Abstract

A unified treatment for the truncation of finite-difference time-domain lattices, applicable to dispersive and conductive media alike, is proposed. The method is based on periodic boundary conditions, hence necessitating that the medium under study be periodic along the direction of truncation. When this condition (which is satisfied in many practical cases) is met, a much simpler but equally effective alternative to the PML is provided by the combination of periodic boundaries with an array-scanning method. The proposed formulation does not need any additional auxiliary variables when applied to dispersive media, unlike the PML. Applications include a Bragg filter and a negative-refractive-index super lens.

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  1. A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000, ch. 7) pp. 285-348.
  2. A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000, ch. 7.7) pp. 235-283.
  3. G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time domain electromagnetic field equations," IEEE Trans. Electromagn. Compat. EMC-23, 377-382 (1981).
  4. Z. P. Liao, H. L. Wong, B. P. Yang, Y. F. Yuan, "A transmitting boundary for transient wave analysis," Scientia Sinica (Series A) XXVII, 1063-1076 (1984).
  5. J. P. Berenger, "Perfectly matched layer for the FDTD solution of wave-structure interaction problems," IEEE Trans. Antennas Propag. 51, 110-117 (1996).
  6. A. F. Oskooi, L. Zhang, Y. Avniel, S. G. Johnson, "The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers," Opt. Exp. 16, 11 376-11 392 (2008).
  7. S. A. Cummer, "Perfectly matched layer behavior in negative refractive index materials," IEEE Antennas Wireless Propag. Lett. 3, 172-175 (2004).
  8. R. Qiang, J. Chen, F. Capolino, D. R. Jackson, D. R. Wilton, "ASM-FDTD: A technique for calculating the field of a finite source in the presence of an infinite periodic artificial material," IEEE Microw. Wireless Compon. Lett. 17, 271-273 (2007).
  9. D. Li, C. D. Sarris, "Efficient finite-difference time-domain modeling of driven periodic structures and related microwave circuit applications," IEEE Trans. Microw. Theory Tech. 56, 1928-1937 (2008).
  10. P. Harms, R. Mittra, W. Ko, "Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures," IEEE Trans. Antennas Propag. 42, 1317-1324 (1994).
  11. B. Munk, G. A. Burrell, "Plane-wave expansion for arrays of arbitrarily oriented piecewise linear elements and its application in determining the impedance of a single linear antenna in a lossy half-space," IEEE Trans. Antennas Propag. 27, 331-343 (1979).
  12. A. V. Oppenheim, Signals and Sysmtems (Prentice Hall, 1996).
  13. A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  14. G. Lovat, P. Burghinmoli, F. Capolino, D. R. Jackson, "Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas," IET Microw. Antennas Propag. 1, 177-183 (2007).
  15. D. M. Sullivan, "Frequency-dependent FDTD methods using Z-transforms," IEEE Trans. Antennas Propag. 40, 1223-1230 (1992).
  16. W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, 1990) pp. 45-76.
  17. D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, J. B. Pendry, "Limitations on sub-diffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).

2008 (2)

A. F. Oskooi, L. Zhang, Y. Avniel, S. G. Johnson, "The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers," Opt. Exp. 16, 11 376-11 392 (2008).

D. Li, C. D. Sarris, "Efficient finite-difference time-domain modeling of driven periodic structures and related microwave circuit applications," IEEE Trans. Microw. Theory Tech. 56, 1928-1937 (2008).

2007 (2)

R. Qiang, J. Chen, F. Capolino, D. R. Jackson, D. R. Wilton, "ASM-FDTD: A technique for calculating the field of a finite source in the presence of an infinite periodic artificial material," IEEE Microw. Wireless Compon. Lett. 17, 271-273 (2007).

G. Lovat, P. Burghinmoli, F. Capolino, D. R. Jackson, "Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas," IET Microw. Antennas Propag. 1, 177-183 (2007).

2004 (1)

S. A. Cummer, "Perfectly matched layer behavior in negative refractive index materials," IEEE Antennas Wireless Propag. Lett. 3, 172-175 (2004).

