Abstract

The one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is reformulated for simulating general electrically dispersive media. It models material dispersive properties with equivalent polarization currents. These currents are then solved with the auxiliary differential equation (ADE) and then incorporated into the one-step leapfrog ADI-FDTD method. The final equations are presented in the form similar to that of the conventional FDTD method but with second-order perturbation. The adapted method is then applied to characterize (a) electromagnetic wave propagation in a rectangular waveguide loaded with a magnetized plasma slab, (b) transmission coefficient of a plane wave normally incident on a monolayer graphene sheet biased by a magnetostatic field, and (c) surface plasmon polaritons (SPPs) propagation along a monolayer graphene sheet biased by an electrostatic field. The numerical results verify the stability, accuracy and computational efficiency of the proposed one-step leapfrog ADI-FDTD algorithm in comparison with analytical results and the results obtained with the other methods.

© 2013 Optical Society of America

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    [CrossRef]
  31. T. H. Gan and E. L. Tan, “Analysis of the divergence properties for the three-dimensional leapfrog ADI-FDTD method,” IEEE Trans. Antenn. Propag.60(12), 5801–5808 (2012).
    [CrossRef]
  32. T. H. Gan and E. L. Tan, “Unconditionally stable leapfrog ADI-FDTD method for lossy media,” Progress In Electromagnetics Research M26, 173–186 (2012).
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  34. J. Y. Gao and H. X. Zheng, “One-Step leapfrog ADI-FDTD method for lossy media and its stability analysis,” Progress In Electromagnetics Research Letters40, 49–60 (2013).
  35. D. L. Sounas and C. Caloz, “Gyrotropy and nonreciprocity of graphene for microwave applications,” IEEE Trans. Microw. Theory Tech.60(4), 901–914 (2012).
    [CrossRef]
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  37. H. Lin, M. F. Pantoja, L. D. Angulo, J. Alvarez, R. G. Martin, and S. G. Garcia, “FDTD modeling of graphene devices using complex conjugate dispersion material model,” IEEE Microw. Wirel. Compon. Lett.22(12), 612–614 (2012).
    [CrossRef]

2013 (7)

A. Al-Jabr, M. Alsunaidi, T. Khee, and B. S. Ooi, “A simple FDTD algorithm for simulating EM-wave propagation in general dispersive anisotropic material,” IEEE Trans. Antenn. Propag.61(3), 1321–1326 (2013).
[CrossRef]

J. Y. Gao and H. X. Zheng, “One-Step leapfrog ADI-FDTD method for lossy media and its stability analysis,” Progress In Electromagnetics Research Letters40, 49–60 (2013).

Y. F. Mao, B. Chen, J. L. Xia, J. Chen, and J. Z. Tang, “Application of the leapfrog ADI-FDTD method to periodic structures,” IEEE Antennas Wirel. Propag. Lett.12, 599–602 (2013).
[CrossRef]

D. T. Nguyen and R. A. Norwood, “Label-free, single-object sensing with a microring resonator: FDTD simulation,” Opt. Express21(1), 49–59 (2013).
[CrossRef] [PubMed]

I. R. Çapoğlu, A. Taflove, and V. Backman, “Computation of tightly-focused laser beams in the FDTD method,” Opt. Express21(1), 87–101 (2013).
[CrossRef] [PubMed]

C. Lundgren, R. Lopez, J. Redwing, and K. Melde, “FDTD modeling of solar energy absorption in silicon branched nanowires,” Opt. Express21(9), 329–400 (2013).
[PubMed]

E. H. Khoo, I. Ahmed, R. S. M. Goh, K. H. Lee, T. G. G. Hung, and E. P. Li, “Efficient analysis of mode profiles in elliptical microcavity using dynamic-thermal electron-quantum medium FDTD method,” Opt. Express21(5), 5910–5923 (2013).
[CrossRef] [PubMed]

2012 (10)

T. H. Gan and E. L. Tan, “Analysis of the divergence properties for the three-dimensional leapfrog ADI-FDTD method,” IEEE Trans. Antenn. Propag.60(12), 5801–5808 (2012).
[CrossRef]

T. H. Gan and E. L. Tan, “Unconditionally stable leapfrog ADI-FDTD method for lossy media,” Progress In Electromagnetics Research M26, 173–186 (2012).

G. Singh, E. L. Tan, and Z. N. Chen, “Split-step finite-difference time-domain method with perfectly matched layers for efficient analysis of two-dimensional photonic crystals with anisotropic media,” Opt. Lett.37(3), 326–328 (2012).
[CrossRef] [PubMed]

S. Buil, J. Laverdant, B. Berini, P. Maso, J. P. Hermier, and X. Quélin, “FDTD simulations of localization and enhancements on fractal plasmonics nanostructures,” Opt. Express20(11), 11968–11975 (2012).
[CrossRef] [PubMed]

G. Singh, K. Ravi, Q. Wang, and S. T. Ho, “Complex-envelope alternating-direction-implicit FDTD method for simulating active photonic devices with semiconductor/solid-state media,” Opt. Lett.37(12), 2361–2363 (2012).
[CrossRef] [PubMed]

D. L. Sounas and C. Caloz, “Gyrotropy and nonreciprocity of graphene for microwave applications,” IEEE Trans. Microw. Theory Tech.60(4), 901–914 (2012).
[CrossRef]

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett.100(13), 131111 (2012).
[CrossRef]

