for one-dimensional systems, that the Green function quantization is indeed consistent with the case of nonabsorbing media [28], there were only some arguments for the general case, based on the fact that one has to include a small background absorption until the very end of the calculations [22,32].…”

Section: Introductionmentioning

confidence: 99%

Fluctuation-dissipation theorem and fundamental photon commutation relations in lossy nanostructures using quasinormal modes

Franke

Ren

Hughes

et al. 2020

Phys. Rev. Research

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We provide theory and formal insight on the Green function quantization method for absorptive and dispersive spatial-inhomogeneous media in the context of dielectric media. We show that a fundamental Green function identity, which appears, e.g., in the fundamental commutation relation of the electromagnetic fields, is also valid in the limit of nonabsorbing media. We also demonstrate how the zero-point field fluctuations yields a nonvanishing surface term in configurations without absorption, when using a more formal procedure of the Green function quantization method. We then apply the presented method to a recently developed theory of photon quantization using quasinormal modes [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)] for finite nanostructures embedded in a lossless background medium. We discuss the strict dielectric limit of the commutation relations of the quasinormal mode operators and present different methods to obtain them, connected to the radiative loss for nonabsorptive but open resonators. We show exemplary calculations of a fully three-dimensional photonic crystal beam cavity, including the lossless limit, which supports a single quasinormal mode and discuss the limits of the commutation relation for vanishing damping.

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Equivalence between the Hamiltonian and Langevin noise descriptions of plasmon polaritons in a dispersive and lossy inhomogeneous medium

Cited by 20 publications

References 82 publications

On the theory of light propagation in crystalline dielectrics

On the theory of light propagation in crystalline dielectrics

Quantized quasinormal-mode description of nonlinear cavity-QED effects from coupled resonators with a Fano-like resonance

Fluctuation-dissipation theorem and fundamental photon commutation relations in lossy nanostructures using quasinormal modes

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