Abstract

Finite-difference time-domain (FDTD) simulations of any electromagnetic problem require truncation of an often-unbounded physical region by an electromagnetically bounded region by deploying an artificial construct known as the perfectly matched layer (PML). As it is not possible to construct a universal PML that is non-reflective for different materials, PMLs that are tailored to a specific problem are required. For example, depending on the number of dispersive materials being truncated at the boundaries of a simulation region, an FDTD code may contain multiple sets of update equations for PML implementations. However, such an approach is prone to introducing coding errors. It also makes it extremely difficult to maintain and upgrade an existing FDTD code. In this paper, we solve this problem by developing a new, unified PML algorithm that can effectively truncate all types of linearly dispersive materials. The unification of the algorithm is achieved by employing a general form of the medium permittivity that includes three types of dielectric response functions, known as the Debye, Lorentz, and Drude response functions, as particular cases. We demonstrate the versatility and flexibility of the new formulation by implementing a single FDTD code to simulate absorption of electromagnetic pulse inside a medium that is adjacent to dispersive materials described by different dispersion models. The proposed algorithm can also be used for simulations of optical phenomena in metamaterials and materials exhibiting negative refractive indices.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
    [CrossRef]
  2. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  3. P. Petropoulos, "Stability and phase error analysis of FD-TD in dispersive dielectrics," IEEE Trans. Antennas Propag. 42, 62-69 (1994).
    [CrossRef]
  4. M. Premaratne and S. K. Halgamuge, "Rigorous analysis of numerical phase and group velocity bounds in Yee’s FDTD grid," IEEE Microwave Wirel. Compon. Lett. 17, 556-558 (2007).
    [CrossRef]
  5. 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. 32, 222-227 (1990).
    [CrossRef]
  6. D. Kelley and R. Luebbers, "Piecewise linear recursive convolution for dispersive media using FDTD," IEEE Trans. Antennas Propag. 44, 792-797 (1996).
    [CrossRef]
  7. J. Young, "Propagation in linear dispersive media: Finite difference time-domain methodologies," IEEE Trans. Antennas Propag. 43, 422-426 (1995).
    [CrossRef]
  8. D. Sullivan, "Z-transform theory and the FDTD method," IEEE Trans. Antennas Propag. 44, 28-34 (1996).
    [CrossRef]
  9. M. Okoniewski, M. Mrozowski, and M. Stuchly, "Simple treatment of multi-term dispersion in FDTD," IEEE Microwave Guided Wave Lett. 7, 121-123 (1997).
    [CrossRef]
  10. Y. Takayama and W. Klaus, "Reinterpretation of the auxiliary differential equation method for FDTD," IEEE Microwave Wirel. Compon. Lett. 12, 102-104 (2002).
    [CrossRef]
  11. M. Han, R. Dutton, and S. Fan, "Model dispersive media in finite-difference time-domain method with complexconjugate pole-residue pairs," IEEE Microwave Compon. Lett. 16, 119-121 (2006).
    [CrossRef]
  12. K. P. Prokopidis, "On the development of efficient FDTD-PML formulations for general dispersive media," Int. J. Numer. Model. 21, 395-411 (2008).
    [CrossRef]
  13. R. Luebbers, F. Hunsberger, and K. Kunz, "A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma," IEEE Trans. Antennas Propag. 39, 29-34 (1991).
    [CrossRef]
  14. W. C. Chew and W. H. Weedon, "A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates," Microwave Opt. Tech. Lett 7, 599-604 (1994).
    [CrossRef]
  15. S. Gedney, "An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices," IEEE Trans. Antennas Propag. 44, 1630-1639 (1996).
    [CrossRef]
  16. M. Kuzuoglu and R. Mittra, "Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers," IEEE Microwave Guided Wave Lett. 6, 447-449 (1996).
    [CrossRef]
  17. S. Gedney, "Scaled CFS-PML: It is more robust, more accurate, more efficient, and simple to implement. Why aren’t you using it?" in Antennas and Propagation Society International Symposium 364-367 (2005).
  18. D. Correia and J.-M. Jin, "Performance of regular PML, CFS-PML, and second-order PML for waveguide problems," Microwave Opt. Technol. Lett. 48, 2121-2126 (2006).
    [CrossRef]
  19. J.-P. Berenger, "Numerical reflection from FDTD-PMLs: A comparison of the split PML with the unsplit and CFS PMLs," IEEE Trans. Antennas Propag. 50, 258-265 (2002).
    [CrossRef]
  20. D. Correia and J.-M. Jin, "On the development of a higher-order PML," IEEE Trans. Antennas Propag. 53, 4157-4163 (2005).
    [CrossRef]
  21. J.-P. Berenger, "Application of the CFS PML to the absorption of evanescent waves in waveguides," IEEE Microwave Wirel. Compon. Lett. 12, 218-220 (2002).
    [CrossRef]
  22. Y. Rickard and N. Georgieva, "Problem-independent enhancement of PML ABC for the FDTD method," IEEE Trans. Antennas Propag. 51, 3002-3006 (2003).
    [CrossRef]
  23. S. Cummer, "Perfectly matched layer behavior in negative refractive index materials," IEEE Antennas Wirel. Propag. Lett. 3, 172-175 (2004).
    [CrossRef]
  24. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, 1975).
  25. J.-P. Berenger, "Three-dimensional perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 127, 363-379 (1996).
    [CrossRef]
  26. O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microwave Theory Tech. 41, 658-665 (1993).
    [CrossRef]
  27. W. D. Hurt, "Multiterm Debye dispersion relations for permittivity of muscle," IEEE Trans. Bio. Eng. 32, 60-64 (1985).
    [CrossRef]
  28. K. E. Oughstun, "Computational methods in ultrafast time-domain optics," Comput. Sci. Eng. 5, 22-32 (2003).
    [CrossRef]
  29. J. Xi and M. Premaratne, "Analysis of the optical force dependency on beam polarization: Dielectric/metallic spherical shell in a Gaussian beam," J. Opt. Soc. Am. B 26, 973-980 (2009).
    [CrossRef]
  30. A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. L. Chapelle, "Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416(1-7) (2005).
    [CrossRef]

