Abstract

An efficient algorithm for modeling dispersive media in finite-difference time-domain methods is presented. It is based on the auxiliary differential equation method for treatment of Lorentz media with an arbitrary number of relaxations. The algorithm shows excellent accuracy of second order in time and space and is efficient in both memory requirements and computational effort.

© 1997 Optical Society of America

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References

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  1. R. Luebbers, D. Steich, and K. Kunz, IEEE Trans. Antennas Propag. 41, 1249 (1993).
    [CrossRef]
  2. D. M. Sullivan, IEEE Trans. Antennas Propag. 40, 1223 (1992).
    [CrossRef]
  3. R. M. Joseph, S. C. Hagness, and A. Taflove, Opt. Lett. 16, 1412 (1991).
    [CrossRef] [PubMed]
  4. A. Taflove, Computational Electrodynamics—The Finite-Difference-Time-Domain Method (Artech House, Norwood, Mass., 1995).
  5. M. Okoniewsky, M. Mrozowski, and M. A. Stuchly, IEEE Microwave Guided Wave Lett. 7, 121 (1997).
    [CrossRef]

1997 (1)

M. Okoniewsky, M. Mrozowski, and M. A. Stuchly, IEEE Microwave Guided Wave Lett. 7, 121 (1997).
[CrossRef]

1993 (1)

R. Luebbers, D. Steich, and K. Kunz, IEEE Trans. Antennas Propag. 41, 1249 (1993).
[CrossRef]

1992 (1)

D. M. Sullivan, IEEE Trans. Antennas Propag. 40, 1223 (1992).
[CrossRef]

1991 (1)

Hagness, S. C.

Joseph, R. M.

Kunz, K.

R. Luebbers, D. Steich, and K. Kunz, IEEE Trans. Antennas Propag. 41, 1249 (1993).
[CrossRef]

Luebbers, R.

R. Luebbers, D. Steich, and K. Kunz, IEEE Trans. Antennas Propag. 41, 1249 (1993).
[CrossRef]

Mrozowski, M.

M. Okoniewsky, M. Mrozowski, and M. A. Stuchly, IEEE Microwave Guided Wave Lett. 7, 121 (1997).
[CrossRef]

Okoniewsky, M.

M. Okoniewsky, M. Mrozowski, and M. A. Stuchly, IEEE Microwave Guided Wave Lett. 7, 121 (1997).
[CrossRef]

Steich, D.

R. Luebbers, D. Steich, and K. Kunz, IEEE Trans. Antennas Propag. 41, 1249 (1993).
[CrossRef]

Stuchly, M. A.

M. Okoniewsky, M. Mrozowski, and M. A. Stuchly, IEEE Microwave Guided Wave Lett. 7, 121 (1997).
[CrossRef]

Sullivan, D. M.

D. M. Sullivan, IEEE Trans. Antennas Propag. 40, 1223 (1992).
[CrossRef]

Taflove, A.

R. M. Joseph, S. C. Hagness, and A. Taflove, Opt. Lett. 16, 1412 (1991).
[CrossRef] [PubMed]

A. Taflove, Computational Electrodynamics—The Finite-Difference-Time-Domain Method (Artech House, Norwood, Mass., 1995).

IEEE Microwave Guided Wave Lett. (1)

M. Okoniewsky, M. Mrozowski, and M. A. Stuchly, IEEE Microwave Guided Wave Lett. 7, 121 (1997).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

R. Luebbers, D. Steich, and K. Kunz, IEEE Trans. Antennas Propag. 41, 1249 (1993).
[CrossRef]

D. M. Sullivan, IEEE Trans. Antennas Propag. 40, 1223 (1992).
[CrossRef]

Opt. Lett. (1)

Other (1)

A. Taflove, Computational Electrodynamics—The Finite-Difference-Time-Domain Method (Artech House, Norwood, Mass., 1995).

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Figures (2)

Fig. 1
Fig. 1

Errors in the magnitude of the reflection coefficient ranalytical-rFDTD as a function of frequency. The solid curve was computed with the ADE algorithm presented in this Letter, and the dashed–dotted curve was computed with the algorithm described in Ref.  4.

Fig. 2
Fig. 2

As in Fig.  1 but for the error in the phase of the reflection coefficient.

Tables (1)

Tables Icon

Table 1 Accuracy of the Numerically Computed Reflection Coefficient and Computational Effort for a Test Example

Equations (9)

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Dr, t=0Er, t+Pr, t.
Pl=00tχlt-τEτdτ,
χlω=glωl2s-ωl2+2iωδl-ω2,
Eω=l=1NPl0l=1Nχl=D-l=1NPl0=Pk0χk,
P¨k+2δkP˙k+ωk2Pk=ωk2bkD-l=1NPl,
Pkn+1-2Pkn+Pkn-1/Δt2+δkPkn+1-Pkn-1/Δt+ωk2Pkn=ωk2bkDn-l=1NPln.
Pkn+1=a1,kPkn+a2,kPkn-1+a3,kDn-l=1NPln,
a1,k=2-ωk2Δt2/δkΔt+1, a2,k=δkΔt-1/δkΔt+1, a3,k=ωk2Δt2bk/δkΔt+1
Dn+1=Dn+Δt×Hn+1/2, Pkn+1=a1,kPkn+a2,kPkn-1+a4,kEn, En+1=Dn+1-l=1NPln+10,

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