Abstract

Efficient unconditionally stable FDTD method is developed for the electromagnetic analysis of dispersive media. Toward this purpose, a quadratic complex rational function (QCRF) dispersion model is applied to the alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method. The 3-D update equations of QCRF-ADI-FDTD are derived using Maxwell’s curl equations and the constitutive relation. The periodic boundary condition of QCRF-ADI-FDTD is discussed in detail. A 3-D numerical example shows that the time-step size can be increased by the proposed QCRF-ADI-FDTD beyond the Courant-Friedrich-Levy (CFL) number, without numerical instability. It is observed that, for refined computational cells, the computational time of QCRF-ADI-FDTD is reduced to 28.08 % of QCRF-FDTD, while the L2 relative error norm of a field distribution is 6.92 %.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  4. K.-Y. Jung, S. Ju, and F. L. Teixeira, “Application of the modal CFS-PML-FDTD to the analysis of magnetic photonic crystal waveguides,” IEEE Microw. Wireless Compat. Lett. 21(4), 179–181 (2011).
    [Crossref]
  5. S. K. Pradhan, B. Xiao, J. R. Skuza, K. Santiago, R. Mundle, and A. K. Pradhan, “Effects of dielectric thickness on optical behavior and tunability of one-dimensional Ag/SiO2 multilayered metamaterials,” Opt. Express 22(10), 12486–12498 (2014).
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    [Crossref]
  8. H. Chung, J. Cho, S.-G. Ha, S. Ju, and K.-Y. Jung, “Accurate FDTD dispersive modeling for concrete materials,” ETRI J. 35(5), 915–918 (2013).
    [Crossref]
  9. H. Chung, K.-Y. Jung, X. T. Tee, and P. Bermel, “Time domain simulation of tandem silicon solar cells with optimal textured light trapping enabled by the quadratic complex rational function,” Opt. Express 22(S3), A818–A832 (2014).
    [Crossref] [PubMed]
  10. T. Wuren, T. Takai, M. Fujii, and I. Sakagami, “Effective 2-Debye-pole FDTD model of electromagnetic interaction between human body and UWB radiation,” IEEE Microw. Wireless Compat. Lett. 17(7), 483–485 (2007).
    [Crossref]
  11. K.-Y. Jung, F. L. Teixeira, and R. M. Reano, “Au/SiO2 nanoring plasmon waveguides at optical communication band,” J. Lightw. Technol. 25(9), 2757–2765 (2007).
    [Crossref]
  12. S. Aksoy, “An alternative algorithm for both narrowband and wideband Lorentzian dispersive materials modeling in the finite-difference time-domain method,” IEEE Trans. Microw. Theory Tech. 55(4), 703–708 (2007).
    [Crossref]
  13. W.-J. Yoon, K.-Y. Jung, J. Liu, T. Duraisamy, R. Revur, F. L. Teixeira, S. Sengupta, and P. R. Berger, “Plasmon-enhanced optical absorption and photocurrent in organic bulk heterojunction photovoltaic devices using self-assembled layer of silver nanoparticles,” Sol. Energy Mater. Sol. Cells 94(2), 128–132 (2010).
    [Crossref]
  14. D. Y. Na, J. H. Kim, K.-Y. Jung, and Y. B. Park, “Mode-matching analysis of a coaxially fed annular slot surrounded with corrugations,” Electromagn. 34(2), 92–110 (2014).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  18. K.-Y. Jung, F. L. Teixeira, S. G. Garcia, and R. Lee, “On numerical artifacts of the complex envelope ADI-FDTD method,” IEEE Trans. Antennas Propagat. 57(2), 491–498 (2009).
    [Crossref]
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    [Crossref]
  21. K.-Y. Jung, S. Ju, and F. L. Teixeira, “Two-stage perfectly matched layer for the analysis of plasmonic structures,” IEICE Trans. Electronics,  E93-C(8), 1371–1374 (2010)
    [Crossref]
  22. S. Wang, J. Chen, and P. Ruchhoeft, “An ADI-FDTD method for periodic structures,” IEEE Trans. Antennas Propagat. 53(7), 2343–2346 (2005).
    [Crossref]
  23. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambrige University, 3, 1995).
  24. K.-Y. Jung and F. L. Teixeira, “An iterative unconditionally stable stable LOD-FDTD method,” IEEE Microw”, Wireless Compat. Lett. 18(2), 76–78 (2008).
    [Crossref]
  25. Q. H. Liu, “The PSTD algorithm: A time-domain method requiring only two cells per wavelength,” Microwave Opt. Technol. Lett. 15(3), 158–165 (1997).
    [Crossref]
  26. M. W. Feise, J. B. Schneider, and P. J. Bevelacqua, “Finite-difference and pseudospectral time-domain methods applied to backward-wave metamaterials,” IEEE Trans. Antennas Propagat. 52(11), 2955–2962 (2004).
    [Crossref]
  27. C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Trans. 113(13), 1728–1740 (2012).
    [Crossref]

2014 (4)

2013 (3)

