Nonstandard FDTD Simulations

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Since 5 Jan. 2011.

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Nonstandard FDTD Theory

Morpho Butterfly Rendering

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Open this homepage! (5 Jan. 2011)

Welcome to Nonstandard FDTD Simulations!

(a) Whispering Gallery Mode	(b) Rendered Morpho Butterfly CG

In this website you can find researches based on the nonstandard finite difference time domain (FDTD) algorithm. The nonstandard FDTD algorithm is much more accurate than conventional FDTD (Yee) algorithm by optimizing to monochromatic waves in electromagnetic computation. We introduce the nonstandard FDTD theory and learning examples in http://nsfdtd.org/theory/.

Figure (a) is an result of the whispering gallery mode simulation using the nonstandard FDTD algorithm. Whispering gallery modes are resonances in the interior of highly symmetric structures and require a large number of wave periods to obtain convergence in the simulation. The conventional FDTD algorithm cannot accurately simulate whispering gallery modes, whereas the nonstandard FDTD algorithm has successfully.

Figure (b) is a rendered image of a Morpho butterfy based on the nonstandard FDTD analysis. Our CG animation and real one of Morpho butterflies can be seen at Youtube:

CG animation	Real one (Morpho helena)

The male of a species of Morpho butterfly native to Central and South America, is known as the "jewel of the Amazon," and displays a mysterious and brilliant blue color, which is not due to pigments. This brilliant blue originates from optical interference in nano-structures on the wing, and is called "structure coloring." Structural colors are difficult to render even using the most advanced rendering methods, because these rendering methods are based on geometric optics which are of no use on sub-wavelength structures. We developed a new rendering method besed on the nonstandard FDTD computation and rendered photorealistic Morpho butterfly images.

What is the FDTD algorithm?

The finite difference time domain (FDTD) algorithm is a useful scheme to numerically solve the Maxwell's equations. In 1966, K. S. Yee developed the FDTD algorithm based on a simple central finite difference model and it is also called "Yee algorithm" [1]. At that time, however, the FDTD algorithm did not get attention because computers were less-developed. In the 1970s and 1980s, the FDTD algorithm came under the spotlight with drastic advancements in electronics technology. Recently, the FDTD algorithm is used in many electromagnetic analyses and utility device designs such as optical fiber, antenna, meta-materials, and so on.

What is the Nonstandard FDTD algorithm?

The nonstandard FDTD algorithm is an advanced FDTD theory optimized to monochromatic wave propagation. In 1994, R. E. Mickens proposed a general nonstandard finite difference model for some differential equations [2]. In 1995, J. B. Cole developed the nonstandard FDTD algorithm for the Maxwell's equations [3][4]. The nonstandard FDTD algorithm provides remarkably high accuracy even on a coarse grid without increasing computational cost.

Bibliography:

1. K. S. Yee, "Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. 14, 3, pp. 302-307 (1966).
2. R. E. Mickens, "Nonstandard Finite Difference Models of Differential Equation," World Scientific (1994).
3. J. B. Cole, "A high accuracy FDTD algorithm to solve microwave propagation and scattering problems on a coarse grid" IEEE Trans. Microwave Theory and Tech., 43, 9, pp. 2053-2058 (1995).
4. J. B. Cole, "A high-accuracy realization of the Yee algorithm using non-standard finite differences," IEEE Trans. Microwave Theory and Tech., 45, 6, pp. 991-996 (1997).

Copyright (C) 2011 Naoki Okada, All Rights Reserved.