A Perspective on the 40-Year History of FDTD Computational Electrodynamics

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boundary value problems involving

Maxwell’s equations in isotropic media,”

IEEE Trans. Antennas Propagat., vol. 14, pp.

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K. L. Shlager and J. B. Schneider, “A Survey

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tional Electrodynamics: The Finite-Difference

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, 1980.

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difference time-domain method to sinusoidal

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Compat., vol. 22, pp. 191–202, 1980.

G. Mur, “Absorbing boundary conditions for

the finite-difference approximation of the

time-domain electromagnetic field equations,”

IEEE Trans. Electromagn. Compat., vol. 23,

pp. 377–382, 1981.

K. R. Umashankar and A. Taflove, “A novel

method to analyze electromagnetic scattering

of complex objects,” IEEE Trans.

Electromagn. Compat., vol. 24, pp. 397–405,

A. Taflove and K. R. Umashankar, “Radar

cross section of general three-dimensional

scatterers,” IEEE Trans. Electromagn.

Compat., vol. 25, pp. 433–440, 1983.

Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F.

Yuan, “A transmitting boundary for transient

wave analyses,” Scientia Sinica (series A),

vol. XXVII, pp. 1063–1076, 1984.

TAFLOVE: 40-YEAR HISTORY OF FDTD

W. Gwarek, “Analysis of an arbitrarily

shaped planar circuit — A time-domain

approach,” IEEE Trans. Microwave Theory

Tech., vol. 33, pp. 1067–1072, 1985.

D. H. Choi and W. J. Hoefer, “The finite-

difference time-domain method and its

application to eigenvalue problems,” IEEE

Trans. Microwave Theory Tech., vol. 34, pp.

–1470, 1986.

G. A. Kriegsmann, A. Taflove, and K. R.

Umashankar, “A new formulation of electro-

magnetic wave scattering using an on-surface

radiation boundary condition approach,”

IEEE Trans. Antennas Propagat., vol. 35, pp.

–161, 1987.

T. G. Moore, J. G. Blaschak, A. Taflove, and

G. A. Kriegsmann, “Theory and application

of radiation boundary operators,” IEEE

Trans. Antennas Propagat., vol. 36, pp.

–1812, 1988.

K. R. Umashankar, A. Taflove, and B. Beker,

“Calculation and experimental validation of

induced currents on coupled wires in an

arbitrary shaped cavity,” IEEE Trans.

Antennas Propagat., vol. 35, pp. 1248–1257,

A. Taflove, K. R. Umashankar, B. Beker, F.

A. Harfoush, and K. S. Yee, “Detailed FDTD

analysis of electromagnetic fields penetrating

narrow slots and lapped joints in thick

conducting screens,” IEEE Trans. Antennas

Propagat., vol. 36, pp. 247–257, 1988.

T. G. Jurgens, A. Taflove, K. R. Umashankar,

and T. G. Moore, “Finite-difference time-

domain modeling of curved surfaces,” IEEE

Trans. Antennas Propagat., vol. 40, pp. 357–

, 1992.

A. C. Cangellaris, C.-C. Lin, and K. K. Mei,

“Point-matched time-domain finite element

methods for electromagnetic radiation and

scattering,” IEEE Trans. Antennas Propagat.,

vol. 35, pp. 1160–1173, 1987.

V. Shankar, A. H. Mohammadian, and W. F.

Hall, “A time-domain finite-volume treatment

for the Maxwell equations,” Electromag-

netics, vol. 10, pp. 127–145, 1990.

N. K. Madsen and R. W. Ziolkowski, “A

three-dimensional modified finite volume

technique for Maxwell’s equations,”

Electromagnetics, vol. 10, pp. 147–161,

D. M. Sullivan, O. P. Gandhi, and A. Taflove,

“Use of the finite-difference time-domain

method in calculating EM absorption in man

models,” IEEE Trans. Biomed. Engrg., vol.

, pp. 179–186, 1988.

X. Zhang, J. Fang, K. K. Mei, and Y. Liu,

“Calculation of the dispersive characteristics

of microstrips by the time-domain finite-

difference method,” IEEE Trans. Microwave

Theory Tech., vol. 36, pp. 263–267, 1988.

J. Fang, Time-Domain Finite Difference

Computations for Maxwell’s Equations,

Ph.D. dissertation, EECS Dept., Univ. of

California, Berkeley, CA, 1989.

T. Kashiwa and I. Fukai, “A treatment by

FDTD method of dispersive characteristics

associated with electronic polarization,”

Microwave Optics Tech. Lett., vol. 3, pp.

–205, 1990.

