Abstract

The discontinuous Galerkin time domain (DGTD) method and its recent flavor, the continuous-discontinuous Galerkin time domain (CDGTD) method, have been extensively applied to simulations in the radio frequency (RF) and microwave (MW) regimes due to their inherent ability to efficiently model multiscale problems. We propose to extend the CDGTD method to nanophotonics while exploiting its advantages which have already been established in the RF and MW regimes, such as domain decomposition, non-conformal meshing, high-order elements, and hp-refinement. However, at optical frequencies many materials are highly dispersive, so the modeling of nanophotonic devices requires accurate handling of different dielectric functions, including those of plasmonic elements, dielectrics, and tunable materials. In this paper, we propose a CDGTD method that incorporates a generalized dispersive material (GDM) model which is an efficient way to implement a wide range of optical dispersion models with a universal analytic function. Physics-based dispersion models, such as the Drude, Debye, Lorentz, and critical points as well as more complicated behavior founded on ab-initio principles can all be obtained as special cases of the universal GDM approach. The accuracy and convergence of this GDM-incorporated CDGTD are verified by numerical examples. The CDGTD method, equipped with the GDM model, paves the way to the efficient design and optimization of large scale photonic devices with a diverse range of optical dispersive materials.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

2017 (3)

Q. Sun, Q. Zhan, Q. Ren, and Q. H. Liu, “Wave equation-based implicit subdomain DGTD method for modeling of electrically small problems,” IEEE Trans. Microw. Theory Tech. 65(4), 1111–1119 (2017).
[Crossref]

Q. Ren, Q. Zhan, and Q. H. Liu, “An improved subdomain level non-conformal discontinuous Galerkin time domain (DGTD) method for materials with full-tensor constitutive parameters,” IEEE Photonics J. 9(2), 2600113 (2017).
[Crossref]

Q. Ren, Y. Bian, L. Kang, P. L. Werner, and D. H. Werner, “Leap-frog continuous-discontinuous Galerkin time domain method for nanoarchitectures with the Drude model,” J. Lightwave Technol. 35(22), 4888–4896 (2017).
[Crossref]

2016 (1)

Q. Ren, Q. Sun, L. Tobón, Q. Zhan, and Q. H. Liu, “EB scheme based hybrid SE-FE DGTD method for multiscale EM simulations,” IEEE. Trans. Antennas Propagat. 64(9), 4088–4091 (2016).
[Crossref]

2015 (5)

Q. Ren, L. E. Tobón, Q. Sun, and Q. H. Liu, “A new 3D non-spurious discontinuous Galerkin spectral element time domain (DG-SETD) method for Maxwell’s equations,” IEEE. Trans. Antennas Propagat. 63(6), 2585–2594 (2015).
[Crossref]

L. E. Tobón, Q. Ren, and Q. H. Liu, “A new efficient 3D discontinuous Galerkin time domain (DGTD) method for large and multiscale electromagnetic simulations,” J. Comput. Phys. 283, 374–387 (2015).
[Crossref]

N. K. Emani, D. Wang, T.-F. Chung, L. J. Prokopeva, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Plasmon resonance in multilayer graphene nanoribbons,” Laser Photonics Rev. 9(6), 650–655 (2015).
[Crossref]

J. F. M. Werra, C. Wolff, C. Matyssek, and K. Busch, “Current sheets in the discontinuous Galerkin time-domain method: an application to graphene,” Proc. SPIE 9502, 95020E (2015).
[Crossref]

L. D. Angulo, J. Alvarez, F. L. Teixeira, M. F. Pantoja, and S. G. Garcia, “A nodal continuous-discontinuous Galerkin time-domain method for Maxwell’s equations,” IEEE Trans. Microw. Theory Tech. 63(10), 3081–3093 (2015).
[Crossref]

2013 (2)