I.-Y. Oh, Y. Hong, and J.-G. Yook, “Extremely low numerical dispersion FDTD method based on H(2,4) scheme of lossy material,” J. Electromagn. Eng. Sci. 13(3), 158–164 (2013).
[Crossref]

S.-G. Ha, J. Cho, J. Choi, H. Kim, and K.-Y. Jung, “FDTD dispersive modeling of human tissue based on quadratic complex rational function,” IEEE Trans. Antennas Propagat. 61(2), 996–999 (2013).
[Crossref]

H. Chung, J. Cho, S.-G. Ha, S. Ju, and K.-Y. Jung, “Accurate FDTD dispersive modeling for concrete materials,” ETRI J. 35(5), 915–918 (2013).
[Crossref]

2012 (2)

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. Express 20(11), 11968–11975 (2012).
[Crossref] [PubMed]

C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Trans. 113(13), 1728–1740 (2012).
[Crossref]

2011 (1)

K.-Y. Jung, S. Ju, and F. L. Teixeira, “Application of the modal CFS-PML-FDTD to the analysis of magnetic photonic crystal waveguides,” IEEE Microw. Wireless Compat. Lett. 21(4), 179–181 (2011).
[Crossref]

2010 (2)

W.-J. Yoon, K.-Y. Jung, J. Liu, T. Duraisamy, R. Revur, F. L. Teixeira, S. Sengupta, and P. R. Berger, “Plasmon-enhanced optical absorption and photocurrent in organic bulk heterojunction photovoltaic devices using self-assembled layer of silver nanoparticles,” Sol. Energy Mater. Sol. Cells 94(2), 128–132 (2010).
[Crossref]

K.-Y. Jung, S. Ju, and F. L. Teixeira, “Two-stage perfectly matched layer for the analysis of plasmonic structures,” IEICE Trans. Electronics,  E93-C(8), 1371–1374 (2010)
[Crossref]

2009 (2)

K.-Y. Jung, F. L. Teixeira, and R. M. Reano, “Surface plasmon coplanar waveguides: Mode characteristics and mode conversion losses,” IEEE Photon. Technol. Lett. 21(10), 630–632 (2009).
[Crossref]

K.-Y. Jung, F. L. Teixeira, S. G. Garcia, and R. Lee, “On numerical artifacts of the complex envelope ADI-FDTD method,” IEEE Trans. Antennas Propagat. 57(2), 491–498 (2009).
[Crossref]

2008 (1)

K.-Y. Jung and F. L. Teixeira, “An iterative unconditionally stable stable LOD-FDTD method,” IEEE Microw”, Wireless Compat. Lett. 18(2), 76–78 (2008).
[Crossref]

2007 (4)

K.-Y. Jung and F. L. Teixeira, “Multispecies ADI-FDTD algorithm for nanoscale three-dimensional photonic metallic structures,” IEEE Photon. Technol. Lett. 19(8), 586–588 (2007).
[Crossref]

T. Wuren, T. Takai, M. Fujii, and I. Sakagami, “Effective 2-Debye-pole FDTD model of electromagnetic interaction between human body and UWB radiation,” IEEE Microw. Wireless Compat. Lett. 17(7), 483–485 (2007).
[Crossref]

K.-Y. Jung, F. L. Teixeira, and R. M. Reano, “Au/SiO2 nanoring plasmon waveguides at optical communication band,” J. Lightw. Technol. 25(9), 2757–2765 (2007).
[Crossref]

S. Aksoy, “An alternative algorithm for both narrowband and wideband Lorentzian dispersive materials modeling in the finite-difference time-domain method,” IEEE Trans. Microw. Theory Tech. 55(4), 703–708 (2007).
[Crossref]

2005 (1)

S. Wang, J. Chen, and P. Ruchhoeft, “An ADI-FDTD method for periodic structures,” IEEE Trans. Antennas Propagat. 53(7), 2343–2346 (2005).
[Crossref]

2004 (1)

M. W. Feise, J. B. Schneider, and P. J. Bevelacqua, “Finite-difference and pseudospectral time-domain methods applied to backward-wave metamaterials,” IEEE Trans. Antennas Propagat. 52(11), 2955–2962 (2004).
[Crossref]

2001 (1)

S. Gedney, G. Liu, J. Roden, and A. Zhu, “Perfectly matched layer media with CFS for an unconditionally stable ADI-FDTD method,” IEEE Trans. Antennas Propagat.  49(11), 1554–1559 (2001).
[Crossref]

1999 (1)

F. Zheng, “A finite-difference time-domain method without the courant stability conditions,” IEEE Microwave Guided Wave Let. 9(11), 441–443 (1999).
[Crossref]

1997 (1)

Q. H. Liu, “The PSTD algorithm: A time-domain method requiring only two cells per wavelength,” Microwave Opt. Technol. Lett. 15(3), 158–165 (1997).
[Crossref]

Aksoy, S.

S. Aksoy, “An alternative algorithm for both narrowband and wideband Lorentzian dispersive materials modeling in the finite-difference time-domain method,” IEEE Trans. Microw. Theory Tech. 55(4), 703–708 (2007).
[Crossref]

Berger, P. R.