H. Lin, M. F. Pantoja, L. D. Angulo, J. Alvarez, R. G. Martin, and S. G. Garcia, “FDTD modeling of graphene devices using complex conjugate dispersion material model,” IEEE Microw. Wirel. Compon. Lett.22(12), 612–614 (2012).
[CrossRef]

L. Han, D. Zhou, K. Li, X. Li, and W. P. Huang, “A rational-fraction dispersion model for efficient simulation of dispersive material in FDTD method,” IEEE J. Light. Tech.30(13), 2216–2225 (2012).
[CrossRef]

X. H. Wang, W. Y. Yin, Y. Q. Yu, Z. Chen, J. Wang, and Y. Guo, “A convolutional perfect matched layer (CPML) for one-step leapfrog ADI-FDTD method and its applications to EMC problems,” IEEE Trans. Electromagn. Compat.54(5), 1066–1076 (2012).
[CrossRef]

2011 (1)

2010 (2)

C. M. Dissanayake, M. Premaratne, I. D. Rukhlenko, and G. P. Agrawal, “FDTD modeling of anisotropic nonlinear optical phenomena in silicon waveguides,” Opt. Express18(20), 21427–21448 (2010).
[CrossRef] [PubMed]

Y. Yu and J. Simpson, “An EJ collocated 3-D FDTD model of electromagnetic wave propagation in magnetized cold plasma,” IEEE Trans. Antenn. Propag.58(2), 469–478 (2010).
[CrossRef]

2009 (3)

D. Y. Heh and E. L. Tan, “FDTD modeling for dispersive media using matrix exponential method,” IEEE Microw. Wirel. Compon. Lett.19(2), 53–55 (2009).
[CrossRef]

S. J. Cooke, M. Botton, T. M. Antonsen, and B. Levush, “A leapfrog formulation of the 3D ADI-FDTD algorithm,” Int. J. Numer. Model.22(2), 187–200 (2009).
[CrossRef]

M. Alsunaidi and A. Al-Jabr, “A general ADE-FDTD algorithm for the simulation of dispersive structures,” IEEE Photon. Technol. Lett.21(12), 817–819 (2009).
[CrossRef]

2008 (2)

E. L. Tan, “Fundamental schemes for efficient unconditionally stable implicit finite-difference time-domain methods,” IEEE Trans. Antenn. Propag.56(1), 170–177 (2008).
[CrossRef]

S. Liu and S. Liu, “Runge-Kutta exponential time differencing FDTD method for anisotropic magnetized plasma,” IEEE Antennas Wirel. Propag. Lett.7, 306–309 (2008).
[CrossRef]

2006 (3)

L. J. Xu and N. C. Yuan, “FDTD formulations for scattering from 3-D anisotropic magnetized plasma objects,” IEEE Antennas Wirel. Propag. Lett.5(1), 335–338 (2006).
[CrossRef]

M. Han, R. Dutton, and S. Fan, “Model dispersive media in finite-difference time-domain method with complex-conjugate pole-residue pairs,” IEEE Microw. Wirel. Compon. Lett.16(3), 119–121 (2006).
[CrossRef]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys.125(16), 164705 (2006).
[CrossRef] [PubMed]

2005 (1)

S. Huang and F. Li, “FDTD implementation for magnetoplasma medium using exponential time differencing,” IEEE Microw. Wirel. Compon. Lett.15(3), 183–185 (2005).
[CrossRef]

2000 (1)

F. Zheng, Z. Chen, and J. Zhang, “Toward the development of a three dimensional unconditionally stable finite-different time-domain method,” IEEE Trans. Microw. Theory Tech.48(9), 1550–1558 (2000).
[CrossRef]

1997 (1)

W. H. Weedon and C. M. Rappaport, “A general method for FDTD modeling of wave propagation in arbitrary frequency-dispersive media,” IEEE Trans. Antenn. Propag.45(3), 401–410 (1997).
[CrossRef]

1996 (1)

D. F. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antenn. Propag.44(6), 792–797 (1996).
[CrossRef]

1995 (1)

D. Sullivan, “Nonlinear FDTD formulations using Z transforms,” IEEE Trans. Microw. Theory Tech.43(3), 676–682 (1995).
[CrossRef]

1992 (1)

R. J. Luebbers and F. Hunsberger, “FDTD Nth-order dispersive media,” IEEE Trans. Antenn. Propag.40(11), 1297–1301 (1992).
[CrossRef]

Agrawal, G. P.

Ahmed, I.

Al-Jabr, A.

A. Al-Jabr, M. Alsunaidi, T. Khee, and B. S. Ooi, “A simple FDTD algorithm for simulating EM-wave propagation in general dispersive anisotropic material,” IEEE Trans. Antenn. Propag.61(3), 1321–1326 (2013).
[CrossRef]

M. Alsunaidi and A. Al-Jabr, “A general ADE-FDTD algorithm for the simulation of dispersive structures,” IEEE Photon. Technol. Lett.21(12), 817–819 (2009).
[CrossRef]

Alsunaidi, M.

A. Al-Jabr, M. Alsunaidi, T. Khee, and B. S. Ooi, “A simple FDTD algorithm for simulating EM-wave propagation in general dispersive anisotropic material,” IEEE Trans. Antenn. Propag.61(3), 1321–1326 (2013).
[CrossRef]

M. Alsunaidi and A. Al-Jabr, “A general ADE-FDTD algorithm for the simulation of dispersive structures,” IEEE Photon. Technol. Lett.21(12), 817–819 (2009).
[CrossRef]

Alvarez, J.