K. P. Prokopidis and D. C. Zografopoulos, “A unified FDTD/PML scheme based on critical points for accurate studies of plasmonic structures,” J. Lightwave Technol. 31(15), 2467–2476 (2013).
[Crossref]

Q. Ren, L. E. Tobón, and Q. H. Liu, “A new 2D non-spurious discontinuous Galerkin finite element time domain (DG-FETD) method for Maxwell’s equations,” Prog. Electromagnetics Res. 143, 385–404 (2013).
[Crossref]

2012 (3)

S. D. Gedney, J. C. Young, T. C. Kramer, and J. A. Roden, “A discontinuous Galerkin finite element time-domain method modeling of dispersive media,” IEEE. Trans. Antennas Propagat. 60(4), 1969–1977 (2012).
[Crossref]

F. G. Hu and C. F. Wang, “Modeling of waveguide structures using DG-FETD method with higher-order tetrahedral elements,” IEEE Trans. Microw. Theory Tech. 60(7), 2046–2054 (2012).
[Crossref]

J. Schafer, S. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

2011 (3)

J. Chen, L. E. Tobón, M. Chai, J. A. Mix, and Q. H. Liu, “Efficient implicit-explicit time stepping scheme with domain decomposition for multiscale modeling of layered structures,” IEEE Trans. Compon. Packaging Manuf. Technol. 1(9), 1438–1446 (2011).
[Crossref]

L. J. Prokopeva, J. D. Borneman, and A. V. Kildishev, “Optical dispersion models for time-domain modeling of metal-dielectric nanostructures,” IEEE Trans. Magn. 47(5), 1150–1153 (2011).
[Crossref]

M. D. Thoreson, J. Fang, A. V. Kildishev, L. J. Prokopeva, P. Nyga, U. K. Chettiar, V. M. Shalaev, and V. P. Drachev, “Fabrication and realistic modeling of three-dimensional metal-dielectric composites,” J. Nanophotonics 5(1), 051513 (2011).
[Crossref]

2010 (2)

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

J. Chen, Q. H. Liu, M. Chai, and J. A. Mix, “A non-spurious 3-D vector discontinuous Galerkin finite-element time-domain method,” IEEE Microw. Wirel. Compon. Lett. 20(1), 1–3 (2010).
[Crossref]

2009 (1)

2008 (1)

N. Theethayi, Y. Baba, F. Rachidi, and R. Thottappillil, “On the choice between transmission line equations and full-wave Maxwell’s equations for transient analysis of buried wires,” IEEE Trans. Electromagn. Compat. 50(2), 347–357 (2008).
[Crossref]

2007 (3)

F. Hao and P. Nordlander, “Efficient dielectric function for FDTD simulation of the optical properties of silver and gold nanoparticles,” Chem. Phys. Lett. 446(1-3), 115–118 (2007).
[Crossref]

A. Vial and T. Laroche, “Description of dispersion properties of metals by means of the critical points model and application to the study of resonant structures using the FDTD method,” J. Phys. D Appl. Phys. 40(22), 7152–7158 (2007).
[Crossref]

P. G. Etchegoin, E. C. L. Ru, and M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127(18), 189901 (2007).
[Crossref]

2006 (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]

2005 (1)

H. Chen and W. Z. Shen, “Perspectives in the characteristics and applications of Tauc-Lorentz dielectric function model,” Eur. Phys. J. B Cond. Matter Complex Syst. 43(4), 503–507 (2005).
[Crossref]

2003 (2)

A. Bruner, D. Eger, M. B. Oron, P. Blau, M. Katz, and S. Ruschin, “Temperature-dependent Sellmeier equation for the refractive index of stoichiometric lithium tantalate,” Opt. Lett. 28(3), 194–196 (2003).
[Crossref] [PubMed]

M. M. Ilic and B. N. Notaros, “Higher order hierarchical curved hexahedral vector finite elements for electromagnetic modeling,” IEEE Trans. Microw. Theory Tech. 51(3), 1026–1033 (2003).
[Crossref]

1997 (1)

Q. H. Liu, “An FDTD algorithm with perfectly matched layers for conductive media,” Microw. Opt. Technol. Lett. 14(2), 134–137 (1997).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Accanto, N.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Aizpurua, J.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Alvarez, J.

