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Advances in finite-difference time-domain calculation methods

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Light Scattering Reviews, Vol. 6

Abstract

Although the finite-difference time-domain (FDTD) method was developed in the 1960s, beginning with Yee’s famous algorithm [1], and many advances have been made since then, FDTD is still an active field of research.

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References

  1. K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Antenna Propagation, AP-14, 302–307 (1966).

    ADS  Google Scholar 

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

    Google Scholar 

  3. R. E. Mickens, Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore (1994).

    MATH  Google Scholar 

  4. J. B. Cole, High accuracy Yee algorithm based on nonstandard finite differences: new developments and verification, IEEE Trans. Antennas and Propagation, 50, no. 9, 1185–1191 (2002).

    Article  MathSciNet  ADS  Google Scholar 

  5. J. B. Cole, High accuracy FDTD solution of the absorbing wave equation, and conducting Maxwell’s equations based on a nonstandard finite difference model, IEEE Trans. on Antennas and Propagation, 53, no. 2, 725–729 (2004).

    Article  ADS  Google Scholar 

  6. J. B. Cole, S. Banerjee, M. I. Haftel, High accuracy nonstandard finite-difference time-domain algorithms for computational electromagnetics: applications to optics and photonics, Chapter 4, pp. 89–109 in Advances in the Applications of Nonstandard Finite Difference Schemes, R. E. Mickens, ed., Scientific (Singapore, 2005).

    Chapter  Google Scholar 

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

    Book  Google Scholar 

  8. N. Okada, J. B. Cole, Simulation of whispering gallery modes in the Mie regime using the nonstandard finite difference time domain algorithm, J. Optical Society of America B, 27, issue 4, 631–639 (2010).

    Article  ADS  Google Scholar 

  9. We thank Dr. Till Plewe for this idea; private discussions, unpublished.

    Google Scholar 

  10. T. Ohtani, K. Taguchi, T. Kashiwa, T. Kanai, J. B. Cole, Nonstandard FDTD method for wideband analysis, IEEE Trans. on Antennas and Propagation, 57, issue 8, 2386–2396 (2009).

    Article  MathSciNet  ADS  Google Scholar 

  11. L. Rayleigh, The problem of the whispering gallery, Philos. Mag., 20, 1001–1004 (1910).

    Google Scholar 

  12. C. G. B. Garrett, W. Kaiser, W. L. Bond, Stimulated emission into optical whispering gallery modes of spheres, Phys. Rev., 124, 1807–1809 (1961).

    Article  ADS  Google Scholar 

  13. P. Chyek, V. Ramaswamy, A. Ashkin, and J. M. Dziedzic, Simultaneous determination of refractive index and size of spherical dielectric particles from light scattering data, Appl. Opt., 22, 2302–2307 (1983).

    Article  ADS  Google Scholar 

  14. A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, L. Maleki, Review of applications of whispering gallery mode resonators in photonics and nonlinear optics, IPN Progress Report, pp. 42–162 (2005).

    Google Scholar 

  15. J. P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, Journal of Computational Physics, 114, 185–200 (1994).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. N. Okada, J. B. Cole, High-accuracy finite-difference time domain algorithm for the coupled wave equation, J. Opt. Soc. Am. B, 27, 7, 1409-1413 (2010).

    Article  Google Scholar 

  17. A. Taflove and S. C. Hagness: Computational Electrodynamics, the Finite Difference Time-Domain Method, 3rd ed., Chap. 8, p. 329, Chap. 9, p. 355, Artech House, Boston, 2005.

    Google Scholar 

  18. S. Banerjee, T. Hoshino and J. B. Cole, Simulation of subwavelength metallic gratings using a new implementation of recursive convolution FDTD, JOSA A, 25, no. 8, 1921 (2008).

    Article  MathSciNet  ADS  Google Scholar 

  19. A. Vial, A. S. Grimault, D. Macias, D. Barchiesi, and M. L. de la Chapelle, Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method, Phys. Rev. B 71, 085416-1 (2005).

