Nonstandard Finite Difference Time Domain Methodology to Simulate Light Propagation in Nonlinear Materials

Authors

  • James B. Cole University of Tsukuba, Japan

DOI:

https://doi.org/10.13052/2024.ACES.J.390303

Keywords:

Finite difference time domain (FDTD), Nonlinear optics, Nonlinear susceptibility, nonstandard FDTD, quantum electrodynamics, superconductivity

Abstract

We extend the nonstandard (NS) finite difference time domain (FDTD) methodology, originally developed to solve Maxwell’s equations in linear materials, to nonlinear ones. We validate it by computing harmonics generation in a nonlinear dielectric and comparing with theory. The methodology also applies to the quantum electrodynamics that describes the interaction of charged particles with electromagnetic fields, and also to the Ginzburg-Landau model of superconductivity.

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Author Biography

James B. Cole, University of Tsukuba, Japan

James B. Cole graduated from the University of Maryland, PhD particle physics. After a post-doctoral fellowship (US National Research Council) at the NASA-Goddard Space Flight Center, he was a research physicist at several US National Laboratories, before joining the faculty of University of Tsukuba (Japan).

After returning to the US, he was a senior research fellow of the National Academy of Sciences, and is now a corporate research physicist. He specializes in mathematical models and high precision algorithm development for applications to computational optics and photonics, quantum mechanics, and machine learning. He is one of the pioneers of the methodology of nonstandard finite differences, and has published numerous papers and a book on the subject.

References

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics. Boca Raton: CRC Press, 1993.

J. B. Cole and S. Banerjee, Computing the Flow of Light, Bellingham: SPIE Press, 2017.

R. Mickens, Advances in the Applications of Nonstandard Finite Difference Difference Schemes, Singapore: World Scientific, 2005.

E. Merzbacher, Quantum Mechanics, 2nd ed. Hoboken: John Wiley, 1970.

R. W. Boyd, Nonlinear Optics, 3rd

ed. Cambridge, MA: Academic Press, 2008.

J. Strikwerda, Finite Difference Schemes and Partial Differential Equations, 2nd ed. Philadelphia: SIAM, 2004.

J. R. Pierce, An Introduction to Information Theory: Symbols, Signalsand Noise, 2nd ed. New York: Dover Publications, 1980.

A. Kiran Güçoğlu, The Solution of Some Differential Equations by Nonstandard Finite Difference Method, MS Dissertation, İzmir Institute of Technology, Türkiye, 2005.

B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Mathematics of Computation, vol. 31, pp. 629–651, 1977.

G. Mur, “Absorbing boundary conditions for the finite- difference approximation of the time domain electromagnetic field equations,” IEEE Transactions on Electromagnetic Compatibility, vol. 23, pp. 377–382, 1981.

J. A. Stratton, Electromagnetic Theory. New York: McGraw-Hill Book Company, 1941.

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods, World Scientific, Singapore, 1990.

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Published

2024-03-31

How to Cite

[1]
J. B. Cole, “Nonstandard Finite Difference Time Domain Methodology to Simulate Light Propagation in Nonlinear Materials”, ACES Journal, vol. 39, no. 03, pp. 183–188, Mar. 2024.

Issue

2024: Vol 39 Iss 3

Section

Special issue on Finite Difference Methodologies for Microwave, Optical .....