L. D. Angulo, J. Alvarez, F. L. Teixeira, M. F. Pantoja, and S. G. Garcia, “A nodal continuous-discontinuous Galerkin time-domain method for Maxwell’s equations,” IEEE Trans. Microw. Theory Tech. 63(10), 3081–3093 (2015).
[Crossref]

Angulo, L. D.

L. D. Angulo, J. Alvarez, F. L. Teixeira, M. F. Pantoja, and S. G. Garcia, “A nodal continuous-discontinuous Galerkin time-domain method for Maxwell’s equations,” IEEE Trans. Microw. Theory Tech. 63(10), 3081–3093 (2015).
[Crossref]

Arnold, N.

S. I. Azzam, J. Fang, J. Liu, Z. Wang, N. Arnold, T. Klar, L. J. Prokopeva, X. Meng, V. M. Shalaev, and A. V. Kildishev, “Time-resolved dynamics of plasmonic systems with gain,” (unpublished).

Azzam, S. I.

S. I. Azzam, J. Fang, J. Liu, Z. Wang, N. Arnold, T. Klar, L. J. Prokopeva, X. Meng, V. M. Shalaev, and A. V. Kildishev, “Time-resolved dynamics of plasmonic systems with gain,” (unpublished).

Baba, Y.

N. Theethayi, Y. Baba, F. Rachidi, and R. Thottappillil, “On the choice between transmission line equations and full-wave Maxwell’s equations for transient analysis of buried wires,” IEEE Trans. Electromagn. Compat. 50(2), 347–357 (2008).
[Crossref]

Barton, D. R.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Bian, Y.

Blau, P.

Boltasseva, A.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

N. K. Emani, D. Wang, T.-F. Chung, L. J. Prokopeva, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Plasmon resonance in multilayer graphene nanoribbons,” Laser Photonics Rev. 9(6), 650–655 (2015).
[Crossref]

Boriskina, S. V.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Borneman, J. D.

L. J. Prokopeva, J. D. Borneman, and A. V. Kildishev, “Optical dispersion models for time-domain modeling of metal-dielectric nanostructures,” IEEE Trans. Magn. 47(5), 1150–1153 (2011).
[Crossref]

Bozhevolnyi, S. I.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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Busch, K.

J. F. M. Werra, C. Wolff, C. Matyssek, and K. Busch, “Current sheets in the discontinuous Galerkin time-domain method: an application to graphene,” Proc. SPIE 9502, 95020E (2015).
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Chai, M.

J. Chen, L. E. Tobón, M. Chai, J. A. Mix, and Q. H. Liu, “Efficient implicit-explicit time stepping scheme with domain decomposition for multiscale modeling of layered structures,” IEEE Trans. Compon. Packaging Manuf. Technol. 1(9), 1438–1446 (2011).
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J. Chen, Q. H. Liu, M. Chai, and J. A. Mix, “A non-spurious 3-D vector discontinuous Galerkin finite-element time-domain method,” IEEE Microw. Wirel. Compon. Lett. 20(1), 1–3 (2010).
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Chang, Y. H.

Chen, H.

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Chen, J.

J. Chen, L. E. Tobón, M. Chai, J. A. Mix, and Q. H. Liu, “Efficient implicit-explicit time stepping scheme with domain decomposition for multiscale modeling of layered structures,” IEEE Trans. Compon. Packaging Manuf. Technol. 1(9), 1438–1446 (2011).
[Crossref]

J. Chen, Q. H. Liu, M. Chai, and J. A. Mix, “A non-spurious 3-D vector discontinuous Galerkin finite-element time-domain method,” IEEE Microw. Wirel. Compon. Lett. 20(1), 1–3 (2010).
[Crossref]

Chen, Y. P.