2009

2008

K. P. Prokopidis, "On the development of efficient FDTD-PML formulations for general dispersive media," Int. J. Numer. Model. 21, 395-411 (2008).
[CrossRef]

2007

M. Premaratne and S. K. Halgamuge, "Rigorous analysis of numerical phase and group velocity bounds in Yee’s FDTD grid," IEEE Microwave Wirel. Compon. Lett. 17, 556-558 (2007).
[CrossRef]

2006

M. Han, R. Dutton, and S. Fan, "Model dispersive media in finite-difference time-domain method with complexconjugate pole-residue pairs," IEEE Microwave Compon. Lett. 16, 119-121 (2006).
[CrossRef]

D. Correia and J.-M. Jin, "Performance of regular PML, CFS-PML, and second-order PML for waveguide problems," Microwave Opt. Technol. Lett. 48, 2121-2126 (2006).
[CrossRef]

2005

D. Correia and J.-M. Jin, "On the development of a higher-order PML," IEEE Trans. Antennas Propag. 53, 4157-4163 (2005).
[CrossRef]

2004

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

2003

Y. Rickard and N. Georgieva, "Problem-independent enhancement of PML ABC for the FDTD method," IEEE Trans. Antennas Propag. 51, 3002-3006 (2003).
[CrossRef]

K. E. Oughstun, "Computational methods in ultrafast time-domain optics," Comput. Sci. Eng. 5, 22-32 (2003).
[CrossRef]

2002

J.-P. Berenger, "Application of the CFS PML to the absorption of evanescent waves in waveguides," IEEE Microwave Wirel. Compon. Lett. 12, 218-220 (2002).
[CrossRef]