R. Luebbers, F. Hunsberger, K. Kunz, R.

Standler, and M. Schneider, “A frequency-

dependent finite-difference time-domain

formulation for dispersive materials,” IEEE

Trans. Electromagn. Compat., vol. 32, pp.

–229, 1990.

R. M. Joseph, S. C. Hagness, and A. Taflove,

“Direct time integration of Maxwell’s

equations in linear dispersive media with

absorption for scattering and propagation of

femtosecond electromagnetic pulses,” Optics

Lett., vol. 16, pp. 1412–1414, 1991.

J. G. Maloney, G. S. Smith, and W. R. Scott,

Jr., “Accurate computation of the radiation

from simple antennas using the finite-

difference time-domain method,” IEEE

Trans. Antennas Propagat., vol. 38, pp.

–1065, 1990.

D. S. Katz, A. Taflove, M. J. Piket-May, and

K. R. Umashankar, “FDTD analysis of

electromagnetic wave radiation from systems

containing horn antennas,” IEEE Trans.

Antennas Propagat., vol. 39, pp. 1203–1212,

P. A. Tirkas and C. A. Balanis, “Finite-

difference time-domain technique for

radiation by horn antennas,” Proc. 1991 IEEE

Antennas Propagat. Soc. Intl. Symp., vol. 3,

pp. 1750–1753, 1991.

ACES JOURNAL, VOL. 22, NO. 1, MARCH 2007

E. Sano and T. Shibata, “Fullwave analysis of

picosecond photoconductive switches,” IEEE

J. Quantum Electron., vol. 26, pp. 372–377,

S. M. El-Ghazaly, R. P. Joshi, and R. O.

Grondin, “Electromagnetic and transport

considerations in subpicosecond photo-

conductive switch modeling,” IEEE Trans.

Microwave Theory Tech., vol. 38, pp. 629–

, 1990.

R. J. Luebbers, K. S. Kunz, M. Schneider,

and F. Hunsberger, “A finite-difference time-

domain near zone to far zone transformation,”

IEEE Trans. Antennas Propagat., vol. 39,

pp. 429–433, 1991.

P. M. Goorjian and A. Taflove, “Direct time

integration of Maxwell’s equations in

nonlinear dispersive media for propagation

and scattering of femtosecond electromag-

netic solitons,” Optics Lett., vol. 17, pp. 180–

, 1992.

R. W. Ziolkowski and J. B. Jerkins, “Full-

wave vector Maxwell’s equations modeling

of self-focusing of ultra-short optical pulses

in a nonlinear Kerr medium exhibiting a finite

response time,” J. Optical Soc. America B,

vol. 10, pp. 186–198, 1993.

R. M. Joseph and A. Taflove, “Spatial soliton

deflection mechanism indicated by FDTD

Maxwell’s equations modeling,” IEEE

Photonics Tech. Lett., vol. 2, pp. 1251–1254,

W. L. Ko and R. Mittra, “A combination of

FDTD and Prony’s methods for analyzing

microwave integrated circuits,” IEEE Trans.

Microwave Theory Tech., vol. 39, pp. 2176–

, 1991.

J. A. Pereda, L. A. Vielva, and A. Prieto,

“Computation of resonant frequencies and

quality factors of open dielectric resonators

by a combination of the finite-difference

time-domain (FDTD) and Prony’s methods,”

IEEE Microwave Guided Wave Lett., vol. 2,

pp. 431–433, 1992.

J. Chen, C. Wu, T. K. Y. Lo, K.-L. Wu, and J.

Litva, “Using linear and nonlinear predictors

to improve the computational efficiency of

the FDTD algorithm,” IEEE Trans.

Microwave Theory Tech., vol. 42, pp. 1992–

, 1994.

V. Jandhyala, E. Michielssen, and R. Mittra,

“FDTD signal extrapolation using the

forward-backward autoregressive (AR)

model,” IEEE Microwave Guided Wave Lett.,

vol. 4, pp. 163–165, 1994.

S. Dey and R. Mittra, “Efficient computation

of resonant frequencies and quality factors of

cavities via a combination of the finite-

difference time-domain technique and the

Padé approximation,” IEEE Microwave

Guided Wave Lett., vol. 8, pp. 415–417, 1998.

W. Sui, D. A. Christensen, and C. H. Durney,

“Extending the two-dimensional FDTD

method to hybrid electromagnetic systems

with active and passive lumped elements,”

IEEE Trans. Microwave Theory Tech., vol.

, pp. 724–730, 1992.

B. Toland, B. Houshmand, and T. Itoh,

“Modeling of nonlinear active regions with

the FDTD method,” IEEE Microwave Guided

Wave Lett., vol. 3, pp. 333–335, 1993.