N. K. Emani, D. Wang, T.-F. Chung, L. J. Prokopeva, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Plasmon resonance in multilayer graphene nanoribbons,” Laser Photonics Rev. 9(6), 650–655 (2015).
[Crossref]

Chettiar, U. K.

M. D. Thoreson, J. Fang, A. V. Kildishev, L. J. Prokopeva, P. Nyga, U. K. Chettiar, V. M. Shalaev, and V. P. Drachev, “Fabrication and realistic modeling of three-dimensional metal-dielectric composites,” J. Nanophotonics 5(1), 051513 (2011).
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Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
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Chung, T.-F.

N. K. Emani, D. Wang, T.-F. Chung, L. J. Prokopeva, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Plasmon resonance in multilayer graphene nanoribbons,” Laser Photonics Rev. 9(6), 650–655 (2015).
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de Roque, P. M.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Dionne, J. A.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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Drachev, V. P.

M. D. Thoreson, J. Fang, A. V. Kildishev, L. J. Prokopeva, P. Nyga, U. K. Chettiar, V. M. Shalaev, and V. P. Drachev, “Fabrication and realistic modeling of three-dimensional metal-dielectric composites,” J. Nanophotonics 5(1), 051513 (2011).
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Dutta, A.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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Eger, D.

Emani, N. K.

N. K. Emani, D. Wang, T.-F. Chung, L. J. Prokopeva, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Plasmon resonance in multilayer graphene nanoribbons,” Laser Photonics Rev. 9(6), 650–655 (2015).
[Crossref]

Esteban, R.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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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).
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Fang, J.

M. D. Thoreson, J. Fang, A. V. Kildishev, L. J. Prokopeva, P. Nyga, U. K. Chettiar, V. M. Shalaev, and V. P. Drachev, “Fabrication and realistic modeling of three-dimensional metal-dielectric composites,” J. Nanophotonics 5(1), 051513 (2011).
[Crossref]

S. I. Azzam, J. Fang, J. Liu, Z. Wang, N. Arnold, T. Klar, L. J. Prokopeva, X. Meng, V. M. Shalaev, and A. V. Kildishev, “Time-resolved dynamics of plasmonic systems with gain,” (unpublished).

Garcia, S. G.

L. D. Angulo, J. Alvarez, F. L. Teixeira, M. F. Pantoja, and S. G. Garcia, “A nodal continuous-discontinuous Galerkin time-domain method for Maxwell’s equations,” IEEE Trans. Microw. Theory Tech. 63(10), 3081–3093 (2015).
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Gedney, S. D.

S. D. Gedney, J. C. Young, T. C. Kramer, and J. A. Roden, “A discontinuous Galerkin finite element time-domain method modeling of dispersive media,” IEEE. Trans. Antennas Propagat. 60(4), 1969–1977 (2012).
[Crossref]

Gholipour, B.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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Groß, P.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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Guler, U.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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Hancu, I. M.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
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Kang, L.

Katz, M.

Kienle, A.

J. Schafer, S. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

Kildishev, A. V.

N. K. Emani, D. Wang, T.-F. Chung, L. J. Prokopeva, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Plasmon resonance in multilayer graphene nanoribbons,” Laser Photonics Rev. 9(6), 650–655 (2015).
[Crossref]

M. D. Thoreson, J. Fang, A. V. Kildishev, L. J. Prokopeva, P. Nyga, U. K. Chettiar, V. M. Shalaev, and V. P. Drachev, “Fabrication and realistic modeling of three-dimensional metal-dielectric composites,” J. Nanophotonics 5(1), 051513 (2011).
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L. J. Prokopeva, J. D. Borneman, and A. V. Kildishev, “Optical dispersion models for time-domain modeling of metal-dielectric nanostructures,” IEEE Trans. Magn. 47(5), 1150–1153 (2011).
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S. I. Azzam, J. Fang, J. Liu, Z. Wang, N. Arnold, T. Klar, L. J. Prokopeva, X. Meng, V. M. Shalaev, and A. V. Kildishev, “Time-resolved dynamics of plasmonic systems with gain,” (unpublished).