H. Lin, M. F. Pantoja, L. D. Angulo, J. Alvarez, R. G. Martin, and S. G. Garcia, “FDTD modeling of graphene devices using complex conjugate dispersion material model,” IEEE Microw. Wirel. Compon. Lett.22(12), 612–614 (2012).
[CrossRef]

Angulo, L. D.

H. Lin, M. F. Pantoja, L. D. Angulo, J. Alvarez, R. G. Martin, and S. G. Garcia, “FDTD modeling of graphene devices using complex conjugate dispersion material model,” IEEE Microw. Wirel. Compon. Lett.22(12), 612–614 (2012).
[CrossRef]

Antonsen, T. M.

S. J. Cooke, M. Botton, T. M. Antonsen, and B. Levush, “A leapfrog formulation of the 3D ADI-FDTD algorithm,” Int. J. Numer. Model.22(2), 187–200 (2009).
[CrossRef]

Backman, V.

Berini, B.

Botton, M.

S. J. Cooke, M. Botton, T. M. Antonsen, and B. Levush, “A leapfrog formulation of the 3D ADI-FDTD algorithm,” Int. J. Numer. Model.22(2), 187–200 (2009).
[CrossRef]

Buil, S.

Caloz, C.

D. L. Sounas and C. Caloz, “Gyrotropy and nonreciprocity of graphene for microwave applications,” IEEE Trans. Microw. Theory Tech.60(4), 901–914 (2012).
[CrossRef]

Çapoglu, I. R.

Chen, B.

Y. F. Mao, B. Chen, J. L. Xia, J. Chen, and J. Z. Tang, “Application of the leapfrog ADI-FDTD method to periodic structures,” IEEE Antennas Wirel. Propag. Lett.12, 599–602 (2013).
[CrossRef]

Chen, J.

Y. F. Mao, B. Chen, J. L. Xia, J. Chen, and J. Z. Tang, “Application of the leapfrog ADI-FDTD method to periodic structures,” IEEE Antennas Wirel. Propag. Lett.12, 599–602 (2013).
[CrossRef]

Chen, Z.

X. H. Wang, W. Y. Yin, Y. Q. Yu, Z. Chen, J. Wang, and Y. Guo, “A convolutional perfect matched layer (CPML) for one-step leapfrog ADI-FDTD method and its applications to EMC problems,” IEEE Trans. Electromagn. Compat.54(5), 1066–1076 (2012).
[CrossRef]

F. Zheng, Z. Chen, and J. Zhang, “Toward the development of a three dimensional unconditionally stable finite-different time-domain method,” IEEE Trans. Microw. Theory Tech.48(9), 1550–1558 (2000).
[CrossRef]

Chen, Z. N.

Cooke, S. J.

S. J. Cooke, M. Botton, T. M. Antonsen, and B. Levush, “A leapfrog formulation of the 3D ADI-FDTD algorithm,” Int. J. Numer. Model.22(2), 187–200 (2009).
[CrossRef]

Dissanayake, C. M.

Dutton, R.

M. Han, R. Dutton, and S. Fan, “Model dispersive media in finite-difference time-domain method with complex-conjugate pole-residue pairs,” IEEE Microw. Wirel. Compon. Lett.16(3), 119–121 (2006).
[CrossRef]

Etchegoin, P. G.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys.125(16), 164705 (2006).
[CrossRef] [PubMed]

Fan, S.

M. Han, R. Dutton, and S. Fan, “Model dispersive media in finite-difference time-domain method with complex-conjugate pole-residue pairs,” IEEE Microw. Wirel. Compon. Lett.16(3), 119–121 (2006).
[CrossRef]

Gan, T. H.

T. H. Gan and E. L. Tan, “Unconditionally stable leapfrog ADI-FDTD method for lossy media,” Progress In Electromagnetics Research M26, 173–186 (2012).

T. H. Gan and E. L. Tan, “Analysis of the divergence properties for the three-dimensional leapfrog ADI-FDTD method,” IEEE Trans. Antenn. Propag.60(12), 5801–5808 (2012).
[CrossRef]

Gao, J. Y.

J. Y. Gao and H. X. Zheng, “One-Step leapfrog ADI-FDTD method for lossy media and its stability analysis,” Progress In Electromagnetics Research Letters40, 49–60 (2013).

Garcia, S. G.

H. Lin, M. F. Pantoja, L. D. Angulo, J. Alvarez, R. G. Martin, and S. G. Garcia, “FDTD modeling of graphene devices using complex conjugate dispersion material model,” IEEE Microw. Wirel. Compon. Lett.22(12), 612–614 (2012).
[CrossRef]

Goh, R. S. M.

Guo, Y.

X. H. Wang, W. Y. Yin, Y. Q. Yu, Z. Chen, J. Wang, and Y. Guo, “A convolutional perfect matched layer (CPML) for one-step leapfrog ADI-FDTD method and its applications to EMC problems,” IEEE Trans. Electromagn. Compat.54(5), 1066–1076 (2012).
[CrossRef]

Han, L.

L. Han, D. Zhou, K. Li, X. Li, and W. P. Huang, “A rational-fraction dispersion model for efficient simulation of dispersive material in FDTD method,” IEEE J. Light. Tech.30(13), 2216–2225 (2012).
[CrossRef]

Han, M.

M. Han, R. Dutton, and S. Fan, “Model dispersive media in finite-difference time-domain method with complex-conjugate pole-residue pairs,” IEEE Microw. Wirel. Compon. Lett.16(3), 119–121 (2006).
[CrossRef]

Heh, D. Y.

