Abstract

This Letter introduces a novel finite-difference time-domain (FDTD) formulation for solving transverse electromagnetic systems in dispersive media. Based on the auxiliary differential equation approach, the Debye dispersion model is coupled with Maxwell’s equations to derive a supplementary ordinary differential equation for describing the regularity changes in electromagnetic fields at the dispersive interface. The resulting time-dependent jump conditions are rigorously enforced in the FDTD discretization by means of the matched interface and boundary scheme. High-order convergences are numerically achieved for the first time in the literature in the FDTD simulations of dispersive inhomogeneous media.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. M. Joseph, S. C. Hagness, and A. Taflove, Opt. Lett. 16, 1412 (1991).
    [CrossRef] [PubMed]
  2. O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, IEEE Trans. Microwave Theory Tech. 41, 658 (1993).
    [CrossRef]
  3. J. Li, J. Comput. Appl. Math. 188, 107 (2006).
    [CrossRef]
  4. T. Lu, P. Zhang, and W. Cai, J. Comput. Phys. 200, 549 (2004).
    [CrossRef]
  5. Y. Q. Huang and J. Li, J. Sci. Comput. 41, 321 (2009).
    [CrossRef]
  6. B. Wang, Z. Xie, and Z. Zhang, J. Comput. Phys. 229, 8552 (2010).
    [CrossRef]
  7. Y. Zhao and Y. Hao, IEEE Trans. Antennas Propag. 55, 3070 (2007).
    [CrossRef]
  8. A. Deinega and I. Valuev, Opt. Lett. 32, 3429 (2007).
    [CrossRef] [PubMed]
  9. A. Mohammadi, T. Jalali, and M. Agio, Opt. Express 16, 7397 (2008).
    [CrossRef] [PubMed]
  10. J. S. Hesthaven, Adv. Imaging Electron Phys. 127, 59(2003).
    [CrossRef]
  11. S. Zhao and G. W. Wei, J. Comput. Phys. 200, 60 (2004).
    [CrossRef]
  12. S. Zhao, J. Comput. Phys. 229, 3155 (2010).
    [CrossRef]
  13. S. Zhao and G. W. Wei, Int. J. Numer. Methods Eng. 77, 1690 (2009).
    [CrossRef] [PubMed]

2010 (2)

B. Wang, Z. Xie, and Z. Zhang, J. Comput. Phys. 229, 8552 (2010).
[CrossRef]

S. Zhao, J. Comput. Phys. 229, 3155 (2010).
[CrossRef]

2009 (2)

S. Zhao and G. W. Wei, Int. J. Numer. Methods Eng. 77, 1690 (2009).
[CrossRef] [PubMed]

Y. Q. Huang and J. Li, J. Sci. Comput. 41, 321 (2009).
[CrossRef]

2008 (1)

2007 (2)

Y. Zhao and Y. Hao, IEEE Trans. Antennas Propag. 55, 3070 (2007).
[CrossRef]

A. Deinega and I. Valuev, Opt. Lett. 32, 3429 (2007).
[CrossRef] [PubMed]

2006 (1)

J. Li, J. Comput. Appl. Math. 188, 107 (2006).
[CrossRef]

2004 (2)

T. Lu, P. Zhang, and W. Cai, J. Comput. Phys. 200, 549 (2004).
[CrossRef]

S. Zhao and G. W. Wei, J. Comput. Phys. 200, 60 (2004).
[CrossRef]

2003 (1)

J. S. Hesthaven, Adv. Imaging Electron Phys. 127, 59(2003).
[CrossRef]

1993 (1)

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, IEEE Trans. Microwave Theory Tech. 41, 658 (1993).
[CrossRef]

1991 (1)

Agio, M.

Cai, W.

T. Lu, P. Zhang, and W. Cai, J. Comput. Phys. 200, 549 (2004).
[CrossRef]

Chen, J.-Y.

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, IEEE Trans. Microwave Theory Tech. 41, 658 (1993).
[CrossRef]

Deinega, A.

Gandhi, O. P.

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, IEEE Trans. Microwave Theory Tech. 41, 658 (1993).
[CrossRef]

Gao, B.-Q.

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, IEEE Trans. Microwave Theory Tech. 41, 658 (1993).
[CrossRef]

Hagness, S. C.

Hao, Y.

Y. Zhao and Y. Hao, IEEE Trans. Antennas Propag. 55, 3070 (2007).
[CrossRef]

Hesthaven, J. S.

J. S. Hesthaven, Adv. Imaging Electron Phys. 127, 59(2003).
[CrossRef]

Huang, Y. Q.