J.-P. Berenger, "Numerical reflection from FDTD-PMLs: A comparison of the split PML with the unsplit and CFS PMLs," IEEE Trans. Antennas Propag. 50, 258-265 (2002).
[CrossRef]

Y. Takayama and W. Klaus, "Reinterpretation of the auxiliary differential equation method for FDTD," IEEE Microwave Wirel. Compon. Lett. 12, 102-104 (2002).
[CrossRef]

1997

M. Okoniewski, M. Mrozowski, and M. Stuchly, "Simple treatment of multi-term dispersion in FDTD," IEEE Microwave Guided Wave Lett. 7, 121-123 (1997).
[CrossRef]

1996

D. Sullivan, "Z-transform theory and the FDTD method," IEEE Trans. Antennas Propag. 44, 28-34 (1996).
[CrossRef]

D. Kelley and R. Luebbers, "Piecewise linear recursive convolution for dispersive media using FDTD," IEEE Trans. Antennas Propag. 44, 792-797 (1996).
[CrossRef]

S. Gedney, "An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices," IEEE Trans. Antennas Propag. 44, 1630-1639 (1996).
[CrossRef]

M. Kuzuoglu and R. Mittra, "Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers," IEEE Microwave Guided Wave Lett. 6, 447-449 (1996).
[CrossRef]

J.-P. Berenger, "Three-dimensional perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 127, 363-379 (1996).
[CrossRef]

1995

J. Young, "Propagation in linear dispersive media: Finite difference time-domain methodologies," IEEE Trans. Antennas Propag. 43, 422-426 (1995).
[CrossRef]

1994

P. Petropoulos, "Stability and phase error analysis of FD-TD in dispersive dielectrics," IEEE Trans. Antennas Propag. 42, 62-69 (1994).
[CrossRef]

W. C. Chew and W. H. Weedon, "A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates," Microwave Opt. Tech. Lett 7, 599-604 (1994).
[CrossRef]

1993

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microwave Theory Tech. 41, 658-665 (1993).
[CrossRef]

1991

R. Luebbers, F. Hunsberger, and K. Kunz, "A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma," IEEE Trans. Antennas Propag. 39, 29-34 (1991).
[CrossRef]

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. 32, 222-227 (1990).
[CrossRef]

1985

W. D. Hurt, "Multiterm Debye dispersion relations for permittivity of muscle," IEEE Trans. Bio. Eng. 32, 60-64 (1985).
[CrossRef]

1966

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Barchiesi, D.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. L. Chapelle, "Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416(1-7) (2005).
[CrossRef]

Berenger, J.-P.

J.-P. Berenger, "Numerical reflection from FDTD-PMLs: A comparison of the split PML with the unsplit and CFS PMLs," IEEE Trans. Antennas Propag. 50, 258-265 (2002).
[CrossRef]

J.-P. Berenger, "Application of the CFS PML to the absorption of evanescent waves in waveguides," IEEE Microwave Wirel. Compon. Lett. 12, 218-220 (2002).
[CrossRef]

J.-P. Berenger, "Three-dimensional perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 127, 363-379 (1996).
[CrossRef]

Chapelle, M. L.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. L. Chapelle, "Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416(1-7) (2005).
[CrossRef]

Chen, J.-Y.

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microwave Theory Tech. 41, 658-665 (1993).
[CrossRef]

Chew, W. C.

W. C. Chew and W. H. Weedon, "A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates," Microwave Opt. Tech. Lett 7, 599-604 (1994).
[CrossRef]

Correia, D.

D. Correia and J.-M. Jin, "Performance of regular PML, CFS-PML, and second-order PML for waveguide problems," Microwave Opt. Technol. Lett. 48, 2121-2126 (2006).
[CrossRef]

D. Correia and J.-M. Jin, "On the development of a higher-order PML," IEEE Trans. Antennas Propag. 53, 4157-4163 (2005).
[CrossRef]

Cummer, S.

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

Dutton, R.