V. A. Thomas, M. E. Jones, M. J. Piket-May,

A. Taflove, and E. Harrigan, “The use of

SPICE lumped circuits as sub-grid models for

FDTD high-speed electronic circuit design,”

IEEE Microwave Guided Wave Lett., vol. 4,

pp. 141–143, 1994.

J. P. Berenger, “A perfectly matched layer for

the absorption of electromagnetic waves,”

J. Comp. Phys., vol. 114, pp. 185–200, 1994.

D. S. Katz, E. T. Thiele, and A. Taflove,

“Validation and extension to three

dimensions of the Berenger PML absorbing

boundary condition for FDTD meshes,” IEEE

Microwave Guided Wave Lett., vol. 4, pp.

–270, 1994.

C. E. Reuter, R. M. Joseph, E. T. Thiele, D.

S. Katz, and A. Taflove, “Ultrawideband

absorbing boundary condition for termination

of waveguiding structures in FDTD

simulations,” IEEE Microwave Guided Wave

Lett., vol. 4, pp. 344–346, 1994.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.

F. Lee, “A perfectly matched anisotropic

absorber for use as an absorbing boundary

condition,” IEEE Trans. Antennas Propagat.,

vol. 43, pp. 1460–1463, 1995.

TAFLOVE: 40-YEAR HISTORY OF FDTD

S. D. Gedney, “An anisotropic perfectly

matched layer absorbing media for the

truncation of FDTD lattices,” IEEE Trans.

Antennas Propagat., vol. 44, pp. 1630–1639,

R. W. Ziolkowski, J. M. Arnold, and D. M.

Gogny, “Ultrafast pulse interactions with

two-level atoms,” Phys. Rev. A , vol. 52, pp.

–3094, 1995.

A. S. Nagra and R. A. York, “FDTD analysis

of wave propagation in nonlinear absorbing

and gain media,” IEEE Trans. Antennas

Propagat., vol. 46, pp. 334–340, 1998.

Y. Huang, Simulation of Semiconductor

Materials Using FDTD Method, M.S. thesis,

Northwestern University, Evanston, IL, 2002.

S.-H. Chang and A. Taflove, “Finite-

difference time-domain model of lasing

action in a four-level two-electron atomic

system,” Optics Express, vol. 12, pp. 3827–

, 2004.

M. Krumpholz and L. P. B. Katehi, “MRTD:

New time-domain schemes based on

multiresolution analysis,” IEEE Trans.

Microwave Theory Tech., vol. 44, pp. 555–

, 1996.

Q. H. Liu, The PSTD Algorithm: A Time-

Domain Method Requiring Only Two Grids

Per Wavelength, New Mexico State Univ.,

Las Cruces, NM, Tech. Rept. NMSU-ECE96-

, 1996.

Q. H. Liu, “The pseudospectral time-domain

(PSTD) method: A new algorithm for

solutions of Maxwell’s equations,” Proc.

I EEE Antennas Propagat. Soc. Intl.

Symp., vol. 1, pp. 122–125, 1997.

O. M. Ramahi, “The complementary

operators method in FDTD simulations,”

IEEE Antennas Propagat. Mag., vol. 39, pp.

–45, Dec. 1997.

S. Dey and R. Mittra, “A locally conformal

finite-difference time-domain algorithm for

modeling three-dimensional perfectly

conducting objects,” IEEE Microwave

Guided Wave Lett., vol. 7, pp. 273–275, 1997.

J. G. Maloney and M. P. Kesler, “Analysis of

Periodic Structures,” Chap. 6 in Advances in

Computational Electrodynamics: The Finite-

Difference Time-Domain Method, A. Taflove,

(ed.), Norwood, MA: Artech House, 1998.

J. B. Schneider and C. L. Wagner, “FDTD

dispersion revisited: Faster-than-light

propagation,” IEEE Microwave Guided Wave

Lett., vol. 9, pp. 54–56, 1999.

T. Namiki, “3-D ADI-FDTD method —

Unconditionally stable time-domain

algorithm for solving full vector Maxwell’s

equations,” IEEE Trans. Microwave Theory

Tech., vol. 48, pp. 1743–1748, 2000.

F. Zheng, Z. Chen, and J. Zhang, “Toward the

development of a three-dimensional

unconditionally stable finite-difference time-

domain method,” IEEE Trans. Microwave

Theory Tech., vol. 48, pp. 1550–1558, 2000.

J. A. Roden and S. D. Gedney, “Convolu-

tional PML (CPML): An efficient FDTD

implementation of the CFS-PML for arbitrary

media,” Microwave Optical Tech. Lett., vol.

, pp. 334–339, 2000.