Y. Q. Huang and J. Li, J. Sci. Comput. 41, 321 (2009).
[CrossRef]

Jalali, T.

Joseph, R. M.

Li, J.

Y. Q. Huang and J. Li, J. Sci. Comput. 41, 321 (2009).
[CrossRef]

J. Li, J. Comput. Appl. Math. 188, 107 (2006).
[CrossRef]

Lu, T.

T. Lu, P. Zhang, and W. Cai, J. Comput. Phys. 200, 549 (2004).
[CrossRef]

Mohammadi, A.

Taflove, A.

Valuev, I.

Wang, B.

B. Wang, Z. Xie, and Z. Zhang, J. Comput. Phys. 229, 8552 (2010).
[CrossRef]

Wei, G. W.

S. Zhao and G. W. Wei, Int. J. Numer. Methods Eng. 77, 1690 (2009).
[CrossRef] [PubMed]

S. Zhao and G. W. Wei, J. Comput. Phys. 200, 60 (2004).
[CrossRef]

Xie, Z.

B. Wang, Z. Xie, and Z. Zhang, J. Comput. Phys. 229, 8552 (2010).
[CrossRef]

Zhang, P.

T. Lu, P. Zhang, and W. Cai, J. Comput. Phys. 200, 549 (2004).
[CrossRef]

Zhang, Z.

B. Wang, Z. Xie, and Z. Zhang, J. Comput. Phys. 229, 8552 (2010).
[CrossRef]

Zhao, S.

S. Zhao, J. Comput. Phys. 229, 3155 (2010).
[CrossRef]

S. Zhao and G. W. Wei, Int. J. Numer. Methods Eng. 77, 1690 (2009).
[CrossRef] [PubMed]

S. Zhao and G. W. Wei, J. Comput. Phys. 200, 60 (2004).
[CrossRef]

Zhao, Y.

Y. Zhao and Y. Hao, IEEE Trans. Antennas Propag. 55, 3070 (2007).
[CrossRef]

Adv. Imaging Electron Phys. (1)

J. S. Hesthaven, Adv. Imaging Electron Phys. 127, 59(2003).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

Y. Zhao and Y. Hao, IEEE Trans. Antennas Propag. 55, 3070 (2007).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, IEEE Trans. Microwave Theory Tech. 41, 658 (1993).
[CrossRef]

Int. J. Numer. Methods Eng. (1)

S. Zhao and G. W. Wei, Int. J. Numer. Methods Eng. 77, 1690 (2009).
[CrossRef] [PubMed]

J. Comput. Appl. Math. (1)

J. Li, J. Comput. Appl. Math. 188, 107 (2006).
[CrossRef]

J. Comput. Phys. (4)

T. Lu, P. Zhang, and W. Cai, J. Comput. Phys. 200, 549 (2004).
[CrossRef]

B. Wang, Z. Xie, and Z. Zhang, J. Comput. Phys. 229, 8552 (2010).
[CrossRef]

S. Zhao and G. W. Wei, J. Comput. Phys. 200, 60 (2004).
[CrossRef]

S. Zhao, J. Comput. Phys. 229, 3155 (2010).
[CrossRef]

J. Sci. Comput. (1)

Y. Q. Huang and J. Li, J. Sci. Comput. 41, 321 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

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 (3)

Fig. 1
Fig. 1

Reflection coefficient at an air–water interface.

Fig. 2
Fig. 2

MIBTD6 solution with N = 401 at t = 140 ps . Top, E z ; bottom, H y .

Fig. 3
Fig. 3

Numerical convergence tests of E z .

Equations (8)

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

D z t = H y x , H y t = 1 μ E z x ,
ϵ ^ ( ω ) = ϵ 0 [ ϵ + ϵ s ϵ 1 + j ω γ ] ,
γ D z t + D z = ϵ 0 ϵ γ E z t + ϵ 0 ϵ s E z .
[ E z ] = 0 , [ E z x ] = 0 ,
γ ψ ( t ) + ψ ( t ) = ϵ 0 γ [ ϵ E ˙ z ] + ϵ 0 [ ϵ s E z ] ,
E ˙ z t = ϵ s ϵ γ E ˙ z + 1 ϵ 0 μ 0 ϵ 2 E z x 2 + 1 ϵ 0 ϵ γ H y x ,
E z t = E ˙ z , H y t = 1 μ 0 E z x .
[ H y ] = 0 , [ H y x ] = ψ ( t ) ,

Metrics