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454 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS VOL 5 2006 Analytic Field Propagation TFSF Boundary for FDTD Problems Involving Planar Interfaces Lossy Material and Evanescent Fields Kakhkhor Abdijalilov and John B Schneider Member IEEE Abstract Recently total field scattered field TFSF boundaries have been developed for the finite difference time domain FDTD method which are essentially perfect The implementation requires an analytic description of the incident field and hence is termed the analytic field propagation AFP TFSF method Previous papers described the implementation for problems involving homogeneous as well as layered media In this work we provide the details for problems involving lossy media Additionally the case of fields incident beyond the critical angle are considered i e when for lossless material there is total reflection of the incoming wave and the fields in the second medium are evanescent Index Terms Finite difference time domain FDTD methods I INTRODUCTION T HE total field scattered field TFSF boundary first proposed in 1 is a method for introducing incident fields into finite difference time domain FDTD grids The TFSF boundary separates FDTD grids into a total field TF and a scattered field SF region The nodes in the TF region represent the sum of the incident and any scattered field while the nodes in the SF region corresponds to only scattered fields Nodes tangential to the TFSF boundary will have a neighboring node on the other side of the boundary To obtain consistent update equations the incident field will either have to be subtracted from or added to the value of that neighbor The TFSF boundary requires that one specify the incident field for all nodes tangential to the boundary for all time steps An excellent description of the implementation of the TFSF boundary can be found in 2 Here we build upon the work presented in 3 5 which we term the analytic field propagation AFP technique This technique uses the dispersion relation to



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