Finite-Difference Time-Domain Method

The finite-difference time-domain (FDTD) method [1] is one of the most frequently used techniques in electromagnetics. It involves the space and time discretization of the whole working space and the finite-difference approximation to Maxwell s differential equations. For the analysis of the 

Its disadvantages are given as follows (1) it is inefficient compared with the method of moments (MoM) (2) it cannot deal with oblique boundaries that are not aligned with the Cartesian grid and (3) it would require a complex procedure for implementing dispersive materials (materials with frequency-dependent constitutive constants). 

FDTD cell with x-, y-, and 2-directed components of electric and magnetic fields. 

Rearranging Equation 5.13, the updating equation for electric field at time step n from its one-time-step previous value E and half-time-step previous magnetic-field rotation H (V2) jg obtained as follows  

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Futamata, M., Maruyama, Y. and Ishikawa, M. (2003) Local electric field and scattering cross section of Ag nanopartides under surface plasmon resonance by finite difference time domain method. J. Phys. Chem. B, 107, 7607-7617. 

Chu, S.T. and Chaudhuri, S.K., 1989, A finite-difference time domain method for the design and analysis of guided-wave optical structures, J. Lightwave Technol. 7 2033-2038. 

A. Taflove and S.C. Hagness, Computational electrodynamics the finite-difference time-domain method, 2 ed., (ArtechHouse, Norwood, 2000). 

Many interesting phenomena can arise in nonlinear periodic structures that possess the Kerr nonlinearity. For analytic description of such effects, the slowly varying amplitude (or envelope) approximation is usually applied. Alternatively, in order to avoid any approximation, we can use various numerical methods that solve Maxwell s equations or the wave equation directly. Examples of these rigorous methods that were applied to the modelling of nonlinear periodical structures are the finite-difference time-domain method, transmission-line modelling and the finite-element frequency-domain method." ... 

K. L. Shlager, and J. B. Schneider, A survey of the finite-difference time domain literature, in A. Taflove (Ed,), Advances in computational electrodynamics the finite difference time domain method (Artech House, 1998), pp. 1- 62. 

Kunz, K. S., and Luebbers, R. J. 1999. The finite difference time domain method for electromagnetics. Boca Raton CRC Press. 

FDTD finite difference time domain (method)... 

Oubre, C. and Nordlander, P. (2004) Optical properties of metallodielectric nanostrucmres calculated using the finite difference time domain method. Journal of Physical Chemistry B, 108, 17740-17747. 

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

A. Taflove and S. C. Hagness, Computational Electrodynamics The Finite-Difference Time-Domain Method, 3rd ed. Norwood, MA Artech House, 2005. 

G. Sun and C. W. Trueman, Optimized finite-difference time-domain methods based on the (2,4) stencil, IEEE Trans. Microw. Theory Tech., vol. 53, no. 3, pp. 832-842, Mar. 

E. A. Navarro, C. Wu, R Y. Chung, and J. Litva, Some considerations about the finite difference time domain method in general curvilinear coordinates, IEEE Microw. Guided Wave Lett., vol. 6, pp. 193-195, June 1996.doi 10.1109/75.491502... 

S. D. Gedney, J. A. Roden, N. K. Madsen. A. H. Mohammadian, W. F. Hall, V. Sankar, and C. Rowell, Explicit time-domain solutions of Maxwell s equations via generalized grids, in Advances in Computational Electrodynamics The Finite-Difference Time-Domain Method, A. Taflove, Ed. Norwood, MA Artech House, 1998, ch. 4, pp. 163—262. 

M. Feliziani, F. Maradei, and G. Tribellini, Field analysis of penetrable conductive shields by the finite-difference time-domain method with impedance network boundary conditions (INBC s), IEEE Trans. Electromagn. Compat., vol. 41, pp. 307-319, Nov. 1999.doi 10.1109/15.809801... 

N. Farahat, W. Yu, and R. Mittra, A fast near-to-far-field transformation in body of revolution finite-difference time-domain method, IEEE Trans. Antennas Propag., vol. 51, no. 9, pp. 2534-2540, Sep. 2003.doi 10.1109/TAP.2003.816360... 

A modified approach in [23] is to apply a transmission line model with Finite-Difference Time-Domain method (FDTD). But this method has some drawbacks. 

The radiation characteristics of axisymmetric spheroidal microorganisms, such a C. reinhardtii (Fig. lA), with major and minor chameten a and b can be predicted numerically using (i) the T-matrix method (Waterman, 1965 Mackowski, 1994 Mishchenko et al., 2002, 1995), (ii) the discrete-dipole approximation (Draine, 1988), and (iii) the finite-difference time-domain method (Liou, 2002). Most often, however, they have been approximated as homogeneous spheres with some equivalent radius r and some effective complex index of refraction nix = n +ikx (Pettier et al., 2005 Berbero u et al., 2007 Dauchet et al., 2015), as discussed in Section 3.6.1. 

Kriezis, E. E. Elston, S. J. (1999). Finite-difference time domain method for light wave propagation within liquid crystal devices. Opt Commun., Vol. 165, No. 1-3, (July... 

Oh, C. Escuti, M. J. (2007). Numerical analysis of polarization gratings using the finite-difference time-domain method. Phys. Rea. A, Vol. 76, No. 043815, (October 2007), pp. 1-8, ISSN 1050-2947... 

FDTD Finite Difference Time Domain Method... 

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