2004/07/06 by L.G. Suttorp, L. G. Suttorp, Martijn Wubs +1 · 133 citations
Mathematics · Physics and Astronomy · #Canonical quantization #Condensed matter physics #Dielectric #Electromagnetic field #Hamiltonian (control theory) #Laplace transform #Mathematical analysis #Mathematics #Mechanical and Optical Resonators #Physics #Polarization (electrochemistry) #Quantization (signal processing) #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Strong Light-Matter Interactions #quant-ph
paper · pdf · doi:10.1103/physreva.70.013816
published in Physical Review A 70(1) (American Physical Society) · 19 pages
arxiv created 2004/07/06 · openalex publication_date 2004/07/30 · arxiv updated 2018/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
The quantization of the electromagnetic field in a three-dimensional inhomogeneous dielectric medium with losses is carried out in the framework of a damped-polariton model with an arbitrary spatial dependence of its parameters. The equations of motion for the canonical variables are solved explicitly by means of Laplace transformations for both positive and negative time. The dielectric susceptibility and the quantum noise-current density are identified in terms of the dynamical variables and parameters of the model. The operators that diagonalize the Hamiltonian are found as linear combinations of the canonical variables, with coefficients depending on the electric susceptibility and the dielectric Green function. The complete time dependence of the electromagnetic field and of the dielectric polarization is determined. Our results provide a microscopic justification of the phenomenological quantization scheme for the electromagnetic field in inhomogeneous dielectrics.