Finite Difference Time Domain (FDTD) (2 Sessions)

1. Finite Difference Time Domain (FDTD) (2 Sessions)

2. History of FDTD Method • A Perspective on 40-YearHistory of FDTD Computational Electrodynamics.

3. History of FDTD Method • Paper Number 1: Kane Yee • IEEE AP-S Transactions, May 1966. • 2441 citations as of March 7, 2006. • IEEE MTT, Aug. 1975 • IEEE EMC, Aug. 1980 • IEEE MTT, Aug. 1975

4. History of FDTD Method • Timeline 1966 to 1980: • Timeline 1981 to 1990:

5. History of FDTD Method • Timeline 1991 to 1995: • Timeline 1996 to 2000:

6. Emerging Applications • Some Major Technical Paths Since Yee • Absorbing boundary conditions • Numerical dispersion • Numerical stability • Conforming grids • Digital signal processing • Dispersive and nonlinear materials • Multi-physics coupling to Maxwell’s equations • Some Interesting Emerging Applications • Earth / ionosphere models in geophysics. • Wireless personal communications devices. • Ultra wideband microwave detection of early-stage. • Breast Cancer. • Ultra high-speed band pass digital interconnects. • Micron / nanometer-scale photonic devices. • Bio photonics, especially optical detection of early. • Stage Epithelial Cancers. • Timeline 2000 to 2005:

7. Emerging Applications • Earth/Ionosphere Models in Geophysics: • There is a rich history of investigation of ELF and VLF electromagnetic wave propagation within the Earth ionosphere waveguide. • Applications: • Submarine communications • Remote-sensing of lightning and sprites • Global temperature change • Subsurface structures • Potential earthquake precursors • Snapshots of FDTD-Computed Global Propagation of ELF Electromagnetic Pulse Generated by Vertical Lightning Strike off South America Coast.

8. Emerging Applications • Wireless Personal Communications Devices: • Motorola T250Cellphone: • High-resolution FDTD model: • Lattice-cell size is as fine as 0.1mm to resolve individual circuit board layers and the helical antenna.

9. Emerging Applications • Final Head Model Results: • Head model has 121 slices. • 1mm thick in ear region & 3mm thick elsewhere. • Having a transverse resolution of 0.2mm. • Phantom Head Validation at 1.8GHz: • Ultra-wideband microwave detection of early-stage breast cancer. • Modeled detection of a 2mm tumor. • FDTD simulation of UWB microwave detection of a 2mm diameter malignant tumor embedded 3cm within an MRI derived numerical breast model. • The cancer’s signature is 15 to 30db stronger than the clutter due to the surrounding normal tissues. • Source: Bond et al., IEEE trans. Antennas and propagation, 2003, pp. 1690–1705.

10. Emerging Applications • Substrate Integrated Waveguides (SIW): • Pass band is 27-81GHzwith negligible multimoding. • It is confirmed by measurements at Intel Corporation. • Photonic Band-gap Defect Mode Cavities:

11. Emerging Applications • Photonic Band-gap Defect Mode Laser Cavities • Laterally Coupled Photonic Disk Resonators:

12. Emerging Applications • Vertically Coupled Photonic Racetrack (Fully 3-D Model): • Pulse Propagation in the Vertically Coupled Racetrack :

13. Emerging Applications • Nanoplasmonics: • Enhanced Transmission Through a Sub-Micron Hole in a Gold Film. • Focusing Plasmonic Lens:

14. Emerging Applications • Backscattering Spectroscopy: • FDTD modeling has shown that observing spectrum of retro-reflected light from living tissues yields much greater information regarding health of these tissues than existing diagnostic techniques. • Backscattering Detection of Nano-scale Features: • Lasing in a Random Clump of ZnOParticles:

15. Emerging Applications • following practical examples demonstrate some of outstanding simulation capabilities of time-domain solvers. • For these examples, finite integration technique (FIT) method in time domain and TLM are used. • Simulations were performed with commercial software packages • Conformal UWB Antenna: • Lightning Strike on an Airplane: • TDM is the most appropriate, for two reasons: • The input signal is known in the time domain • The structure is typically very large.

16. Emerging Applications • Lightning Strike on an Airplane (cont.): • Magnitude of the surface current: • This example was set up using 300,000mesh. • That is ensures an accuracy of wave resolution well above typical limit. • Total number of unknown field components to be calculated is 1.9 million. • Over the relatively long pulse duration required here, a total of 120,000 time steps must be executed. • The simulation time for creating the mesh is so short that it cannot be measured. • It takes 46sto calculate the matrix coefficients and 44minto perform entire time stepping on an office PC with an INTEL Core 2 Duo running at 3.16GHz.

17. Emerging Applications • EMC Simulation of an Airplane: • While previous example of lightning strike is a comparably small example with only 1.9 million unknowns. • Problem size becomes much larger when we investigate a plane wave at 900MHz hitting same airplane but now equipped with passenger and interior detail as shown: • In order to obtain a solution of reasonable quality, at least ten steps per wavelengthare employed. • This yields a problem size of over 2500 million unknownsrequiring only moderate memory usage of 52GB. • Besides ability of TDM to solve such very large problems, one also obtains fields over full frequency band from 0-950MHz. • This results in 414 million mesh cells and aforementioned over 2500 million unknown field components to be calculated at 15,000 time steps. • Calculation of matrix coefficients takes 330min, and time stepping roughly 28hof CPU time on an INTELWorkstation with two XEONs X5472 running at 3GHzin 64-bit mode. • As TDM can be parallelized, CPU time may be scaled down easily by adding more CPUs, typically in a cluster of pizza-box PCs.