W.-J. Yoon, K.-Y. Jung, J. Liu, T. Duraisamy, R. Revur, F. L. Teixeira, S. Sengupta, and P. R. Berger, “Plasmon-enhanced optical absorption and photocurrent in organic bulk heterojunction photovoltaic devices using self-assembled layer of silver nanoparticles,” Sol. Energy Mater. Sol. Cells 94(2), 128–132 (2010).
[Crossref]

Berini, B.

Bermel, P.

Bevelacqua, P. J.

M. W. Feise, J. B. Schneider, and P. J. Bevelacqua, “Finite-difference and pseudospectral time-domain methods applied to backward-wave metamaterials,” IEEE Trans. Antennas Propagat. 52(11), 2955–2962 (2004).
[Crossref]

Buil, S.

Chen, J.

S. Wang, J. Chen, and P. Ruchhoeft, “An ADI-FDTD method for periodic structures,” IEEE Trans. Antennas Propagat. 53(7), 2343–2346 (2005).
[Crossref]

Cho, J.

S.-G. Ha, J. Cho, J. Choi, H. Kim, and K.-Y. Jung, “FDTD dispersive modeling of human tissue based on quadratic complex rational function,” IEEE Trans. Antennas Propagat. 61(2), 996–999 (2013).
[Crossref]

H. Chung, J. Cho, S.-G. Ha, S. Ju, and K.-Y. Jung, “Accurate FDTD dispersive modeling for concrete materials,” ETRI J. 35(5), 915–918 (2013).
[Crossref]

Choi, J.

S.-G. Ha, J. Cho, J. Choi, H. Kim, and K.-Y. Jung, “FDTD dispersive modeling of human tissue based on quadratic complex rational function,” IEEE Trans. Antennas Propagat. 61(2), 996–999 (2013).
[Crossref]

Choi, W. K.

Chung, H.

Duraisamy, T.

W.-J. Yoon, K.-Y. Jung, J. Liu, T. Duraisamy, R. Revur, F. L. Teixeira, S. Sengupta, and P. R. Berger, “Plasmon-enhanced optical absorption and photocurrent in organic bulk heterojunction photovoltaic devices using self-assembled layer of silver nanoparticles,” Sol. Energy Mater. Sol. Cells 94(2), 128–132 (2010).
[Crossref]

Feise, M. W.

M. W. Feise, J. B. Schneider, and P. J. Bevelacqua, “Finite-difference and pseudospectral time-domain methods applied to backward-wave metamaterials,” IEEE Trans. Antennas Propagat. 52(11), 2955–2962 (2004).
[Crossref]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambrige University, 3, 1995).

Fujii, M.

T. Wuren, T. Takai, M. Fujii, and I. Sakagami, “Effective 2-Debye-pole FDTD model of electromagnetic interaction between human body and UWB radiation,” IEEE Microw. Wireless Compat. Lett. 17(7), 483–485 (2007).
[Crossref]

Garcia, S. G.

K.-Y. Jung, F. L. Teixeira, S. G. Garcia, and R. Lee, “On numerical artifacts of the complex envelope ADI-FDTD method,” IEEE Trans. Antennas Propagat. 57(2), 491–498 (2009).
[Crossref]

Gedney, S.

S. Gedney, G. Liu, J. Roden, and A. Zhu, “Perfectly matched layer media with CFS for an unconditionally stable ADI-FDTD method,” IEEE Trans. Antennas Propagat.  49(11), 1554–1559 (2001).
[Crossref]

Ha, S.-G.

S.-G. Ha, J. Cho, J. Choi, H. Kim, and K.-Y. Jung, “FDTD dispersive modeling of human tissue based on quadratic complex rational function,” IEEE Trans. Antennas Propagat. 61(2), 996–999 (2013).
[Crossref]

H. Chung, J. Cho, S.-G. Ha, S. Ju, and K.-Y. Jung, “Accurate FDTD dispersive modeling for concrete materials,” ETRI J. 35(5), 915–918 (2013).
[Crossref]

Hagness, S. C.

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

Hermier, J.-P.

Hong, Y.

I.-Y. Oh, Y. Hong, and J.-G. Yook, “Extremely low numerical dispersion FDTD method based on H(2,4) scheme of lossy material,” J. Electromagn. Eng. Sci. 13(3), 158–164 (2013).
[Crossref]

Hwang, D. K.

Ju, B.-K.

Ju, S.

H. Chung, J. Cho, S.-G. Ha, S. Ju, and K.-Y. Jung, “Accurate FDTD dispersive modeling for concrete materials,” ETRI J. 35(5), 915–918 (2013).
[Crossref]

K.-Y. Jung, S. Ju, and F. L. Teixeira, “Application of the modal CFS-PML-FDTD to the analysis of magnetic photonic crystal waveguides,” IEEE Microw. Wireless Compat. Lett. 21(4), 179–181 (2011).
[Crossref]

K.-Y. Jung, S. Ju, and F. L. Teixeira, “Two-stage perfectly matched layer for the analysis of plasmonic structures,” IEICE Trans. Electronics,  E93-C(8), 1371–1374 (2010)
[Crossref]

Jung, K.-Y.