Kinsey, N.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Klar, T.

S. I. Azzam, J. Fang, J. Liu, Z. Wang, N. Arnold, T. Klar, L. J. Prokopeva, X. Meng, V. M. Shalaev, and A. V. Kildishev, “Time-resolved dynamics of plasmonic systems with gain,” (unpublished).

Kling, M. F.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Kneipp, K.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Kramer, T. C.

S. D. Gedney, J. C. Young, T. C. Kramer, and J. A. Roden, “A discontinuous Galerkin finite element time-domain method modeling of dispersive media,” IEEE. Trans. Antennas Propagat. 60(4), 1969–1977 (2012).
[Crossref]

Krishnamoorthy, H. N. S.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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Laroche, T.

A. Vial and T. Laroche, “Description of dispersion properties of metals by means of the critical points model and application to the study of resonant structures using the FDTD method,” J. Phys. D Appl. Phys. 40(22), 7152–7158 (2007).
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Lawrence, M.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

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, S.

J. Schafer, S. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

Lienau, C.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Liu, J.

S. I. Azzam, J. Fang, J. Liu, Z. Wang, N. Arnold, T. Klar, L. J. Prokopeva, X. Meng, V. M. Shalaev, and A. V. Kildishev, “Time-resolved dynamics of plasmonic systems with gain,” (unpublished).

Liu, Q. H.

Q. Ren, Q. Zhan, and Q. H. Liu, “An improved subdomain level non-conformal discontinuous Galerkin time domain (DGTD) method for materials with full-tensor constitutive parameters,” IEEE Photonics J. 9(2), 2600113 (2017).
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Q. Sun, Q. Zhan, Q. Ren, and Q. H. Liu, “Wave equation-based implicit subdomain DGTD method for modeling of electrically small problems,” IEEE Trans. Microw. Theory Tech. 65(4), 1111–1119 (2017).
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Q. Ren, Q. Sun, L. Tobón, Q. Zhan, and Q. H. Liu, “EB scheme based hybrid SE-FE DGTD method for multiscale EM simulations,” IEEE. Trans. Antennas Propagat. 64(9), 4088–4091 (2016).
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Q. Ren, L. E. Tobón, Q. Sun, and Q. H. Liu, “A new 3D non-spurious discontinuous Galerkin spectral element time domain (DG-SETD) method for Maxwell’s equations,” IEEE. Trans. Antennas Propagat. 63(6), 2585–2594 (2015).
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L. E. Tobón, Q. Ren, and Q. H. Liu, “A new efficient 3D discontinuous Galerkin time domain (DGTD) method for large and multiscale electromagnetic simulations,” J. Comput. Phys. 283, 374–387 (2015).
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Q. Ren, L. E. Tobón, and Q. H. Liu, “A new 2D non-spurious discontinuous Galerkin finite element time domain (DG-FETD) method for Maxwell’s equations,” Prog. Electromagnetics Res. 143, 385–404 (2013).
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J. Chen, L. E. Tobón, M. Chai, J. A. Mix, and Q. H. Liu, “Efficient implicit-explicit time stepping scheme with domain decomposition for multiscale modeling of layered structures,” IEEE Trans. Compon. Packaging Manuf. Technol. 1(9), 1438–1446 (2011).
[Crossref]

J. Chen, Q. H. Liu, M. Chai, and J. A. Mix, “A non-spurious 3-D vector discontinuous Galerkin finite-element time-domain method,” IEEE Microw. Wirel. Compon. Lett. 20(1), 1–3 (2010).
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Q. H. Liu, “An FDTD algorithm with perfectly matched layers for conductive media,” Microw. Opt. Technol. Lett. 14(2), 134–137 (1997).
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Lu, J. Y.