    Article  ADS  Google Scholar 

  20. A. Vial, Problems encountered when modeling dispersive materials using the FDTD method˚A, Proceedings of Workshop, Nano particles, nano structures and near field computation, T. Wriedt, Y. Eremin, W. Hergert, Eds., Bremen, pp. 56, 2010.

    Google Scholar 

  21. H. Tamada, T. Doumuki, T. Yamaguchi, and S. Matsumoto, Al wire-grid polarizer using the s-polarization resonance effect at the 0.8-mm-wavelength band, Opt. Lett., 22, no. 6, 419 (1997).

    Article  ADS  Google Scholar 

  22. M. A. Jensen and G. P. Nordin, Finite-aperture wire grid polarizers, JOSA A, 17, no. 12, 2191 (2000).

    Article  ADS  Google Scholar 

  23. M. Xu, H. P. Urbach, D. K. G de Boer, and H. J. Cornelissen, Wire-grid diffraction gratings used as polarizing beam splitter for visible light and applied in liquid crystal on silicon, Opt. Exp., 13, no. 7, 2303 (2005).

    Article  ADS  Google Scholar 

  24. X. D. Mi, D. Kessler, L. W. Tutt, and L. W. Brophy, Low fill-factor wire grid polarizers for LCD backlighting, Society for Information Display (SID) Digest 2005, p. 1004.

    Google Scholar 

  25. M. Paukshto, Simulation of sub-100 nm gratings incorporated in LCD stack, Society for Information Display (SID) Digest 2006, p. 848.

    Google Scholar 

  26. S. Banerjee and K. Nakatsuka, Compact design of light guides using metal grating based polarizing optical controller element, Proc. International Display Workshop 2007, Sapporo, Japan, p. 2087.

    Google Scholar 

  27. J. H. Lee, Y. W. Song, J. G. Lee, J. Ha, K. H. Hwang, and D. S. Zang, Optically bifacial thin-film wire-grid polarizers with nano-patterns of a graded metal-dielectric composite layer, Optics Express, 16, no. 21, 16867 (2008).

    Google Scholar 

  28. E. H. Land, Some aspects of the development of sheet polarizers, JOSA, 41, no. 12, 957 (1951).

    Article  ADS  Google Scholar 

  29. S. Banerjee, J. B. Cole and T. Yatagai, Colour characterization of a Morpho butterfly wing-scale using a high accuracy nonstandard finite-difference time-domain method, Micron, 38, 97–103 (2007).

    Article  Google Scholar 

  30. C. L. Foiles, Optical properties of pure metals and binary alloys, Chapter 4 of Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology New Series, Vol. 15, Subvolume b, K.-H. Hellwege and J. L. Olsen, Eds., Springer-Verlag, Berlin, 1985, p. 228.

    Google Scholar 

  31. M. Born, and E. Wolf, Principles of Optics, 7th (expanded) ed., Chap. XIV. Cambridge University Press, San Francisco, 1999.

    Google Scholar 

  32. S. Banerjee and L. N. Hazra, Experiments with a genetic algorithm for structural design of cemented doublets with prespecified aberration targets, App. Opt., 40, no. 34, 6265 (2001).

    Article  ADS  Google Scholar 

  33. J. B. Cole and D. Zhu, Improved version of the second-order Mur absorbing boundary condition based on a nonstandard finite difference model, J. Applied Computational Electromagnetics Society, 24, no. 4 (2009).

    Google Scholar 

  34. D. E. Aspnes and A. A. Studna, Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV, Phys. Rev. B, 27, 985 (1983).

    Article  ADS  Google Scholar 

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Cole, J.B., Okada, N., Banerjee, S. (2012). Advances in finite-difference time-domain calculation methods. In: Kokhanovsky, A. (eds) Light Scattering Reviews, Vol. 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15531-4_4

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  • DOI: https://doi.org/10.1007/978-3-642-15531-4_4

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