D. Y. Na, J. H. Kim, K.-Y. Jung, and Y. B. Park, “Mode-matching analysis of a coaxially fed annular slot surrounded with corrugations,” Electromagn. 34(2), 92–110 (2014).
[Crossref]

H. Chung, K.-Y. Jung, X. T. Tee, and P. Bermel, “Time domain simulation of tandem silicon solar cells with optimal textured light trapping enabled by the quadratic complex rational function,” Opt. Express 22(S3), A818–A832 (2014).
[Crossref] [PubMed]

H. Chung, J. Cho, S.-G. Ha, S. Ju, and K.-Y. Jung, “Accurate FDTD dispersive modeling for concrete materials,” ETRI J. 35(5), 915–918 (2013).
[Crossref]

S.-G. Ha, J. Cho, J. Choi, H. Kim, and K.-Y. Jung, “FDTD dispersive modeling of human tissue based on quadratic complex rational function,” IEEE Trans. Antennas Propagat. 61(2), 996–999 (2013).
[Crossref]

K.-Y. Jung, S. Ju, and F. L. Teixeira, “Application of the modal CFS-PML-FDTD to the analysis of magnetic photonic crystal waveguides,” IEEE Microw. Wireless Compat. Lett. 21(4), 179–181 (2011).
[Crossref]

W.-J. Yoon, K.-Y. Jung, J. Liu, T. Duraisamy, R. Revur, F. L. Teixeira, S. Sengupta, and P. R. Berger, “Plasmon-enhanced optical absorption and photocurrent in organic bulk heterojunction photovoltaic devices using self-assembled layer of silver nanoparticles,” Sol. Energy Mater. Sol. Cells 94(2), 128–132 (2010).
[Crossref]

K.-Y. Jung, S. Ju, and F. L. Teixeira, “Two-stage perfectly matched layer for the analysis of plasmonic structures,” IEICE Trans. Electronics,  E93-C(8), 1371–1374 (2010)
[Crossref]

K.-Y. Jung, F. L. Teixeira, S. G. Garcia, and R. Lee, “On numerical artifacts of the complex envelope ADI-FDTD method,” IEEE Trans. Antennas Propagat. 57(2), 491–498 (2009).
[Crossref]

K.-Y. Jung, F. L. Teixeira, and R. M. Reano, “Surface plasmon coplanar waveguides: Mode characteristics and mode conversion losses,” IEEE Photon. Technol. Lett. 21(10), 630–632 (2009).
[Crossref]

K.-Y. Jung and F. L. Teixeira, “An iterative unconditionally stable stable LOD-FDTD method,” IEEE Microw”, Wireless Compat. Lett. 18(2), 76–78 (2008).
[Crossref]

K.-Y. Jung, F. L. Teixeira, and R. M. Reano, “Au/SiO2 nanoring plasmon waveguides at optical communication band,” J. Lightw. Technol. 25(9), 2757–2765 (2007).
[Crossref]

K.-Y. Jung and F. L. Teixeira, “Multispecies ADI-FDTD algorithm for nanoscale three-dimensional photonic metallic structures,” IEEE Photon. Technol. Lett. 19(8), 586–588 (2007).
[Crossref]

Kim, H.

S.-G. Ha, J. Cho, J. Choi, H. Kim, and K.-Y. Jung, “FDTD dispersive modeling of human tissue based on quadratic complex rational function,” IEEE Trans. Antennas Propagat. 61(2), 996–999 (2013).
[Crossref]

Kim, J. H.

D. Y. Na, J. H. Kim, K.-Y. Jung, and Y. B. Park, “Mode-matching analysis of a coaxially fed annular slot surrounded with corrugations,” Electromagn. 34(2), 92–110 (2014).
[Crossref]

Laverdant, J.

Lee, R.

K.-Y. Jung, F. L. Teixeira, S. G. Garcia, and R. Lee, “On numerical artifacts of the complex envelope ADI-FDTD method,” IEEE Trans. Antennas Propagat. 57(2), 491–498 (2009).
[Crossref]

Lee, Y. T.

Lim, J. W.

Liu, C.

C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Trans. 113(13), 1728–1740 (2012).
[Crossref]

Liu, G.

S. Gedney, G. Liu, J. Roden, and A. Zhu, “Perfectly matched layer media with CFS for an unconditionally stable ADI-FDTD method,” IEEE Trans. Antennas Propagat.  49(11), 1554–1559 (2001).
[Crossref]

Liu, J.

W.-J. Yoon, K.-Y. Jung, J. Liu, T. Duraisamy, R. Revur, F. L. Teixeira, S. Sengupta, and P. R. Berger, “Plasmon-enhanced optical absorption and photocurrent in organic bulk heterojunction photovoltaic devices using self-assembled layer of silver nanoparticles,” Sol. Energy Mater. Sol. Cells 94(2), 128–132 (2010).
[Crossref]

Liu, Q. H.

Q. H. Liu, “The PSTD algorithm: A time-domain method requiring only two cells per wavelength,” Microwave Opt. Technol. Lett. 15(3), 158–165 (1997).
[Crossref]

Maso, P.