D. Y. Heh and E. L. Tan, “FDTD modeling for dispersive media using matrix exponential method,” IEEE Microw. Wirel. Compon. Lett.19(2), 53–55 (2009).
[CrossRef]

Hermier, J. P.

Ho, S. T.

Huang, S.

S. Huang and F. Li, “FDTD implementation for magnetoplasma medium using exponential time differencing,” IEEE Microw. Wirel. Compon. Lett.15(3), 183–185 (2005).
[CrossRef]

Huang, W. P.

L. Han, D. Zhou, K. Li, X. Li, and W. P. Huang, “A rational-fraction dispersion model for efficient simulation of dispersive material in FDTD method,” IEEE J. Light. Tech.30(13), 2216–2225 (2012).
[CrossRef]

Hung, T. G. G.

Hunsberger, F.

R. J. Luebbers and F. Hunsberger, “FDTD Nth-order dispersive media,” IEEE Trans. Antenn. Propag.40(11), 1297–1301 (1992).
[CrossRef]

Kelley, D. F.

D. F. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antenn. Propag.44(6), 792–797 (1996).
[CrossRef]

Khee, T.

A. Al-Jabr, M. Alsunaidi, T. Khee, and B. S. Ooi, “A simple FDTD algorithm for simulating EM-wave propagation in general dispersive anisotropic material,” IEEE Trans. Antenn. Propag.61(3), 1321–1326 (2013).
[CrossRef]

Khoo, E. H.

Laverdant, J.

Le Ru, E. C.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys.125(16), 164705 (2006).
[CrossRef] [PubMed]

Lee, K. H.

Levush, B.

S. J. Cooke, M. Botton, T. M. Antonsen, and B. Levush, “A leapfrog formulation of the 3D ADI-FDTD algorithm,” Int. J. Numer. Model.22(2), 187–200 (2009).
[CrossRef]

Li, E. P.

Li, F.

S. Huang and F. Li, “FDTD implementation for magnetoplasma medium using exponential time differencing,” IEEE Microw. Wirel. Compon. Lett.15(3), 183–185 (2005).
[CrossRef]

Li, K.

L. Han, D. Zhou, K. Li, X. Li, and W. P. Huang, “A rational-fraction dispersion model for efficient simulation of dispersive material in FDTD method,” IEEE J. Light. Tech.30(13), 2216–2225 (2012).
[CrossRef]

Li, X.

L. Han, D. Zhou, K. Li, X. Li, and W. P. Huang, “A rational-fraction dispersion model for efficient simulation of dispersive material in FDTD method,” IEEE J. Light. Tech.30(13), 2216–2225 (2012).
[CrossRef]

Lin, H.

H. Lin, M. F. Pantoja, L. D. Angulo, J. Alvarez, R. G. Martin, and S. G. Garcia, “FDTD modeling of graphene devices using complex conjugate dispersion material model,” IEEE Microw. Wirel. Compon. Lett.22(12), 612–614 (2012).
[CrossRef]

Liu, S.

S. Liu and S. Liu, “Runge-Kutta exponential time differencing FDTD method for anisotropic magnetized plasma,” IEEE Antennas Wirel. Propag. Lett.7, 306–309 (2008).
[CrossRef]

S. Liu and S. Liu, “Runge-Kutta exponential time differencing FDTD method for anisotropic magnetized plasma,” IEEE Antennas Wirel. Propag. Lett.7, 306–309 (2008).
[CrossRef]

Lopez, R.

Luebbers, R. J.

D. F. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antenn. Propag.44(6), 792–797 (1996).
[CrossRef]

R. J. Luebbers and F. Hunsberger, “FDTD Nth-order dispersive media,” IEEE Trans. Antenn. Propag.40(11), 1297–1301 (1992).
[CrossRef]

Lundgren, C.

Mao, Y. F.

Y. F. Mao, B. Chen, J. L. Xia, J. Chen, and J. Z. Tang, “Application of the leapfrog ADI-FDTD method to periodic structures,” IEEE Antennas Wirel. Propag. Lett.12, 599–602 (2013).
[CrossRef]

Martin, R. G.

H. Lin, M. F. Pantoja, L. D. Angulo, J. Alvarez, R. G. Martin, and S. G. Garcia, “FDTD modeling of graphene devices using complex conjugate dispersion material model,” IEEE Microw. Wirel. Compon. Lett.22(12), 612–614 (2012).
[CrossRef]

Maso, P.

Melde, K.

Meyer, M.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys.125(16), 164705 (2006).
[CrossRef] [PubMed]

Nguyen, D. T.

Norwood, R. A.

Ooi, B. S.

A. Al-Jabr, M. Alsunaidi, T. Khee, and B. S. Ooi, “A simple FDTD algorithm for simulating EM-wave propagation in general dispersive anisotropic material,” IEEE Trans. Antenn. Propag.61(3), 1321–1326 (2013).
[CrossRef]

Pantoja, M. F.

H. Lin, M. F. Pantoja, L. D. Angulo, J. Alvarez, R. G. Martin, and S. G. Garcia, “FDTD modeling of graphene devices using complex conjugate dispersion material model,” IEEE Microw. Wirel. Compon. Lett.22(12), 612–614 (2012).
[CrossRef]

Premaratne, M.

Quélin, X.

Rappaport, C. M.