MacDonald, K. F.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Matyssek, C.

J. F. M. Werra, C. Wolff, C. Matyssek, and K. Busch, “Current sheets in the discontinuous Galerkin time-domain method: an application to graphene,” Proc. SPIE 9502, 95020E (2015).
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Meng, X.

S. I. Azzam, J. Fang, J. Liu, Z. Wang, N. Arnold, T. Klar, L. J. Prokopeva, X. Meng, V. M. Shalaev, and A. V. Kildishev, “Time-resolved dynamics of plasmonic systems with gain,” (unpublished).

Meyer, M.

P. G. Etchegoin, E. C. L. Ru, and M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127(18), 189901 (2007).
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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).
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J. Chen, L. E. Tobón, M. Chai, J. A. Mix, and Q. H. Liu, “Efficient implicit-explicit time stepping scheme with domain decomposition for multiscale modeling of layered structures,” IEEE Trans. Compon. Packaging Manuf. Technol. 1(9), 1438–1446 (2011).
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J. Chen, Q. H. Liu, M. Chai, and J. A. Mix, “A non-spurious 3-D vector discontinuous Galerkin finite-element time-domain method,” IEEE Microw. Wirel. Compon. Lett. 20(1), 1–3 (2010).
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M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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M. D. Thoreson, J. Fang, A. V. Kildishev, L. J. Prokopeva, P. Nyga, U. K. Chettiar, V. M. Shalaev, and V. P. Drachev, “Fabrication and realistic modeling of three-dimensional metal-dielectric composites,” J. Nanophotonics 5(1), 051513 (2011).
[Crossref]

Odom, T. W.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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Oron, M. B.

Pantoja, M. F.

L. D. Angulo, J. Alvarez, F. L. Teixeira, M. F. Pantoja, and S. G. Garcia, “A nodal continuous-discontinuous Galerkin time-domain method for Maxwell’s equations,” IEEE Trans. Microw. Theory Tech. 63(10), 3081–3093 (2015).
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Piatkowski, L.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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Prokopeva, L. J.

N. K. Emani, D. Wang, T.-F. Chung, L. J. Prokopeva, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Plasmon resonance in multilayer graphene nanoribbons,” Laser Photonics Rev. 9(6), 650–655 (2015).
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L. J. Prokopeva, J. D. Borneman, and A. V. Kildishev, “Optical dispersion models for time-domain modeling of metal-dielectric nanostructures,” IEEE Trans. Magn. 47(5), 1150–1153 (2011).
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M. D. Thoreson, J. Fang, A. V. Kildishev, L. J. Prokopeva, P. Nyga, U. K. Chettiar, V. M. Shalaev, and V. P. Drachev, “Fabrication and realistic modeling of three-dimensional metal-dielectric composites,” J. Nanophotonics 5(1), 051513 (2011).
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S. I. Azzam, J. Fang, J. Liu, Z. Wang, N. Arnold, T. Klar, L. J. Prokopeva, X. Meng, V. M. Shalaev, and A. V. Kildishev, “Time-resolved dynamics of plasmonic systems with gain,” (unpublished).

Prokopidis, K. P.

Rachidi, F.

N. Theethayi, Y. Baba, F. Rachidi, and R. Thottappillil, “On the choice between transmission line equations and full-wave Maxwell’s equations for transient analysis of buried wires,” IEEE Trans. Electromagn. Compat. 50(2), 347–357 (2008).
[Crossref]