Mundle, R.

Na, D. Y.

D. Y. Na, J. H. Kim, K.-Y. Jung, and Y. B. Park, “Mode-matching analysis of a coaxially fed annular slot surrounded with corrugations,” Electromagn. 34(2), 92–110 (2014).
[Crossref]

Oh, I.-Y.

I.-Y. Oh, Y. Hong, and J.-G. Yook, “Extremely low numerical dispersion FDTD method based on H(2,4) scheme of lossy material,” J. Electromagn. Eng. Sci. 13(3), 158–164 (2013).
[Crossref]

Pandey, R.

Panetta, R. L.

C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Trans. 113(13), 1728–1740 (2012).
[Crossref]

Park, Y. B.

D. Y. Na, J. H. Kim, K.-Y. Jung, and Y. B. Park, “Mode-matching analysis of a coaxially fed annular slot surrounded with corrugations,” Electromagn. 34(2), 92–110 (2014).
[Crossref]

Pradhan, A. K.

Pradhan, S. K.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambrige University, 3, 1995).

Quélin, X.

Reano, R. M.

K.-Y. Jung, F. L. Teixeira, and R. M. Reano, “Surface plasmon coplanar waveguides: Mode characteristics and mode conversion losses,” IEEE Photon. Technol. Lett. 21(10), 630–632 (2009).
[Crossref]

K.-Y. Jung, F. L. Teixeira, and R. M. Reano, “Au/SiO2 nanoring plasmon waveguides at optical communication band,” J. Lightw. Technol. 25(9), 2757–2765 (2007).
[Crossref]

Revur, R.

W.-J. Yoon, K.-Y. Jung, J. Liu, T. Duraisamy, R. Revur, F. L. Teixeira, S. Sengupta, and P. R. Berger, “Plasmon-enhanced optical absorption and photocurrent in organic bulk heterojunction photovoltaic devices using self-assembled layer of silver nanoparticles,” Sol. Energy Mater. Sol. Cells 94(2), 128–132 (2010).
[Crossref]

Roden, J.

S. Gedney, G. Liu, J. Roden, and A. Zhu, “Perfectly matched layer media with CFS for an unconditionally stable ADI-FDTD method,” IEEE Trans. Antennas Propagat.  49(11), 1554–1559 (2001).
[Crossref]

Ruchhoeft, P.

S. Wang, J. Chen, and P. Ruchhoeft, “An ADI-FDTD method for periodic structures,” IEEE Trans. Antennas Propagat. 53(7), 2343–2346 (2005).
[Crossref]

Sakagami, I.

T. Wuren, T. Takai, M. Fujii, and I. Sakagami, “Effective 2-Debye-pole FDTD model of electromagnetic interaction between human body and UWB radiation,” IEEE Microw. Wireless Compat. Lett. 17(7), 483–485 (2007).
[Crossref]

Sang, B.-I.

Santiago, K.

Schneider, J. B.

M. W. Feise, J. B. Schneider, and P. J. Bevelacqua, “Finite-difference and pseudospectral time-domain methods applied to backward-wave metamaterials,” IEEE Trans. Antennas Propagat. 52(11), 2955–2962 (2004).
[Crossref]

Sengupta, S.

W.-J. Yoon, K.-Y. Jung, J. Liu, T. Duraisamy, R. Revur, F. L. Teixeira, S. Sengupta, and P. R. Berger, “Plasmon-enhanced optical absorption and photocurrent in organic bulk heterojunction photovoltaic devices using self-assembled layer of silver nanoparticles,” Sol. Energy Mater. Sol. Cells 94(2), 128–132 (2010).
[Crossref]

Skuza, J. R.

Taflove, A.

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

Takai, T.

T. Wuren, T. Takai, M. Fujii, and I. Sakagami, “Effective 2-Debye-pole FDTD model of electromagnetic interaction between human body and UWB radiation,” IEEE Microw. Wireless Compat. Lett. 17(7), 483–485 (2007).
[Crossref]

Tee, X. T.

Teixeira, F. L.

K.-Y. Jung, S. Ju, and F. L. Teixeira, “Application of the modal CFS-PML-FDTD to the analysis of magnetic photonic crystal waveguides,” IEEE Microw. Wireless Compat. Lett. 21(4), 179–181 (2011).
[Crossref]

W.-J. Yoon, K.-Y. Jung, J. Liu, T. Duraisamy, R. Revur, F. L. Teixeira, S. Sengupta, and P. R. Berger, “Plasmon-enhanced optical absorption and photocurrent in organic bulk heterojunction photovoltaic devices using self-assembled layer of silver nanoparticles,” Sol. Energy Mater. Sol. Cells 94(2), 128–132 (2010).
[Crossref]

K.-Y. Jung, S. Ju, and F. L. Teixeira, “Two-stage perfectly matched layer for the analysis of plasmonic structures,” IEICE Trans. Electronics,  E93-C(8), 1371–1374 (2010)
[Crossref]