W. H. Weedon and C. M. Rappaport, “A general method for FDTD modeling of wave propagation in arbitrary frequency-dispersive media,” IEEE Trans. Antenn. Propag.45(3), 401–410 (1997).
[CrossRef]

Ravi, K.

Redwing, J.

Rukhlenko, I. D.

Simpson, J.

Y. Yu and J. Simpson, “An EJ collocated 3-D FDTD model of electromagnetic wave propagation in magnetized cold plasma,” IEEE Trans. Antenn. Propag.58(2), 469–478 (2010).
[CrossRef]

Singh, G.

Sounas, D. L.

D. L. Sounas and C. Caloz, “Gyrotropy and nonreciprocity of graphene for microwave applications,” IEEE Trans. Microw. Theory Tech.60(4), 901–914 (2012).
[CrossRef]

Sullivan, D.

D. Sullivan, “Nonlinear FDTD formulations using Z transforms,” IEEE Trans. Microw. Theory Tech.43(3), 676–682 (1995).
[CrossRef]

Taflove, A.

Tan, E. L.

T. H. Gan and E. L. Tan, “Unconditionally stable leapfrog ADI-FDTD method for lossy media,” Progress In Electromagnetics Research M26, 173–186 (2012).

T. H. Gan and E. L. Tan, “Analysis of the divergence properties for the three-dimensional leapfrog ADI-FDTD method,” IEEE Trans. Antenn. Propag.60(12), 5801–5808 (2012).
[CrossRef]

G. Singh, E. L. Tan, and Z. N. Chen, “Split-step finite-difference time-domain method with perfectly matched layers for efficient analysis of two-dimensional photonic crystals with anisotropic media,” Opt. Lett.37(3), 326–328 (2012).
[CrossRef] [PubMed]

D. Y. Heh and E. L. Tan, “FDTD modeling for dispersive media using matrix exponential method,” IEEE Microw. Wirel. Compon. Lett.19(2), 53–55 (2009).
[CrossRef]

E. L. Tan, “Fundamental schemes for efficient unconditionally stable implicit finite-difference time-domain methods,” IEEE Trans. Antenn. Propag.56(1), 170–177 (2008).
[CrossRef]

Tang, J. Z.

Y. F. Mao, B. Chen, J. L. Xia, J. Chen, and J. Z. Tang, “Application of the leapfrog ADI-FDTD method to periodic structures,” IEEE Antennas Wirel. Propag. Lett.12, 599–602 (2013).
[CrossRef]

Teng, J.

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett.100(13), 131111 (2012).
[CrossRef]

Wang, B.

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett.100(13), 131111 (2012).
[CrossRef]

Wang, J.

X. H. Wang, W. Y. Yin, Y. Q. Yu, Z. Chen, J. Wang, and Y. Guo, “A convolutional perfect matched layer (CPML) for one-step leapfrog ADI-FDTD method and its applications to EMC problems,” IEEE Trans. Electromagn. Compat.54(5), 1066–1076 (2012).
[CrossRef]

Wang, Q.

Wang, X. H.

X. H. Wang, W. Y. Yin, Y. Q. Yu, Z. Chen, J. Wang, and Y. Guo, “A convolutional perfect matched layer (CPML) for one-step leapfrog ADI-FDTD method and its applications to EMC problems,” IEEE Trans. Electromagn. Compat.54(5), 1066–1076 (2012).
[CrossRef]

Weedon, W. H.

W. H. Weedon and C. M. Rappaport, “A general method for FDTD modeling of wave propagation in arbitrary frequency-dispersive media,” IEEE Trans. Antenn. Propag.45(3), 401–410 (1997).
[CrossRef]

Xia, J. L.

Y. F. Mao, B. Chen, J. L. Xia, J. Chen, and J. Z. Tang, “Application of the leapfrog ADI-FDTD method to periodic structures,” IEEE Antennas Wirel. Propag. Lett.12, 599–602 (2013).
[CrossRef]

Xu, L. J.

L. J. Xu and N. C. Yuan, “FDTD formulations for scattering from 3-D anisotropic magnetized plasma objects,” IEEE Antennas Wirel. Propag. Lett.5(1), 335–338 (2006).
[CrossRef]

Yin, W. Y.

X. H. Wang, W. Y. Yin, Y. Q. Yu, Z. Chen, J. Wang, and Y. Guo, “A convolutional perfect matched layer (CPML) for one-step leapfrog ADI-FDTD method and its applications to EMC problems,” IEEE Trans. Electromagn. Compat.54(5), 1066–1076 (2012).
[CrossRef]

Yu, Y.

Y. Yu and J. Simpson, “An EJ collocated 3-D FDTD model of electromagnetic wave propagation in magnetized cold plasma,” IEEE Trans. Antenn. Propag.58(2), 469–478 (2010).
[CrossRef]

Yu, Y. Q.

X. H. Wang, W. Y. Yin, Y. Q. Yu, Z. Chen, J. Wang, and Y. Guo, “A convolutional perfect matched layer (CPML) for one-step leapfrog ADI-FDTD method and its applications to EMC problems,” IEEE Trans. Electromagn. Compat.54(5), 1066–1076 (2012).
[CrossRef]

Yuan, N. C.

L. J. Xu and N. C. Yuan, “FDTD formulations for scattering from 3-D anisotropic magnetized plasma objects,” IEEE Antennas Wirel. Propag. Lett.5(1), 335–338 (2006).
[CrossRef]

Yuan, X.

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett.100(13), 131111 (2012).
[CrossRef]

Zhang, J.

