Prospects for Finite-Difference Time-Domain (FDTD) Computational Electrodynamics Allen Taflove Department of Electrical and Computer Engineering Northwestern University, Evanston, IL 60208 Presented at: IEEE Antennas and Propagation / Microwave Theory and Techniques Societies Chicago Section October 24, 2002
The Classic FDTD Algorithm 2nd-order accurate • central space differences 2nd-order accurate • leapfrog time-stepping Absorbing boundary • condition at edge of the space lattice Kane Yee, IEEE Trans. Antennas and Propagation , May 1966.
Yearly Number of FDTD Publications Yee (1966) Source: J. Schneider and K. Shlager (1998)
FDTD Literature Database* www.fdtd.org As of Oct. 22, 2002, the total number of entries in this NSF/ONR - sponsored database was 4793. Breakdown: — Books: 9 — Ph.D. dissertations: 162 — Masters theses: 68 — Journal articles: 2549 — Conference proceedings: 1951 — Technical reports: 15 — Miscellaneous publications: 39 * Maintained by John Schneider, Washington State University
At Least 17 Commercial FDTD Codes are Found on the Web APLAC http://www.aplac.hut.fi/aplac/general.html Apollo Photonics http://www.apollophoton.com/ Applied Simulation Technology http://www.apsimtech.com/ CFD Research http://www.cfdrc.com/datab/software/maxwell/maxwell.html Cray http://lc.cray.com/ Empire http://www.empire.de/ EMS Plus http://www.ems-plus.com/ezfdtd.html ETH http://www.iis.ee.ethz.ch/research/bioemc/em_simulation_platform.en.html Optima Research http://www.optima-research.com/Software/Waveguide/fullwave.htm Optiwave http://www.optiwave.com/ Quick Wave http://www.ire.pw.edu.pl/ztm/pmpwtm/qw3d/ Remcom http://www.remcominc.com/html/index.html RSoft http://www.rsoftinc.com/fullwave_info.htm Schmid http://www.semcad.com/solver_performance.html Vector Fields http://www.vectorfields.com/concerto.htm Virtual Science http://www.virtual-science.co.uk/celia/Celia_code/celia_home.htm Zeland Software http://www.zeland.com/fidelity.html
Why FDTD is Popular • It is conceptually simple and systematic. • It is accurate and robust. • It uses no linear algebra. • It treats impulsive behavior naturally. • It treats nonlinear behavior naturally. • It readily allows multi-physics simulations. • Personal computer capabilities have caught up with the requirements of FDTD for a wide range of important engineering and physics modeling problems.
Goals of This Presentation • Review key FDTD applications and validations in engineering and physics • Discuss emerging modeling areas • Forecast the state of computational electrodynamics modeling by FDTD and its offspring in the time frame of 2015
Review of Key FDTD Applications and Validations Topic 1: Electromagnetic Wave Scattering and Radar Cross Section
Surface Currents on a λ /3 Metal Cube Taflove and Umashankar, IEEE Trans. Electromagnetic Compatibility , 1983.
Monostatic RCS of a 9 × 3 - λ T-Shape Metal Target Taflove and Umashankar, Proc. IEEE , 1989.
Bistatic RCS of Two 1- λ Diameter PEC Spheres FDTD • • • Generalized multipole technique Jurgens and Taflove, IEEE Trans. Antennas and Propagation , 1993.
Visualization of Surface Currents and Mutual Interaction of the Two Spheres
Monostatic RCS of VFY-218 Jet Fighter at 500 MHz Radar cross section (dBsm) Taflove, Computational Electrodynamics: The Finite- Difference Time-Domain Method , 1995. Monostatic angle (degrees)
Review of Key FDTD Applications and Validations Topic 2: Electromagnetic Wave Penetration and Coupling
Penetration into a Circular Cylinder Below Cutoff 300 MHz plane wave axially incident upon a hollow FDTD metal right circular cylinder Freq. domain having a waveguide cutoff integral equation frequency of 900 MHz A. Taflove, IEEE Trans. Electromagnetic Compatibility , 1980.
Coupling to Wires Within the LLNL PLUTO Umashankar, Taflove, et al., IEEE Trans. Antennas and Propagation , 1987.
Microwave Penetration into a Missile Radome Maloney and Smith in Taflove and Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. , 2000.
Review of Key FDTD Applications and Validations Topic 3: Antennas and Radiation
Cylindrical Monopole Antenna Above a Finite Ground Plane Reflected voltage pulse in the coaxial feedline Maloney et al., IEEE Trans. Antennas and Propagation , 1994.