Reddy, H.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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Q. Ren, Y. Bian, L. Kang, P. L. Werner, and D. H. Werner, “Leap-frog continuous-discontinuous Galerkin time domain method for nanoarchitectures with the Drude model,” J. Lightwave Technol. 35(22), 4888–4896 (2017).
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Q. Ren, Q. Zhan, and Q. H. Liu, “An improved subdomain level non-conformal discontinuous Galerkin time domain (DGTD) method for materials with full-tensor constitutive parameters,” IEEE Photonics J. 9(2), 2600113 (2017).
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Q. Sun, Q. Zhan, Q. Ren, and Q. H. Liu, “Wave equation-based implicit subdomain DGTD method for modeling of electrically small problems,” IEEE Trans. Microw. Theory Tech. 65(4), 1111–1119 (2017).
[Crossref]

Q. Ren, Q. Sun, L. Tobón, Q. Zhan, and Q. H. Liu, “EB scheme based hybrid SE-FE DGTD method for multiscale EM simulations,” IEEE. Trans. Antennas Propagat. 64(9), 4088–4091 (2016).
[Crossref]

Q. Ren, L. E. Tobón, Q. Sun, and Q. H. Liu, “A new 3D non-spurious discontinuous Galerkin spectral element time domain (DG-SETD) method for Maxwell’s equations,” IEEE. Trans. Antennas Propagat. 63(6), 2585–2594 (2015).
[Crossref]

L. E. Tobón, Q. Ren, and Q. H. Liu, “A new efficient 3D discontinuous Galerkin time domain (DGTD) method for large and multiscale electromagnetic simulations,” J. Comput. Phys. 283, 374–387 (2015).
[Crossref]

Q. Ren, L. E. Tobón, and Q. H. Liu, “A new 2D non-spurious discontinuous Galerkin finite element time domain (DG-FETD) method for Maxwell’s equations,” Prog. Electromagnetics Res. 143, 385–404 (2013).
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S. D. Gedney, J. C. Young, T. C. Kramer, and J. A. Roden, “A discontinuous Galerkin finite element time-domain method modeling of dispersive media,” IEEE. Trans. Antennas Propagat. 60(4), 1969–1977 (2012).
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Ru, E. C. L.

P. G. Etchegoin, E. C. L. Ru, and M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127(18), 189901 (2007).
[Crossref]

Ruschin, S.

Saha, S.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

N. K. Emani, D. Wang, T.-F. Chung, L. J. Prokopeva, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Plasmon resonance in multilayer graphene nanoribbons,” Laser Photonics Rev. 9(6), 650–655 (2015).
[Crossref]

M. D. Thoreson, J. Fang, A. V. Kildishev, L. J. Prokopeva, P. Nyga, U. K. Chettiar, V. M. Shalaev, and V. P. Drachev, “Fabrication and realistic modeling of three-dimensional metal-dielectric composites,” J. Nanophotonics 5(1), 051513 (2011).
[Crossref]

S. I. Azzam, J. Fang, J. Liu, Z. Wang, N. Arnold, T. Klar, L. J. Prokopeva, X. Meng, V. M. Shalaev, and A. V. Kildishev, “Time-resolved dynamics of plasmonic systems with gain,” (unpublished).

Shen, W. Z.

H. Chen and W. Z. Shen, “Perspectives in the characteristics and applications of Tauc-Lorentz dielectric function model,” Eur. Phys. J. B Cond. Matter Complex Syst. 43(4), 503–507 (2005).
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M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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Soci, C.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Solomon, M. L.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Stockman, M. I.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Sun, Q.

Q. Sun, Q. Zhan, Q. Ren, and Q. H. Liu, “Wave equation-based implicit subdomain DGTD method for modeling of electrically small problems,” IEEE Trans. Microw. Theory Tech. 65(4), 1111–1119 (2017).
[Crossref]

Q. Ren, Q. Sun, L. Tobón, Q. Zhan, and Q. H. Liu, “EB scheme based hybrid SE-FE DGTD method for multiscale EM simulations,” IEEE. Trans. Antennas Propagat. 64(9), 4088–4091 (2016).
[Crossref]

Q. Ren, L. E. Tobón, Q. Sun, and Q. H. Liu, “A new 3D non-spurious discontinuous Galerkin spectral element time domain (DG-SETD) method for Maxwell’s equations,” IEEE. Trans. Antennas Propagat. 63(6), 2585–2594 (2015).
[Crossref]

Teixeira, F. L.