F. Zheng, Z. Chen, and J. Zhang, “Toward the development of a three dimensional unconditionally stable finite-different time-domain method,” IEEE Trans. Microw. Theory Tech.48(9), 1550–1558 (2000).
[CrossRef]

Zhang, X.

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett.100(13), 131111 (2012).
[CrossRef]

Zhao, S.

Zheng, F.

F. Zheng, Z. Chen, and J. Zhang, “Toward the development of a three dimensional unconditionally stable finite-different time-domain method,” IEEE Trans. Microw. Theory Tech.48(9), 1550–1558 (2000).
[CrossRef]

Zheng, H. X.

J. Y. Gao and H. X. Zheng, “One-Step leapfrog ADI-FDTD method for lossy media and its stability analysis,” Progress In Electromagnetics Research Letters40, 49–60 (2013).

Zhou, D.

L. Han, D. Zhou, K. Li, X. Li, and W. P. Huang, “A rational-fraction dispersion model for efficient simulation of dispersive material in FDTD method,” IEEE J. Light. Tech.30(13), 2216–2225 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett.100(13), 131111 (2012).
[CrossRef]

IEEE Antennas Wirel. Propag. Lett. (3)

Y. F. Mao, B. Chen, J. L. Xia, J. Chen, and J. Z. Tang, “Application of the leapfrog ADI-FDTD method to periodic structures,” IEEE Antennas Wirel. Propag. Lett.12, 599–602 (2013).
[CrossRef]

L. J. Xu and N. C. Yuan, “FDTD formulations for scattering from 3-D anisotropic magnetized plasma objects,” IEEE Antennas Wirel. Propag. Lett.5(1), 335–338 (2006).
[CrossRef]

S. Liu and S. Liu, “Runge-Kutta exponential time differencing FDTD method for anisotropic magnetized plasma,” IEEE Antennas Wirel. Propag. Lett.7, 306–309 (2008).
[CrossRef]

IEEE J. Light. Tech. (1)

L. Han, D. Zhou, K. Li, X. Li, and W. P. Huang, “A rational-fraction dispersion model for efficient simulation of dispersive material in FDTD method,” IEEE J. Light. Tech.30(13), 2216–2225 (2012).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett. (4)

M. Han, R. Dutton, and S. Fan, “Model dispersive media in finite-difference time-domain method with complex-conjugate pole-residue pairs,” IEEE Microw. Wirel. Compon. Lett.16(3), 119–121 (2006).
[CrossRef]

D. Y. Heh and E. L. Tan, “FDTD modeling for dispersive media using matrix exponential method,” IEEE Microw. Wirel. Compon. Lett.19(2), 53–55 (2009).
[CrossRef]

S. Huang and F. Li, “FDTD implementation for magnetoplasma medium using exponential time differencing,” IEEE Microw. Wirel. Compon. Lett.15(3), 183–185 (2005).
[CrossRef]

H. Lin, M. F. Pantoja, L. D. Angulo, J. Alvarez, R. G. Martin, and S. G. Garcia, “FDTD modeling of graphene devices using complex conjugate dispersion material model,” IEEE Microw. Wirel. Compon. Lett.22(12), 612–614 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. Alsunaidi and A. Al-Jabr, “A general ADE-FDTD algorithm for the simulation of dispersive structures,” IEEE Photon. Technol. Lett.21(12), 817–819 (2009).
[CrossRef]

IEEE Trans. Antenn. Propag. (7)

A. Al-Jabr, M. Alsunaidi, T. Khee, and B. S. Ooi, “A simple FDTD algorithm for simulating EM-wave propagation in general dispersive anisotropic material,” IEEE Trans. Antenn. Propag.61(3), 1321–1326 (2013).
[CrossRef]

D. F. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antenn. Propag.44(6), 792–797 (1996).
[CrossRef]

Y. Yu and J. Simpson, “An EJ collocated 3-D FDTD model of electromagnetic wave propagation in magnetized cold plasma,” IEEE Trans. Antenn. Propag.58(2), 469–478 (2010).
[CrossRef]

W. H. Weedon and C. M. Rappaport, “A general method for FDTD modeling of wave propagation in arbitrary frequency-dispersive media,” IEEE Trans. Antenn. Propag.45(3), 401–410 (1997).
[CrossRef]

R. J. Luebbers and F. Hunsberger, “FDTD Nth-order dispersive media,” IEEE Trans. Antenn. Propag.40(11), 1297–1301 (1992).
[CrossRef]

E. L. Tan, “Fundamental schemes for efficient unconditionally stable implicit finite-difference time-domain methods,” IEEE Trans. Antenn. Propag.56(1), 170–177 (2008).
[CrossRef]

T. H. Gan and E. L. Tan, “Analysis of the divergence properties for the three-dimensional leapfrog ADI-FDTD method,” IEEE Trans. Antenn. Propag.60(12), 5801–5808 (2012).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

X. H. Wang, W. Y. Yin, Y. Q. Yu, Z. Chen, J. Wang, and Y. Guo, “A convolutional perfect matched layer (CPML) for one-step leapfrog ADI-FDTD method and its applications to EMC problems,” IEEE Trans. Electromagn. Compat.54(5), 1066–1076 (2012).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (3)

F. Zheng, Z. Chen, and J. Zhang, “Toward the development of a three dimensional unconditionally stable finite-different time-domain method,” IEEE Trans. Microw. Theory Tech.48(9), 1550–1558 (2000).
[CrossRef]