18. Emerging Applications • Electromagnetic Compatibility Simulation of a PCB: • EM compatibility (EMC) simulations are an ideal terrain for transient solvers, since EMC issues are inherently broadband. • For example, a typical problem setup consists of a PCB and some shielding mechanism as shown in: • Before device is built and operated, its virtual operation is modeled and simulated, no one can reliably predict in which frequency range problems might occur. • In addition to EM properties of PCB, its radiation may depend on various structural features, such as vents, seams, cables, box dimensions, etc. a metallic enclosure

19. Emerging Applications • Coupled Simulation of Electromagnetic Field and Nonlinear Elements: • Often, 3D components need to be connected in a larger network, which may include various linear and non-linear circuit elements. • It is well known that, for strong nonlinearities, a circuit simulation in time domain is most reliable. • This is because frequency-domain methods, such as harmonic balance, may lead to inaccuracies if an insufficient number of harmonics is considered. • A possible approach would be to first simulate 3D component alone, calculate full S-parametermatrix to obtain a behavioral model for device, and then connect this model (for example ADS format) to circuit to perform transient non-linear simulation. • For applications whose 3D model has a significant number of ports, however, transient co-simulation • approach, in which circuit elements are directly connected to the 3-D model, is more efficient one. • Moreover, this type of transient co-simulation also allows EM field resulting from nonlinear effect to be studied. • An example of such a co-simulation is step-recovery diode (SRD) pulse generator. • The pulse generator contains a 3D EM structure shown in:

20. Emerging Applications • Particle-in-Cell Simulation of Traveling Wave Tubes (TWTs): • TWTs are used to amplify signals to high power at high frequencies. • For this purpose several elements are required: • A continuous electron beam is created in a gun. • Electrons are emitted from heated cathode. • They are accelerated in a static electric field and exit gun section through anode. • Electrons then enter a slow-wave structure, where some fraction of the kinetic energy of electrons is converted into a high-frequency wave. • This wave interacts with particle beam and has to be coupled out of system. • Electron beam is securely dumped in a collector. • A TWT with a micro-machined folded waveguide structure, operating at 220GHz is:

21. Emerging Applications • TWT’s wave forms:

22. Why FDTD Method? • There are seven primary reasons to use FDTD: • FDTD uses no linear algebra: • Being a fully explicit computation, FDTD avoids difficulties with linear algebra. • Linear algebra limit size of frequency-domain IE and finite-element electromagnetics models to generally fewer than 106 electromagnetic field unknowns. • FDTD models with as many as 109field unknowns have been run • There is no intrinsic upper bound to this number. • FDTD is accurate and robust: • Sources of errors in FDTD are well understood, and can be bounded to permit accurate models for a very large variety of electromagnetic wave interaction problems. • FDTD treats impulsive behavior naturally. • Directly calculates impulse response of an electromagnetic system. • Therefore, a single simulation have UWB wave forms or sinusoidal steady-state response at any frequency with in excitation spectrum. • FDTD treats nonlinear behavior naturally. • Being a time-domain technique, FDTD directly calculates nonlinear response of an EM system.

23. Why FDTD Method? • FDTD is a systematic approach. • With FDTD, specifying a new structure to be modeled is reduced to a problem of mesh generation rather than potentially complex reformulation of an IE. • For example, FDTD requires no calculation of structure-dependent Green functions. • Computer memory capacities are increasing rapidly. • While this trend positively influences all numerical techniques, it is of particular advantage to FDTD methods, which are founded on discretizing space over a volume, and therefore inherently require a larger and random access memory. • Computer visualization capabilities are increasing rapidly. • While this trend positively influences all numerical techniques, it is of particular advantage to FDTD methods. • That is, FDTD generate time-marched arrays of field quantities suitable for use in color videos to illustrate field dynamics.

24. Why FDTD Method? • Time-domain versus volumetric frequency-domain methods: • Various higher-order FDTD schemes have been proposed: • Finite-volume Time-domain (FVTD). • Pseudo Spectral Time-domain (PSTD) • Multi Resolution Time-domain (MRTD). • Frequency-domain methods (FDM) miss: • Arbitrary time signals as excitation. • broadband frequency results in a single simulation. • Transient field effects. • Transient far fields for UWB antennas. • nonlinear effects, • FDM, on other hand, are the ideal tool for: • Low-frequency problems. • Highly resonant structures. • Eigen-mode computations.

25. Why FDTD Method? • Method has following Advantages: • FDTD has following inherent advantages over other modeling techniques, such as MOM and TLM: • It is conceptually simple. • Algorithm does not require formulation of integral equations, and relatively complex scatterers can be treated without inversion of large matrices. • It is simple to implement for complicated, inhomogeneous conducting or dielectric structures because constitutive parameters (σ,μ,ε) can be assigned to each lattice point. • Its computer memory requirement is not prohibitive for many complex structures of interest. • Algorithm makes use of memory in a simple sequential order. • It is much easier to obtain frequency domain data from time domain results than converse. Thus, it is more convenient to obtain frequency domain results via time domain when many frequencies are involved. • Method has following disadvantages: • Its implementation necessitates modeling object as well as its surroundings. Thus, required program execution time may be excessive. • Its accuracy is at least one order of magnitude worse than that of the method of moments, for example. • Since computational meshes are rectangular in shape, they do not conform to scatterers with curved surfaces, as is the case of the cylindrical or spherical boundary. • As in all finite difference algorithms, the field quantities are only known at grid nodes.