M. Han, R. Dutton, and S. Fan, "Model dispersive media in finite-difference time-domain method with complexconjugate pole-residue pairs," IEEE Microwave Compon. Lett. 16, 119-121 (2006).
[CrossRef]

Fan, S.

M. Han, R. Dutton, and S. Fan, "Model dispersive media in finite-difference time-domain method with complexconjugate pole-residue pairs," IEEE Microwave Compon. Lett. 16, 119-121 (2006).
[CrossRef]

Gandhi, O. P.

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microwave Theory Tech. 41, 658-665 (1993).
[CrossRef]

Gao, B.-Q.

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microwave Theory Tech. 41, 658-665 (1993).
[CrossRef]

Gedney, S.

S. Gedney, "An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices," IEEE Trans. Antennas Propag. 44, 1630-1639 (1996).
[CrossRef]

Georgieva, N.

Y. Rickard and N. Georgieva, "Problem-independent enhancement of PML ABC for the FDTD method," IEEE Trans. Antennas Propag. 51, 3002-3006 (2003).
[CrossRef]

Grimault, A.-S.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. L. Chapelle, "Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416(1-7) (2005).
[CrossRef]

Halgamuge, S. K.

M. Premaratne and S. K. Halgamuge, "Rigorous analysis of numerical phase and group velocity bounds in Yee’s FDTD grid," IEEE Microwave Wirel. Compon. Lett. 17, 556-558 (2007).
[CrossRef]

Han, M.

M. Han, R. Dutton, and S. Fan, "Model dispersive media in finite-difference time-domain method with complexconjugate pole-residue pairs," IEEE Microwave Compon. Lett. 16, 119-121 (2006).
[CrossRef]

Hunsberger, F.

R. Luebbers, F. Hunsberger, and K. Kunz, "A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma," IEEE Trans. Antennas Propag. 39, 29-34 (1991).
[CrossRef]

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. 32, 222-227 (1990).
[CrossRef]

Hurt, W. D.

W. D. Hurt, "Multiterm Debye dispersion relations for permittivity of muscle," IEEE Trans. Bio. Eng. 32, 60-64 (1985).
[CrossRef]

Jin, J.-M.

D. Correia and J.-M. Jin, "Performance of regular PML, CFS-PML, and second-order PML for waveguide problems," Microwave Opt. Technol. Lett. 48, 2121-2126 (2006).
[CrossRef]

D. Correia and J.-M. Jin, "On the development of a higher-order PML," IEEE Trans. Antennas Propag. 53, 4157-4163 (2005).
[CrossRef]

Kelley, D.

D. Kelley and R. Luebbers, "Piecewise linear recursive convolution for dispersive media using FDTD," IEEE Trans. Antennas Propag. 44, 792-797 (1996).
[CrossRef]

Klaus, W.

Y. Takayama and W. Klaus, "Reinterpretation of the auxiliary differential equation method for FDTD," IEEE Microwave Wirel. Compon. Lett. 12, 102-104 (2002).
[CrossRef]

Kunz, K.

R. Luebbers, F. Hunsberger, and K. Kunz, "A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma," IEEE Trans. Antennas Propag. 39, 29-34 (1991).
[CrossRef]

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. 32, 222-227 (1990).
[CrossRef]

Kuzuoglu, M.

M. Kuzuoglu and R. Mittra, "Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers," IEEE Microwave Guided Wave Lett. 6, 447-449 (1996).
[CrossRef]

Luebbers, R.

D. Kelley and R. Luebbers, "Piecewise linear recursive convolution for dispersive media using FDTD," IEEE Trans. Antennas Propag. 44, 792-797 (1996).
[CrossRef]

R. Luebbers, F. Hunsberger, and K. Kunz, "A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma," IEEE Trans. Antennas Propag. 39, 29-34 (1991).
[CrossRef]

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. 32, 222-227 (1990).
[CrossRef]

Macías, D.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. L. Chapelle, "Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416(1-7) (2005).
[CrossRef]

Mittra, R.