Standard Gain Horn Antenna
Radiation Patterns and Gain of Horn Antenna Boresight gain Maloney and Smith in Taflove and Hagness, Computational Electrodynamics: The Finite- Difference Time-Domain Method , 2nd. ed., 2000. Radiation patterns
8-Element Array of Vivaldi Quads
E-Plane Co-Polarized Radiation Patterns of 8-Element Vivaldi Quad Array o beam steer o beam steer 6 GHz, 0 12 GHz, 45 Thiele and Taflove, IEEE Trans. Antennas and Propagation , 1994.
Review of Key FDTD Applications and Validations Topic 4: Interactions with Human Tissues
Microwave Irradiation of the Human Eye Taflove and Brodwin, IEEE Trans. Microwave Theory and Techniques , Nov. 1975.
Calculated SAR in Human Eye Model at 1.5 GHz Vertical symmetry plane Taflove and Brodwin, IEEE Trans. Microwave Theory and Techniques , Nov. 1975. Horizontal symmetry plane
Experimental Validation for a Brain-Equivalent Phantom Half-wavelength dipole radiating 0.5W at 1900 MHz located at d=5, 15, or 25 mm from the brain phantom. Yu et al., IEEE Trans. Electromagnetic Compatibility , 1999.
Cellphone Interaction With The Human Head Cut plane through the cellphone Maps of the E-field and SAR within the cut plane. Relative intensities are shown in dB. Source: Remcom Inc. website: http://www.remcominc. com/html/index.html
Ultrawideband Plane-Wave Pulse Illuminating a Highly Detailed, Frequency-Dispersive Model of the Human Head Source: Remcom Inc. website: http://www.remcominc. com/html/index.html dB scale
Emerging Modeling Areas Topic 1: High-Speed Electronic Circuits
Coupling and Crosstalk of a High-Speed Logic Pulse Within a Conventional Dual In-Line Integrated Circuit Package Source: Melinda Piket-May, University of Colorado-Boulder
Embedding of Nonlinear and Active Circuits Within the Space Grid: Interface with SPICE I dev (t) + ∆ V dev (t) I N (t) C N Embedded circuit device – I dis (t) Norton Equivalent Circuit “Looking Into” the FDTD Grid Thomas et al., IEEE Microwave and Guided Wave Lett., 1994.
MESFET Transistor Example Mounting in a microstrip circuit Large-signal model of the MESFET integrated with the Thevenin equivalent circuits for the FDTD grid at its gate and drain terminals Kuo et al., IEEE Trans. Microwave Theory and Techniques , 1997.
Validation Relative to HP-MDS 6-GHz amplifier in packaging box Large-signal harmonic generation without the packaging box Kuo et al., IEEE Trans. Microwave Theory and Techniques , 1997.
Emerging Modeling Areas Topic 2: Particle Accelerator Cavities. Design Enabled by Improved Mesh-Generation Techniques.
New Locally Conformal Mesh Generator Staircase FDTD D-FDTD Faceted surface generated FDTD grid resolution can be relaxed by a standard CAD tool is by 4:1 for comparable accuracy in imported into the FDTD grid. calculating resonant frequencies. Waldschmidt and Taflove, IEEE Trans. Antennas and Propagation , submitted.
Twisted Waveguide Slow-Wave Structure
Interior of Twisted Waveguide
Details • Twisted waveguide was designed with ProE and imported into the D-FDTD mesh generator. • Typical mesh for a 4-period twisted waveguide included 50,000 modified FDTD grid edges, and was created in 5 minutes. • Provided error detection for meshing irregularities, and a C ++ visualization tool. • HFSS™ required 500 MB of memory and 4 hours for the solution of a 3-period twisted waveguide. • D-FDTD required 20 MB of memory and 30 minutes for the same solution.
Emerging Modeling Areas Topic 3: Propagation of Electromagnetic Waves and Beams in Dispersive and Nonlinear Dispersive Media
Propagation in a Linear Dispersive Medium Reflection coefficient for a plane Permittivity of a Lorentz medium wave normally incident upon a half- having three resonances in the optical range space composed of this medium Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 1995 .
Calculation of the Sommerfeld Precursor in a Linear Single-Lorentz-Resonance Medium Joseph, Hagness, and Taflove, Optics Letters , 1991.
“Braided” Co-Phased Spatial Solitons Joseph and Taflove, IEEE Photonics Technology Letters , 1994.
Soliton Braiding Transitions to Divergence When the Beamwidth Approaches 1 λ d Joseph and Taflove, IEEE Photonics Technology Letters , 1994.
Light Bullet Goorjian and Silberberg, JOSA B , 1997.
Emerging Modeling Areas Topic 4: Micro-Optical Structures
Photonic Bandgap Waveguides Mingaleev and Kivshar, Optics and Prather Optics and Photonics Photonics News , July 2002. News , June 2002.
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