D. Sullivan, “Nonlinear FDTD formulations using Z transforms,” IEEE Trans. Microw. Theory Tech.43(3), 676–682 (1995).
[CrossRef]

D. L. Sounas and C. Caloz, “Gyrotropy and nonreciprocity of graphene for microwave applications,” IEEE Trans. Microw. Theory Tech.60(4), 901–914 (2012).
[CrossRef]

Int. J. Numer. Model. (1)

S. J. Cooke, M. Botton, T. M. Antonsen, and B. Levush, “A leapfrog formulation of the 3D ADI-FDTD algorithm,” Int. J. Numer. Model.22(2), 187–200 (2009).
[CrossRef]

J. Chem. Phys. (1)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys.125(16), 164705 (2006).
[CrossRef] [PubMed]

Opt. Express (6)

Opt. Lett. (3)

Progress In Electromagnetics Research Letters (1)

J. Y. Gao and H. X. Zheng, “One-Step leapfrog ADI-FDTD method for lossy media and its stability analysis,” Progress In Electromagnetics Research Letters40, 49–60 (2013).

Progress In Electromagnetics Research M (1)

T. H. Gan and E. L. Tan, “Unconditionally stable leapfrog ADI-FDTD method for lossy media,” Progress In Electromagnetics Research M26, 173–186 (2012).

Other (3)

X. H. Wang, W. Y. Yin, and Z. Chen, “One-step leapfrog ADI-FDTD method for anisotropic magnetized plasma,” in proceedings of IEEE International Microwave Symposium, 1–4 (2013).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

T. H. Gan and E. T. Tan, “Mur absorbing boundary condition for 2-D leapfrog ADI-FDTD method,” in proceedings of IEEE Conference on Asia-Pacific Antennas and Propagation, 3–4 (2012).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

A rectangular waveguide of 40mm × 40mm loaded with a magnetized plasma slab of 5 mm in width.

Fig. 2
Fig. 2

The Recorded Ez –component versus time with CFLN = 1, 2, and 3; the result obtained with the conventional FDTD method is also plotted for comparison.

Fig. 3
Fig. 3

(a) The computational domain where a plane wave normally incident on an infinite graphene sheet. (b) The computed transmission coefficient |T| of the plane wave normally incident on an infinite graphene sheet biased by a magnetostatic field B0 = 1 T. The analytical result is also plotted for comparison.

Fig. 4
Fig. 4

Ey-component snapshot at t = 2.5t0 for (a) CFLN = 1 and (b) CFLN = 3, respectively. The field is recorded at 10 cells away from the CPML in the y-z plane.

Fig. 5
Fig. 5

Computational domain for the simulation of SPPs on the graphene sheet.

Fig. 6
Fig. 6

Snapshots of the normalized electric field at time t = 2.887 ps. (a) Ez: leapfrog ADI-FDTD with CFLN = 10; (b) Ey: leapfrog ADI-FDTD with CFLN = 10; (c) Ez: conventional ADE-FDTD with CFLN = 1 [17]; and (d) Ey: conventional ADE-FDTD with CFLN = 1 [17].

Equations (47)