T. Rylander and A. Bondeson, “Stable

FDTD-FEM hybrid method for Maxwell’s

equations,” Comput. Phys. Comm., vol. 125,

pp. 75–82, 2000.

M. Hayakawa and T. Otsuyama, “FDTD

analysis of ELF wave propagation in inhomo-

geneous subionospheric waveguide models,”

ACES J., vol. 17, pp. 239–244, 2002.

J. J. Simpson and A. Taflove, “Three-

dimensional FDTD modeling of impulsive

ELF propagation about the Earth-sphere,”

IEEE Trans. Antennas Propagat., vol. 52, pp.

–451, 2004.

J. J. Simpson, R. P. Heikes, and A. Taflove,

“FDTD modeling of a novel ELF radar for

major oil deposits using a three-dimensional

geodesic grid of the Earth-ionosphere

waveguide,“ IEEE Trans. Antennas

Propagat., vol. 54, pp. 1734-1741, 2006.

H. De Raedt, K. Michielsen, J. S. Kole, and

M. T. Figge, “Solving the Maxwell equations

by the Chebyshev method: A one-step finite

difference time-domain algorithm,” IEEE

Trans. Antennas Propagat., vol. 51, pp.

–3160, 2003.

N. Chavannes, R. Tay, N. Nikoloski, and N.

Kuster, “Suitability of FDTD-based TCAD

tools for RF design of mobile phones,” IEEE

Antennas Propagat. Magazine, vol. 45, pp.

–66, Dec. 2003.

ACES JOURNAL, VOL. 22, NO. 1, MARCH 2007

E. J. Bond, X. Li, S. C. Hagness, and B. D.

Van Veen, “Microwave imaging via space-

time beamforming for early detection of

breast cancer,” IEEE Trans. Antennas

Propagat., vol. 51, pp. 1690– 1705, 2003.

J. J. Simpson, A. Taflove, J. A. Mix, and

H. Heck, “Substrate integrated waveguides

optimized for ultrahigh-speed digital inter-

connects,“ IEEE Trans. Microwave Theory

Tech., vol. 54, pp. 1983-1990, 2006.

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju,

J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H.

Lee, “Electrically driven single-cell photonic

crystal laser,” Science, vol. 305, pp. 1444–

, 2004.

L. Yin, V. K. Vlasko-Vlasov, A. Rydh,

J. Pearson, U. Welp, S.-H. Chang, S. K. Gray,

G. C. Schatz, D. B. Brown, and C. W.

Kimball, “Surface plasmons at single

nanoholes in Au films,” Applied Physics

Lett., vol. 85, pp. 467–469, 2004.

M. F. Yanik, S. Fan, M. Soljacic, and J. D.

Joannopoulos, “All-optical transistor action

with bistable switching in a photonic crystal

cross-waveguide geometry,” Optics Lett., vol.

, pp. 2506–2508, 2003.

X. Li, A. Taflove, and V. Backman, “Recent

progress in exact and reduced-order modeling

of light-scattering properties of complex

structures,” IEEE J. Selected Topics in

Quantum Electronics, Special Issue on

Biophotonics, vol. 11, pp. 759-765, 2005.

H. K. Roy, Y. Liu, R. Wali, Y. L. Kim, A. K.

Kromine, M. J. Goldberg, and V. Backman,

“Four-dimensional elastic light-scattering

fingerprints as preneoplastic markers in the

rat model of colon carcinogenesis,” Gastro-

enterology, vol. 126, pp. 1071–1081, 2004.

H. K. Roy, Y. L. Kim, Y. Liu, R. K. Wali, M.

J. Goldberg, V. Turhitsky, J. Horwitz, and

V. Backman, “Risk-stratification of colon

carcinogenesis through enhanced backscat-

tering (EBS) spectroscopy analysis of the

uninvolved colonic mucosa,” Clinical Cancer

Research, vol. 19, pp. 961–968, 2006.

X. Li, “Synthesis of backscattering

microscope amplitude images from FDTD-

computed near fields,” manuscript in

preparation.

Y. Liu, P. Pradhan, X. Li, Y. L. Kim, R. K.

Wali, H. K. Roy, A. Taflove, and V.

Backman, “Alteration of intracellular

mesoscopic light transport in the earliest stage

of carcinogenesis demonstrated by single-cell

partial-wave spectroscopy,” manuscript in

preparation.

S. H. Tseng, A. Taflove, D. Maitland, and

V. Backman, “Pseudospectral time-domain

simulations of multiple light scattering in

three-dimensional macroscopic random

media,” Radio Science, vol. 41, RS4009,

doi:10.1029/2005RS003408, 2006.