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A unified Hamiltonian solution to Maxwell-Schrodinger equations for modeling electromagnetic field-particle interaction

Chen, YP; Sha, WEI; Jiang, L; Meng, M; Wu, YM; Chew, WC; (2017) A unified Hamiltonian solution to Maxwell-Schrodinger equations for modeling electromagnetic field-particle interaction. Computer Physics Communications , 215 pp. 63-70. 10.1016/j.cpc.2017.02.006. Green open access

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Abstract

A novel unified Hamiltonian approach is proposed to solve Maxwell–Schrödinger equation for modeling the interaction between classical electromagnetic (EM) fields and particles. Based on the Hamiltonian of electromagnetics and quantum mechanics, a unified Maxwell–Schrödinger system is derived by the variational principle. The coupled system is well-posed and symplectic, which ensures energy conserving property during the time evolution. However, due to the disparity of wavelengths of EM waves and that of electron waves, a numerical implementation of the finite-difference time-domain (FDTD) method to the multiscale coupled system is extremely challenging. To overcome this difficulty, a reduced eigenmode expansion technique is first applied to represent the wave function of the particle. Then, a set of ordinary differential equations (ODEs) governing the time evolution of the slowly-varying expansion coefficients are derived to replace the original Schrödinger equation. Finally, Maxwell’s equations represented by the vector potential with a Coulomb gauge, together with the ODEs, are solved self-consistently. For numerical examples, the interaction between EM fields and a particle is investigated for both the closed, open and inhomogeneous electromagnetic systems. The proposed approach not only captures the Rabi oscillation phenomenon in the closed cavity but also captures the effects of radiative decay and shift in the open free space. After comparing with the existing theoretical approximate models, it is found that the approximate models break down in certain cases where a rigorous self-consistent approach is needed. This work is helpful for the EM simulation of emerging nanodevices or next-generation quantum electrodynamic systems.

Type: Article
Title: A unified Hamiltonian solution to Maxwell-Schrodinger equations for modeling electromagnetic field-particle interaction
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.cpc.2017.02.006
Publisher version: https://doi.org/10.1016/j.cpc.2017.02.006
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Maxwell–Schrödinger equation, Hamiltonian, Finite-difference time-domain, Reduced eigenmode expansion, Rabi oscillation, Radiative decay
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI: https://discovery.ucl.ac.uk/id/eprint/10061825
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