K.-Y. Jung, F. L. Teixeira, S. G. Garcia, and R. Lee, “On numerical artifacts of the complex envelope ADI-FDTD method,” IEEE Trans. Antennas Propagat. 57(2), 491–498 (2009).
[Crossref]

K.-Y. Jung, F. L. Teixeira, and R. M. Reano, “Surface plasmon coplanar waveguides: Mode characteristics and mode conversion losses,” IEEE Photon. Technol. Lett. 21(10), 630–632 (2009).
[Crossref]

K.-Y. Jung and F. L. Teixeira, “An iterative unconditionally stable stable LOD-FDTD method,” IEEE Microw”, Wireless Compat. Lett. 18(2), 76–78 (2008).
[Crossref]

K.-Y. Jung, F. L. Teixeira, and R. M. Reano, “Au/SiO2 nanoring plasmon waveguides at optical communication band,” J. Lightw. Technol. 25(9), 2757–2765 (2007).
[Crossref]

K.-Y. Jung and F. L. Teixeira, “Multispecies ADI-FDTD algorithm for nanoscale three-dimensional photonic metallic structures,” IEEE Photon. Technol. Lett. 19(8), 586–588 (2007).
[Crossref]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambrige University, 3, 1995).

Thomas, J. W.

J. W. Thomas, Numerical Partial Differential Equations: Finite Difference Method (Springer, 1995).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambrige University, 3, 1995).

Wang, S.

S. Wang, J. Chen, and P. Ruchhoeft, “An ADI-FDTD method for periodic structures,” IEEE Trans. Antennas Propagat. 53(7), 2343–2346 (2005).
[Crossref]

Wuren, T.

T. Wuren, T. Takai, M. Fujii, and I. Sakagami, “Effective 2-Debye-pole FDTD model of electromagnetic interaction between human body and UWB radiation,” IEEE Microw. Wireless Compat. Lett. 17(7), 483–485 (2007).
[Crossref]

Xiao, B.

Yang, P.

C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Trans. 113(13), 1728–1740 (2012).
[Crossref]

Yoo, T.-H.

Yook, J.-G.

I.-Y. Oh, Y. Hong, and J.-G. Yook, “Extremely low numerical dispersion FDTD method based on H(2,4) scheme of lossy material,” J. Electromagn. Eng. Sci. 13(3), 158–164 (2013).
[Crossref]

Yoon, W.-J.

W.-J. Yoon, K.-Y. Jung, J. Liu, T. Duraisamy, R. Revur, F. L. Teixeira, S. Sengupta, and P. R. Berger, “Plasmon-enhanced optical absorption and photocurrent in organic bulk heterojunction photovoltaic devices using self-assembled layer of silver nanoparticles,” Sol. Energy Mater. Sol. Cells 94(2), 128–132 (2010).
[Crossref]

Zheng, F.

F. Zheng, “A finite-difference time-domain method without the courant stability conditions,” IEEE Microwave Guided Wave Let. 9(11), 441–443 (1999).
[Crossref]

Zhu, A.

S. Gedney, G. Liu, J. Roden, and A. Zhu, “Perfectly matched layer media with CFS for an unconditionally stable ADI-FDTD method,” IEEE Trans. Antennas Propagat.  49(11), 1554–1559 (2001).
[Crossref]

Electromagn. (1)

D. Y. Na, J. H. Kim, K.-Y. Jung, and Y. B. Park, “Mode-matching analysis of a coaxially fed annular slot surrounded with corrugations,” Electromagn. 34(2), 92–110 (2014).
[Crossref]

ETRI J. (1)

H. Chung, J. Cho, S.-G. Ha, S. Ju, and K.-Y. Jung, “Accurate FDTD dispersive modeling for concrete materials,” ETRI J. 35(5), 915–918 (2013).
[Crossref]

IEEE Microw. Wireless Compat. Lett. (2)

K.-Y. Jung, S. Ju, and F. L. Teixeira, “Application of the modal CFS-PML-FDTD to the analysis of magnetic photonic crystal waveguides,” IEEE Microw. Wireless Compat. Lett. 21(4), 179–181 (2011).
[Crossref]

T. Wuren, T. Takai, M. Fujii, and I. Sakagami, “Effective 2-Debye-pole FDTD model of electromagnetic interaction between human body and UWB radiation,” IEEE Microw. Wireless Compat. Lett. 17(7), 483–485 (2007).
[Crossref]

IEEE Microwave Guided Wave Let. (1)

F. Zheng, “A finite-difference time-domain method without the courant stability conditions,” IEEE Microwave Guided Wave Let. 9(11), 441–443 (1999).
[Crossref]

IEEE Photon. Technol. Lett. (2)

K.-Y. Jung and F. L. Teixeira, “Multispecies ADI-FDTD algorithm for nanoscale three-dimensional photonic metallic structures,” IEEE Photon. Technol. Lett. 19(8), 586–588 (2007).
[Crossref]

K.-Y. Jung, F. L. Teixeira, and R. M. Reano, “Surface plasmon coplanar waveguides: Mode characteristics and mode conversion losses,” IEEE Photon. Technol. Lett. 21(10), 630–632 (2009).
[Crossref]