M. Kuzuoglu and R. Mittra, "Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers," IEEE Microwave Guided Wave Lett. 6, 447-449 (1996).
[CrossRef]

Mrozowski, M.

M. Okoniewski, M. Mrozowski, and M. Stuchly, "Simple treatment of multi-term dispersion in FDTD," IEEE Microwave Guided Wave Lett. 7, 121-123 (1997).
[CrossRef]

Okoniewski, M.

M. Okoniewski, M. Mrozowski, and M. Stuchly, "Simple treatment of multi-term dispersion in FDTD," IEEE Microwave Guided Wave Lett. 7, 121-123 (1997).
[CrossRef]

Oughstun, K. E.

K. E. Oughstun, "Computational methods in ultrafast time-domain optics," Comput. Sci. Eng. 5, 22-32 (2003).
[CrossRef]

Petropoulos, P.

P. Petropoulos, "Stability and phase error analysis of FD-TD in dispersive dielectrics," IEEE Trans. Antennas Propag. 42, 62-69 (1994).
[CrossRef]

Premaratne, M.

J. Xi and M. Premaratne, "Analysis of the optical force dependency on beam polarization: Dielectric/metallic spherical shell in a Gaussian beam," J. Opt. Soc. Am. B 26, 973-980 (2009).
[CrossRef]

M. Premaratne and S. K. Halgamuge, "Rigorous analysis of numerical phase and group velocity bounds in Yee’s FDTD grid," IEEE Microwave Wirel. Compon. Lett. 17, 556-558 (2007).
[CrossRef]

Prokopidis, K. P.

K. P. Prokopidis, "On the development of efficient FDTD-PML formulations for general dispersive media," Int. J. Numer. Model. 21, 395-411 (2008).
[CrossRef]

Rickard, Y.

Y. Rickard and N. Georgieva, "Problem-independent enhancement of PML ABC for the FDTD method," IEEE Trans. Antennas Propag. 51, 3002-3006 (2003).
[CrossRef]

Schneider, M.

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. 32, 222-227 (1990).
[CrossRef]

Standler, R.

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. 32, 222-227 (1990).
[CrossRef]

Stuchly, M.

M. Okoniewski, M. Mrozowski, and M. Stuchly, "Simple treatment of multi-term dispersion in FDTD," IEEE Microwave Guided Wave Lett. 7, 121-123 (1997).
[CrossRef]

Sullivan, D.

D. Sullivan, "Z-transform theory and the FDTD method," IEEE Trans. Antennas Propag. 44, 28-34 (1996).
[CrossRef]

Takayama, Y.

Y. Takayama and W. Klaus, "Reinterpretation of the auxiliary differential equation method for FDTD," IEEE Microwave Wirel. Compon. Lett. 12, 102-104 (2002).
[CrossRef]

Vial, A.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. L. Chapelle, "Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416(1-7) (2005).
[CrossRef]

Weedon, W. H.

W. C. Chew and W. H. Weedon, "A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates," Microwave Opt. Tech. Lett 7, 599-604 (1994).
[CrossRef]

Xi, J.

Yee, K. S.

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Young, J.

J. Young, "Propagation in linear dispersive media: Finite difference time-domain methodologies," IEEE Trans. Antennas Propag. 43, 422-426 (1995).
[CrossRef]

Comput. Sci. Eng.

K. E. Oughstun, "Computational methods in ultrafast time-domain optics," Comput. Sci. Eng. 5, 22-32 (2003).
[CrossRef]

IEEE Antennas Wirel. Propag. Lett.

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

IEEE Microwave Compon. Lett.

M. Han, R. Dutton, and S. Fan, "Model dispersive media in finite-difference time-domain method with complexconjugate pole-residue pairs," IEEE Microwave Compon. Lett. 16, 119-121 (2006).
[CrossRef]

IEEE Microwave Guided Wave Lett.

