Diagonalization of Hamiltonian for finite-sized dispersive media: Canonical quantization with numerical mode-decomposition (CQ-NMD)

• URL: http://arxiv.org/abs/2101.12184v2
• Date: Fri, 16 Apr 2021 20:43:43 GMT
• Title: Diagonalization of Hamiltonian for finite-sized dispersive media: Canonical quantization with numerical mode-decomposition (CQ-NMD)
• Authors: Dong-Yeop Na, Jie Zhu, Weng Cho Chew
• Abstract summary: We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition. We provide several numerical simulations that capture the physics of full quantum effects, impossible by classical Maxwell's equations.
• Score: 3.032299122358857
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition, for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the previous Fano-diagonalization methods. The main procedure is to (1) study a system where electromagnetic (EM) fields are coupled to non-uniformly distributed Lorentz oscillators in Hamiltonian mechanics, (2) derive a generalized Hermitian eigenvalue problem for conjugate pairs in coordinate space, (3) apply computational electromagnetics methods to find a countably/finite set of time-harmonic eigenmodes that diagonalizes the Hamiltonian, and (4) perform the subsequent canonical quantization with mode-decomposition. Moreover, we provide several numerical simulations that capture the physics of full quantum effects, impossible by classical Maxwell's equations, such as non-local dispersion cancellation of an entangled photon pair and Hong-Ou-Mandel (HOM) effect in a dispersive beam splitter.

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