Quantum electrodynamics of lossy magnetodielectric samples in vacuum: modified Langevin noise formalism

Abstract

Quantum behavior of the electromagnetic field in unbounded macroscopic media displaying absorption is properly described by the Langevin noise formalism (macroscopic quantum electrodynamics) where the field is assumed to be entirely produced by medium fluctuating sources via the dyadic Green's function. On the other hand, such formalism is able to deal with the case of finite-size lossy objects placed in vacuum only as a limiting situation where the permittivity limit $\mathrm{Im}(\epsilon )\to 0^{+}$ pertaining the regions filled by vacuum is taken at the end of the calculations. Strictly setting $\mathrm{Im}(\epsilon )=0$ is forbidden in the Langevin noise formalism since the field would vanish in the lossless regions and this is physically due to the fact that the contribution of the scattering modes to the field is not separated from the contribution produced by the medium fluctuating sources. Recently, a modified Langevin noise formalism has been proposed to encompass the scattering modes and accordingly it is able to describe the structured lossless situations by strictly setting $\mathrm{Im}(\epsilon )=0$. However such modified formalism has been numerically validated only in few specific geometries. In this paper we analytically derive the modified Langevin noise formalism from the established canonical quantization of the electromagnetic field in macroscopic media, thus proving that it models any possible scenario involving linear, inhomegeneous and magnetodielectric samples. The derivation starts from quantum Maxwell equations in the Heisenberg picture together with their formal solution as the superposition of the medium assisted field and the scattering modes. We analytically prove that each of the two field parts can be expressed in term of particular bosonic operators, which in turn diagonalize the electromagnetic Hamiltonian.

References in corpus (35)

• Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics
• Spontaneous decay in the presence of dispersing and absorbing bodies: general theory and application to a spherical cavity
• Quantum emitters coupled to surface plasmons of a nano-wire: A Green function approach
• Canonical quantization of macroscopic electromagnetism
• QED commutation relations for inhomogeneous Kramers-Kronig dielectrics
• Field quantization in inhomogeneous absorptive dielectrics
• Macroscopic QED for quantum nanophotonics: Emitter-centered modes as a minimal basis for multi-emitter problems
• Quantum local-field corrections and spontaneous decay
• Macroscopic quantum electrodynamics and duality in non-local and Onsager-violating media
• Fano diagonalization of a polariton model for an inhomogeneous absorptive dielectric
• Casimir effect from macroscopic quantum electrodynamics
• Casimir-Polder forces on excited atoms in the strong atom-field coupling regime
• Modulation of Cathodoluminescence Emission by Interference with External Light
• Field quantization in inhomogeneous anisotropic dielectrics with spatio-temporal dispersion
• Electromagnetic field quantization in a linear polarizable and magnetizable medium
• Casimir-Polder Forces between Chiral Objects
• Extension of the Huttner-Barnett model to a magnetodielectric medium
• Quantizing polaritons in inhomogeneous dissipative systems
• Mode-selective quantization and multimodal effective models for spherically layered systems
• Canonical quantization of electromagnetic field in an anisotropic polarizable and magnetizable medium with spatial-temporal dispersion
• Quantum dynamics of the damped harmonic oscillator
• Casimir-Lifshitz Force for Nonreciprocal Media and Applications to Photonic Topological Insulators
• QED of lossy cavities: operator and quantum-state input-output relations
• Equivalence between the Hamiltonian and Langevin noise description of plasmon-polaritons in a dispersive and lossy inhomogeneous medium
• Canonical quantization for quantum plasmonics with finite nanostructures
• Diagonalization of Hamiltonian for finite-sized dispersive media: Canonical quantization with numerical mode-decomposition (CQ-NMD)
• Fluctuation-dissipation theorem and fundamental photon commutation relations in lossy nanostructures using quasinormal modes
• Electromagnetic field quantization in a magnetodielectric medium with external charges
• Cavity-assisted spontaneous emission as a single-photon source: Pulse shape and efficiency of one-photon Fock state preparation
• Interaction of atomic systems with quantum vacuum beyond electric dipole approximation
• Numerical Framework for Modeling Quantum Electromagnetic Systems Involving Finite-Sized Lossy Dielectric Objects in Free Space
• The Langevin Noise Approach for Lossy Media and the Lossless Limit
• Operative Approach to Quantum Electrodynamics in Dispersive Dielectric Objects Based on a Polarization Modal Expansion
• Integral Formulation of Macroscopic Quantum Electrodynamics in Dispersive Dielectric Objects
• Quantum interaction of sub-relativistic aloof electrons with mesoscopic samples

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