M. Kuzuoglu and R. Mittra, "Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers," IEEE Microwave Guided Wave Lett. 6, 447-449 (1996).
[CrossRef]

M. Okoniewski, M. Mrozowski, and M. Stuchly, "Simple treatment of multi-term dispersion in FDTD," IEEE Microwave Guided Wave Lett. 7, 121-123 (1997).
[CrossRef]

IEEE Microwave Wirel. Compon. Lett.

Y. Takayama and W. Klaus, "Reinterpretation of the auxiliary differential equation method for FDTD," IEEE Microwave Wirel. Compon. Lett. 12, 102-104 (2002).
[CrossRef]

M. Premaratne and S. K. Halgamuge, "Rigorous analysis of numerical phase and group velocity bounds in Yee’s FDTD grid," IEEE Microwave Wirel. Compon. Lett. 17, 556-558 (2007).
[CrossRef]

J.-P. Berenger, "Application of the CFS PML to the absorption of evanescent waves in waveguides," IEEE Microwave Wirel. Compon. Lett. 12, 218-220 (2002).
[CrossRef]

IEEE Trans. Antennas Propag.

Y. Rickard and N. Georgieva, "Problem-independent enhancement of PML ABC for the FDTD method," IEEE Trans. Antennas Propag. 51, 3002-3006 (2003).
[CrossRef]

J.-P. Berenger, "Numerical reflection from FDTD-PMLs: A comparison of the split PML with the unsplit and CFS PMLs," IEEE Trans. Antennas Propag. 50, 258-265 (2002).
[CrossRef]

D. Correia and J.-M. Jin, "On the development of a higher-order PML," IEEE Trans. Antennas Propag. 53, 4157-4163 (2005).
[CrossRef]

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

D. Kelley and R. Luebbers, "Piecewise linear recursive convolution for dispersive media using FDTD," IEEE Trans. Antennas Propag. 44, 792-797 (1996).
[CrossRef]

J. Young, "Propagation in linear dispersive media: Finite difference time-domain methodologies," IEEE Trans. Antennas Propag. 43, 422-426 (1995).
[CrossRef]

D. Sullivan, "Z-transform theory and the FDTD method," IEEE Trans. Antennas Propag. 44, 28-34 (1996).
[CrossRef]

P. Petropoulos, "Stability and phase error analysis of FD-TD in dispersive dielectrics," IEEE Trans. Antennas Propag. 42, 62-69 (1994).
[CrossRef]

S. Gedney, "An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices," IEEE Trans. Antennas Propag. 44, 1630-1639 (1996).
[CrossRef]

R. Luebbers, F. Hunsberger, and K. Kunz, "A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma," IEEE Trans. Antennas Propag. 39, 29-34 (1991).
[CrossRef]

IEEE Trans. Bio. Eng.

W. D. Hurt, "Multiterm Debye dispersion relations for permittivity of muscle," IEEE Trans. Bio. Eng. 32, 60-64 (1985).
[CrossRef]

IEEE Trans. Electromagn. Compat.

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. 32, 222-227 (1990).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microwave Theory Tech. 41, 658-665 (1993).
[CrossRef]

Int. J. Numer. Model.

K. P. Prokopidis, "On the development of efficient FDTD-PML formulations for general dispersive media," Int. J. Numer. Model. 21, 395-411 (2008).
[CrossRef]

J. Comput. Phys.

J.-P. Berenger, "Three-dimensional perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 127, 363-379 (1996).
[CrossRef]

J. Opt. Soc. Am. B

Microwave Opt. Tech. Lett

W. C. Chew and W. H. Weedon, "A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates," Microwave Opt. Tech. Lett 7, 599-604 (1994).
[CrossRef]

Microwave Opt. Technol. Lett.

D. Correia and J.-M. Jin, "Performance of regular PML, CFS-PML, and second-order PML for waveguide problems," Microwave Opt. Technol. Lett. 48, 2121-2126 (2006).
[CrossRef]

Other

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, 1975).