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jω ε 0 ε re E(ω)=×H(ω)
ε re (ω)=[ ε xx (ω) ε xy (ω) ε xz (ω) ε yx (ω) ε yy (ω) ε yz (ω) ε zx (ω) ε zy (ω) ε zz (ω) ]
[ ε 0 ε re (ω)E(ω) ] x = ε 0 E x (ω)+ ε 0 ( ε xx 1) E x (ω)+ ε 0 ε xy E y (ω)+ ε 0 ε xz E z (ω) = ε 0 E x (ω)+ P xx (ω)+ P xy (ω)+ P xz (ω)
jω ε 0 E x (ω)+jω[ P xx (ω)+ P xy (ω)+ P xz (ω)]=jω ε 0 E x (ω)+ J x (ω)= [ ×H(ω) ] x
J x (ω)=jω[ P xx (ω)+ P xy (ω)+ P xz (ω)]
J y (ω)=jω[ P yx (ω)+ P yy (ω)+ P yz (ω)]
J z (ω)=jω[ P zx (ω)+ P zy (ω)+ P zz (ω)].
jω ε 0 E(ω)=×H(ω) -J(ω).
dE/dt=[ (AB)HJ ]/ ε 0
A=[ 0 0 /y /z 0 0 0 /x 0 ], B=[ 0 /z 0 0 0 /x /y 0 0 ].
dH/dt=(BA)E/ μ 0
E n+1/2 = E n +(0.5Δt/ ε 0 )(A H n+1/2 B H n J n+ p 1 )
H n+1/2 = H n +(0.5Δt/ μ 0 )(B E n+1/2 A E n )
E n+1 = E n+1/2 +(0.5Δt/ ε 0 )(A H n+1/2 B H n+1 J n+ p 2 )
H n+1 = H n+1/2 +(0.5Δt/ μ 0 )(B E n+1/2 A E n+1 )
E n+1/2 = E n + Δt 2 ε 0 (A H n + Δt 2 μ 0 AB E n+1/2 Δt 2 μ 0 AA E n B H n J n+ p 1 ).
E n = E n1/2 + Δt 2 ε 0 (A H n Δt 2 μ 0 AB E n+1/2 + Δt 2 μ 0 AA E n B H n J n+ p 2 1 ).
(I Δ t 2 4 μ 0 ε 0 AB) E n+1/2 =(I Δ t 2 4 μ 0 ε 0 AB) E n1/2 + Δt ε 0 (A H n B H n ) Δt 2 ε 0 ( J n+ p 1 + J n+ p 2 1 ).
E n = E n+1/2 (0.5Δt/ ε 0 )(A H n+1/2 B H n J n+ p 1 ).
H n+1/2 = H n + Δt 2 μ 0 (B E n+1/2 + Δt 2 ε 0 AA H n+1/2 Δt 2 ε 0 AB H n A E n+1/2 Δt 2 ε 0 A J n+ p 1 ).
H n+1 = H n+1/2 + Δt 2 μ 0 (B E n+1/2 Δt 2 ε 0 AA H n+1/2 + Δt 2 ε 0 AB H n+1 A E n+1/2 + Δt 2 ε 0 A J n+ p 2 ).
(I Δ t 2 4 μ 0 ε 0 AB) H n+1 =(I Δ t 2 4 μ 0 ε 0 AB) H n + Δt μ 0 (B E n+1/2 A E n+1/2 ) + Δ t 2 4 μ 0 ε 0 A( J n+ p 2 J n+ p 1 ).
(I Δ t 2 4 μ 0 ε 0 AB) E n+1/2 =(I Δ t 2 4 μ 0 ε 0 AB) E n1/2 + Δt ε 0 (A H n B H n ) Δt ε 0 J n
(I Δ t 2 4 μ 0 ε 0 AB) H n+1 =(I Δ t 2 4 μ 0 ε 0 AB) H n + Δt μ 0 (B E n+1/2 A E n+1/2 ).
E n+1/2 = E n1/2 + Δt ε 0 (A H n B H n ) Δt ε 0 J n + e n
H n+1 = H n + Δt μ 0 (B E n+1/2 A E n+1/2 )+ h n+1/2
e n = Δ t 2 4 μ 0 ε 0 AB( E n+1/2 E n1/2 ), h n+1/2 = Δ t 2 4 μ 0 ε 0 AB( H n+1 H n ).
σ=[ σ x 0 0 0 σ y 0 0 0 σ z ], ε re (ω)=[ 1+ σ x /jω ε 0 0 0 0 1+ σ y /jω ε 0 0 0 0 1+ σ z /jω ε 0 ].
J n =σ E n =σ( E n+1/2 + E n1/2 )/2.
(I Δ t 2 4 μ 0 ε 0 AB+ Δt 2 ε 0 σ) E n+1/2 =(I Δ t 2 4 μ 0 ε 0 AB Δt 2 ε 0 σ) E n1/2 + Δt ε 0 (A H n B H n ).
ε re (ω)=[ ε d (ω) j ε g (ω) 0 j ε g (ω) ε d (ω) 0 0 0 ε z (ω) ]
ε d (ω)=1+ ω p 2 + ν c ω p 2 /(jω) ( ν c 2 + ω b 2 )+2j ν c ω ω 2 , ε g (ω)= ω b ω p 2 /(jω) ( ν c 2 + ω b 2 )+2j ν c ω ω 2
ε z (ω)=1 ω p 2 j ν c ω+ ω 2
J x (ω)= ε 0 ω p 2 jω+ ε 0 ν c ω p 2 ( ν c 2 + ω b 2 )+2j ν c ω ω 2 E x + ε 0 ω b ω p 2 ( ν c 2 + ω b 2 )+2j ν c ω ω 2 E y .
J(ω)= a 0 + a 1 jω b 0 + b 1 jω+ b 2 (jω) 2 E(ω)
b 0 J+ b 1 dJ dt + b 2 d 2 J d t 2 = a 0 E+ a 1 dE dt .
b 0 J n1 + b 1 J n J n2 2Δt + b 2 J n 2 J n1 + J n2 Δ t 2 = a 0 E n1/2 + E n3/2 2 + a 1 E n1/2 E n3/2 Δt .
J n = 4 b 2 Δt2 b 0 Δ t 2 b 1 Δt+2 b 2 J n1 + b 1 Δt2 b 2 b 1 Δt+2 b 2 J n2 + a 0 Δ t 2 +2 a 1 Δt b 1 Δt+2 b 2 E n1/2 + a 0 Δ t 2 2 a 1 Δt b 1 Δt+2 b 2 E n3/2 .
ε re (ω)=[ ε d (ω) j ε g (ω) 0 j ε g (ω) ε d (ω) 0 0 0 0 ]
ε d (ω)=1+ σ 0 +ν σ 0 /(jω) ( ν 2 + ω c 2 )+2jνω ω 2
ε g (ω)= ω b σ 0 /(jω) ( ν 2 + ω c 2 )+2jνω ω 2
σ 0 = 2 e 2 τ k B Tν π 2 ε 0 Δz ln( 2cosh μ c 2 k B T )
ε d (ω)=1+[ σ 0 /(jω)]/(ν+jω)
E 0 =[e/( ε 0 π 2 v F 2 )] 0 ε[ f d ( ε ) f d ( ε+2 μ c ) ]dε
E x inc (t)=exp[4π (t t 0 ) 2 / τ 2 ]
T analytic (f)= 2 | 2+jω[ ε d ω1] η 0 | 2 + | ε 0 ε g ω 2 η 0 | 2 | ( 2+jω[ ε d ω1] η 0 ) 2 + ( ε 0 ε g ω 2 η 0 ) 2 |
T leapfrog (f)= | FFT( E x,ob (t)) | 2 + | FFT( E y,ob (t)) | 2 | FFT( E in (t)) |

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