2003 (1)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, J. B. Pendry, "Limitations on sub-diffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).

1996 (1)

J. P. Berenger, "Perfectly matched layer for the FDTD solution of wave-structure interaction problems," IEEE Trans. Antennas Propag. 51, 110-117 (1996).

1994 (1)

P. Harms, R. Mittra, W. Ko, "Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures," IEEE Trans. Antennas Propag. 42, 1317-1324 (1994).

1992 (1)

D. M. Sullivan, "Frequency-dependent FDTD methods using Z-transforms," IEEE Trans. Antennas Propag. 40, 1223-1230 (1992).

1984 (1)

Z. P. Liao, H. L. Wong, B. P. Yang, Y. F. Yuan, "A transmitting boundary for transient wave analysis," Scientia Sinica (Series A) XXVII, 1063-1076 (1984).

1981 (1)

G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time domain electromagnetic field equations," IEEE Trans. Electromagn. Compat. EMC-23, 377-382 (1981).

1979 (1)

B. Munk, G. A. Burrell, "Plane-wave expansion for arrays of arbitrarily oriented piecewise linear elements and its application in determining the impedance of a single linear antenna in a lossy half-space," IEEE Trans. Antennas Propag. 27, 331-343 (1979).

Appl. Phys. Lett. (1)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, J. B. Pendry, "Limitations on sub-diffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).

IEEE Antennas Wireless Propag. Lett. (1)

S. A. Cummer, "Perfectly matched layer behavior in negative refractive index materials," IEEE Antennas Wireless Propag. Lett. 3, 172-175 (2004).

IEEE Microw. Wireless Compon. Lett. (1)

R. Qiang, J. Chen, F. Capolino, D. R. Jackson, D. R. Wilton, "ASM-FDTD: A technique for calculating the field of a finite source in the presence of an infinite periodic artificial material," IEEE Microw. Wireless Compon. Lett. 17, 271-273 (2007).

IEEE Trans. Antennas Propag. (4)

J. P. Berenger, "Perfectly matched layer for the FDTD solution of wave-structure interaction problems," IEEE Trans. Antennas Propag. 51, 110-117 (1996).

D. M. Sullivan, "Frequency-dependent FDTD methods using Z-transforms," IEEE Trans. Antennas Propag. 40, 1223-1230 (1992).

P. Harms, R. Mittra, W. Ko, "Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures," IEEE Trans. Antennas Propag. 42, 1317-1324 (1994).

B. Munk, G. A. Burrell, "Plane-wave expansion for arrays of arbitrarily oriented piecewise linear elements and its application in determining the impedance of a single linear antenna in a lossy half-space," IEEE Trans. Antennas Propag. 27, 331-343 (1979).

IEEE Trans. Electromagn. Compat. (1)

G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time domain electromagnetic field equations," IEEE Trans. Electromagn. Compat. EMC-23, 377-382 (1981).

IEEE Trans. Microw. Theory Tech. (1)

D. Li, C. D. Sarris, "Efficient finite-difference time-domain modeling of driven periodic structures and related microwave circuit applications," IEEE Trans. Microw. Theory Tech. 56, 1928-1937 (2008).

IET Microw. Antennas Propag. (1)

G. Lovat, P. Burghinmoli, F. Capolino, D. R. Jackson, "Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas," IET Microw. Antennas Propag. 1, 177-183 (2007).

Opt. Exp. (1)

A. F. Oskooi, L. Zhang, Y. Avniel, S. G. Johnson, "The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers," Opt. Exp. 16, 11 376-11 392 (2008).

Scientia Sinica (Series A) (1)

Z. P. Liao, H. L. Wong, B. P. Yang, Y. F. Yuan, "A transmitting boundary for transient wave analysis," Scientia Sinica (Series A) XXVII, 1063-1076 (1984).

Other (5)

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000, ch. 7) pp. 285-348.

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000, ch. 7.7) pp. 235-283.

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, 1990) pp. 45-76.

A. V. Oppenheim, Signals and Sysmtems (Prentice Hall, 1996).

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

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