IEEE Trans. Antennas Propagat (1)

S. Gedney, G. Liu, J. Roden, and A. Zhu, “Perfectly matched layer media with CFS for an unconditionally stable ADI-FDTD method,” IEEE Trans. Antennas Propagat.  49(11), 1554–1559 (2001).
[Crossref]

IEEE Trans. Antennas Propagat. (4)

S. Wang, J. Chen, and P. Ruchhoeft, “An ADI-FDTD method for periodic structures,” IEEE Trans. Antennas Propagat. 53(7), 2343–2346 (2005).
[Crossref]

M. W. Feise, J. B. Schneider, and P. J. Bevelacqua, “Finite-difference and pseudospectral time-domain methods applied to backward-wave metamaterials,” IEEE Trans. Antennas Propagat. 52(11), 2955–2962 (2004).
[Crossref]

S.-G. Ha, J. Cho, J. Choi, H. Kim, and K.-Y. Jung, “FDTD dispersive modeling of human tissue based on quadratic complex rational function,” IEEE Trans. Antennas Propagat. 61(2), 996–999 (2013).
[Crossref]

K.-Y. Jung, F. L. Teixeira, S. G. Garcia, and R. Lee, “On numerical artifacts of the complex envelope ADI-FDTD method,” IEEE Trans. Antennas Propagat. 57(2), 491–498 (2009).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

S. Aksoy, “An alternative algorithm for both narrowband and wideband Lorentzian dispersive materials modeling in the finite-difference time-domain method,” IEEE Trans. Microw. Theory Tech. 55(4), 703–708 (2007).
[Crossref]

IEICE Trans. Electronics (1)

K.-Y. Jung, S. Ju, and F. L. Teixeira, “Two-stage perfectly matched layer for the analysis of plasmonic structures,” IEICE Trans. Electronics,  E93-C(8), 1371–1374 (2010)
[Crossref]

J. Electromagn. Eng. Sci. (1)

I.-Y. Oh, Y. Hong, and J.-G. Yook, “Extremely low numerical dispersion FDTD method based on H(2,4) scheme of lossy material,” J. Electromagn. Eng. Sci. 13(3), 158–164 (2013).
[Crossref]

J. Lightw. Technol. (1)

K.-Y. Jung, F. L. Teixeira, and R. M. Reano, “Au/SiO2 nanoring plasmon waveguides at optical communication band,” J. Lightw. Technol. 25(9), 2757–2765 (2007).
[Crossref]

J. Quant. Spectrosc. Radiat. Trans. (1)

C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Trans. 113(13), 1728–1740 (2012).
[Crossref]

Microwave Opt. Technol. Lett. (1)

Q. H. Liu, “The PSTD algorithm: A time-domain method requiring only two cells per wavelength,” Microwave Opt. Technol. Lett. 15(3), 158–165 (1997).
[Crossref]

Opt. Express (4)

Sol. Energy Mater. Sol. Cells (1)

W.-J. Yoon, K.-Y. Jung, J. Liu, T. Duraisamy, R. Revur, F. L. Teixeira, S. Sengupta, and P. R. Berger, “Plasmon-enhanced optical absorption and photocurrent in organic bulk heterojunction photovoltaic devices using self-assembled layer of silver nanoparticles,” Sol. Energy Mater. Sol. Cells 94(2), 128–132 (2010).
[Crossref]

Wireless Compat. Lett. (1)

K.-Y. Jung and F. L. Teixeira, “An iterative unconditionally stable stable LOD-FDTD method,” IEEE Microw”, Wireless Compat. Lett. 18(2), 76–78 (2008).
[Crossref]

Other (3)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambrige University, 3, 1995).

J. W. Thomas, Numerical Partial Differential Equations: Finite Difference Method (Springer, 1995).

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

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Figures (6)

Figure 1:
Figure 1: Field location in the computational cell. (a) updating D x n + 1 / 2 at j = 0. (b) updating D x n + 1 / 2 at j = N.
Figure 2:
Figure 2: (a) Geometry of the numerical example. (b) Convergence test of space-step sizes.
Figure 3:
Figure 3: (a) E x field for Δs=0.5 nm. (b) Relative error of E x field for Δs=0.5 nm.
Figure 4:
Figure 4: (a) E x field for Δs=0.25 nm. (b) Relative error of E x field for Δs=0.25 nm.
Figure 5:
Figure 5: Snapshot of E x field for Δs=0.25 nm. (a) QCRF-FDTD with C F L N = 1. (b) QCRF-ADI-FDTD with C F L N = 16.
Figure 6:
Figure 6: Normalized CPU time of QCRF-ADI-FDTD.