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. L. Chapelle, "Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416(1-7) (2005).
[CrossRef]

S. Gedney, "Scaled CFS-PML: It is more robust, more accurate, more efficient, and simple to implement. Why aren’t you using it?" in Antennas and Propagation Society International Symposium 364-367 (2005).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Frequency dependence of the dielectric permittivity of four different materials using (a) a 6-pole Debye, (b) a 2-pole Lorentz, (c) a 2-pole Drude, and (d) a 3-pole Drude–Lorentz models. See Table 2 for material parameters.

Fig. 2.
Fig. 2.

Evolution of global error for four dispersive media shown in Fig. 1: (a) 5-pole Debye medium; (b) 3-pole Lorentz medium; (c) 2-pole Drude medium; (d) 3-pole Drude–Lorentz medium. The inset in panel (a) shows schematically three different PMLs surrounding the simulation region. For simulation parameters, see the text.

Fig. 3.
Fig. 3.

Density plots of the electric field component, Ez , after 2300 (left panel) and 3300 (right panel) FDTD time-steps. A Gaussian pulse, emitted by a point source (cross) located in vacuum (region C) illuminates region A containing fluoride glass and the region B containing gold. The parts of a 10-cell PML marked as A′, B′, and C′ are matched to the regions A, B, and C, respectively. For simulation parameters, see the text.

Fig. 4.
Fig. 4.

Evolution of global error with the time-step number during simulations shown in Fig. 3 (red curve). For comparison, blue and green curves show error evolution for thicker and thinner PMLs. All three curves are calculated for a 380×380 grid and compared to a 1000×1000 reference grid.

Tables (2)

Tables Icon

Table 1. Poles and their residues for CCPR media corresponding to Debye, Lorentz, and Drude models of the dielectric response

Tables Icon

Table 2. Material parameters used in the simulations

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

ε ˜ ( ω ) = ε + p = 0 p ( c p i ω a p + c p * i ω a p * ) ,
A ˜ ( ω ) = + A ( t ) exp ( i ω t ) d t .
× E ˜ = i ω μ 0 μ H ˜ ,
× H ˜ = i ω ε 0 ε ˜ ( ω ) E ˜ ,
' × E ˜ = i ω μ 0 μ Γ ˜ H ˜ ,
' × H ˜ = i ω ε 0 ε ˜ ( ω ) Γ ˜ E ˜ ,
s j = κ j + σ j γ i ω ε 0 .
σ j = σ max ( k / δ j ) m + n ,             κ j = 1 + ( κ max 1 ) ( k / δ j ) n ,
R ˜ E = Γ ˜ E ˜ , R ˜ H = Γ ˜ H ˜ .
× H ˜ = i ω ε 0 ε R ˜ E + p = 0 P ( J ˜ p + K ˜ p ) ,
J ˜ p = i ω ε 0 c p i ω a p R ˜ E , K ˜ p = i ω ε 0 c p * i ω a p * R ˜ E .
J p n + 1 = α p J p n + β p ( R E n + 1 R E n ) , K p n = ( J p n ) * ,
R E n + 1 2 = R E n 1 2 + × H n + [ ( 1 + α p ) J p n 1 2 ] ε 0 ε Δ t ( β p ) .
R H n + 1 = R H n × E n + 1 2 μ 0 μ Δ t .
E x n + 1 = E x n ( e ξ y Δ t + e ξ z Δ t ) E x n 1 e ( ξ y + ξ z ) Δ t
+ κ x κ y κ z [ R E , x n + 1 R E , x n ( e ξ x Δ t + e ξ 0 Δ t ) + R E , x n 1 e ( ξ x + ξ 0 ) Δ t ] .
χ 2 = x = 1 50 y = 1 50 [ E z ( x , y ) E ref , z ( x , y ) ] 2 .
E z ( n ) = exp [ ( n 50 10 ) 2 ] sin ( 2 π f c n Δ t ) ,
ε ˜ ( ω ) = ε ω pl 2 ω ( ω + i ω c ) + Δ ε 1 ω 1 2 ω 1 2 2 i ω δ 1 ω 2 .

Metrics