2024/09/07 by William Barham, Barham, William, Yaman Güçlü +5
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Computational Physics (physics.comp-ph) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2409.04891
openalex publication_date 2024/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A simple Hamiltonian modeling framework for general models in nonlinear optics is given. This framework is specialized to describe the Hamiltonian structure of electromagnetic phenomena in cubicly nonlinear optical media. The model has a simple Poisson bracket structure with the Hamiltonian encoding all of the nonlinear coupling of the fields. The field-independence of the Poisson bracket facilitates a straightforward Hamiltonian structure-preserving discretization using finite element exterior calculus. The generality and relative simplicity of this Hamiltonian framework makes it amenable for simulating a broad class of time-domain nonlinear optical problems. The main contribution of this work is a finite element discretization of Maxwell's equations in cubicly nonlinear media which is energy-stable and exactly conserves Gauss's laws. Moreover, this approach may be readily adapted to consider more general nonlinear media in subsequent work.