Equations (24)

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ε r ( ω ) = A 0 + A 1 ( j ω ) + A 2 ( j ω ) 2 1 + B 1 ( j ω ) + B 2 ( j ω ) 2
D ( ω ) = ε 0 ( A 0 + A 1 ( j ω ) + A 2 ( j ω ) 2 1 + B 1 ( j ω ) + B 2 ( j ω ) 2 ) E ( ω ) .
D n + 1 + 2 D n + D n 1 4 + B 1 D n + 1 D n 1 2 Δ t + B 2 D n + 1 2 D n + D n 1 Δ t 2 = ε 0 A 0 E n + 1 + 2 E n + E n 1 4 + ε 0 A 1 E n + 1 E n 1 2 Δ t + ε 0 A 2 E n + 1 2 E n + E n 1 Δ t 2 .
E n + 1 = C a E n + C b E n 1 + C c D n + 1 + C d D n + C e D n 1
E n + 1 / 2 = C c D n + 1 / 2 + φ n
φ n + 1 / 2 = C a E n + 1 / 2 + C b E n + C d D n + 1 / 2 + C e D n
E n + 1 = C c D n + 1 + φ n + 1 / 2
φ n + 1 = C a E n + 1 + C b E n + 1 / 2 + C d D n + 1 + C e D n + 1 / 2 .
D x | i + 1 / 2 , j , k n + 1 / 2 = D x | i + 1 / 2 , j , k n + Δ t 2 Δ y ( H z | i + 1 / 2 , j + 1 / 2 , k n + 1 / 2 H z | i + 1 / 2 , j 1 / 2 , k n + 1 / 2 ) Δ t 2 Δ z ( H y | i + 1 / 2 , j , k + 1 / 2 n H y | i + 1 / 2 , j , k 1 / 2 n )
H z | i + 1 / 2 , j + 1 / 2 , k n + 1 / 2 = H z | i + 1 / 2 , j + 1 / 2 , k n Δ t 2 μ 0 Δ x ( E y | i + 1 , j + 1 / 2 , k n E y | i , j + 1 / 2 , k n ) + Δ t 2 μ 0 Δ y ( E x | i + 1 / 2 , j + 1 , k n + 1 / 2 E x | i + 1 / 2 , j , k n + 1 / 2 )
C 0 D 0 C c ( Δ y ) 2 D x | i + 1 / 2 , j 1 , k n + 1 / 2 + [ 1 + 2 C 0 D 0 C c ( Δ y ) 2 ] D x | i + 1 / 2 , j , k n + 1 / 2 C 0 D 0 C c ( Δ y ) 2 D x | i + 1 / 2 , j + 1 , k n + 1 / 2 = D x | i + 1 / 2 , j , k n + C 0 Δ y ( H z | i + 1 / 2 , j + 1 / 2 , k n H z | i + 1 / 2 , j 1 / 2 , k n ) C 0 Δ z ( H y | i + 1 / 2 , j , k + 1 / 2 n H y | i + 1 / 2 , j , k 1 / 2 n ) C 0 D 0 Δ y Δ x ( E y | i + 1 , j + 1 / 2 , k n E y | i , j + 1 / 2 , k n E y | i + 1 , j 1 / 2 , k n + E y | i , j 1 / 2 , k n ) + C 0 D 0 ( Δ y ) 2 ( φ x | i + 1 / 2 , j 1 , k n 2 φ x | i + 1 / 2 , j , k n + φ x | i + 1 / 2 , j + 1 , k n )
[ M ] = [ b 0 c 0 0 0 a N 1 a 1 b 1 c 1 0 0 0 0 0 0 a N 2 b N 2 c N 2 c 0 0 0 a N 1 b N 1 ] , x = [ D x | i + 1 / 2,0 , k n + 1 / 2 D x | i + 1 / 2 , j , k n + 1 / 2 D x | i + 1 / 2 , N 1 , k n + 1 / 2 ] , r = [ r | 0 n r | j n r | N 1 n ] .
H z | i + 1 / 2 , 1 / 2 , k n H z | i + 1 / 2 , N 1 / 2 , k n E y | i + 1 , 1 / 2 , k n E y | i + 1 , N 1 / 2 , k n E y | i , 1 / 2 , k n E y | i , N 1 / 2 , k n φ x | i + 1 / 2 , 1 , k n φ x | i + 1 / 2 , N 1 , k n .
D x | i + 1 / 2 , N , k n + 1 / 2 D x | i + 1 / 2,0 , k n + 1 / 2 .
H x | i , 1 / 2 , k + 1 / 2 n H x | i , N 1 / 2 , k + 1 / 2 n .
D z | i , N , k + 1 / 2 n + 1 / 2 D z | i ,0 , k + 1 / 2 n + 1 / 2 .
[ M ] = [ N ] + w z T ,
[ N ] = [ 2 b 0 c 0 0 0 0 a 1 b 1 c 1 0 0 0 0 0 0 a N 2 b N 2 c N 2 0 0 0 a N 1 b N 1 + ( c 1 a N 1 / b 0 ) ] ,
w = [ b 0 , 0 , , 0 , c 0 , ] T , z = [ 1 , 0 , , 0 , a N 1 / b 0 ] T .
[ N ] x 1 = r ,
[ N ] x 2 = w .
x = x 1 + B x 2 ,
B = z T x 1 1 + z T x 2 .
δ 2 = y = 0 40 n m x = 0 40 n m ( E x , A D I E x , F D T D ) 2 y = 0 40 n m x = 0 40 n m ( E x , F D T D ) 2 .

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