L. D. Angulo, J. Alvarez, F. L. Teixeira, M. F. Pantoja, and S. G. Garcia, “A nodal continuous-discontinuous Galerkin time-domain method for Maxwell’s equations,” IEEE Trans. Microw. Theory Tech. 63(10), 3081–3093 (2015).
[Crossref]

Theethayi, N.

N. Theethayi, Y. Baba, F. Rachidi, and R. Thottappillil, “On the choice between transmission line equations and full-wave Maxwell’s equations for transient analysis of buried wires,” IEEE Trans. Electromagn. Compat. 50(2), 347–357 (2008).
[Crossref]

Thoreson, M. D.

M. D. Thoreson, J. Fang, A. V. Kildishev, L. J. Prokopeva, P. Nyga, U. K. Chettiar, V. M. Shalaev, and V. P. Drachev, “Fabrication and realistic modeling of three-dimensional metal-dielectric composites,” J. Nanophotonics 5(1), 051513 (2011).
[Crossref]

Thottappillil, R.

N. Theethayi, Y. Baba, F. Rachidi, and R. Thottappillil, “On the choice between transmission line equations and full-wave Maxwell’s equations for transient analysis of buried wires,” IEEE Trans. Electromagn. Compat. 50(2), 347–357 (2008).
[Crossref]

Tobón, L.

Q. Ren, Q. Sun, L. Tobón, Q. Zhan, and Q. H. Liu, “EB scheme based hybrid SE-FE DGTD method for multiscale EM simulations,” IEEE. Trans. Antennas Propagat. 64(9), 4088–4091 (2016).
[Crossref]

Tobón, L. E.

L. E. Tobón, Q. Ren, and Q. H. Liu, “A new efficient 3D discontinuous Galerkin time domain (DGTD) method for large and multiscale electromagnetic simulations,” J. Comput. Phys. 283, 374–387 (2015).
[Crossref]

Q. Ren, L. E. Tobón, Q. Sun, and Q. H. Liu, “A new 3D non-spurious discontinuous Galerkin spectral element time domain (DG-SETD) method for Maxwell’s equations,” IEEE. Trans. Antennas Propagat. 63(6), 2585–2594 (2015).
[Crossref]

Q. Ren, L. E. Tobón, and Q. H. Liu, “A new 2D non-spurious discontinuous Galerkin finite element time domain (DG-FETD) method for Maxwell’s equations,” Prog. Electromagnetics Res. 143, 385–404 (2013).
[Crossref]

J. Chen, L. E. Tobón, M. Chai, J. A. Mix, and Q. H. Liu, “Efficient implicit-explicit time stepping scheme with domain decomposition for multiscale modeling of layered structures,” IEEE Trans. Compon. Packaging Manuf. Technol. 1(9), 1438–1446 (2011).
[Crossref]

Vadai, M.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

van Hulst, N. F.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
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Wang, D.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

N. K. Emani, D. Wang, T.-F. Chung, L. J. Prokopeva, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Plasmon resonance in multilayer graphene nanoribbons,” Laser Photonics Rev. 9(6), 650–655 (2015).
[Crossref]

Wang, W.

M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, J. Ndukaife, N. Kinsey, H. Reddy, U. Guler, V. M. Shalaev, A. Boltasseva, B. Gholipour, H. N. S. Krishnamoorthy, K. F. MacDonald, C. Soci, N. I. Zheludev, V. Savinov, R. Singh, P. Groß, C. Lienau, M. Vadai, M. L. Solomon, D. R. Barton, M. Lawrence, J. A. Dionne, S. V. Boriskina, R. Esteban, J. Aizpurua, X. Zhang, S. Yang, D. Wang, W. Wang, T. W. Odom, N. Accanto, P. M. de Roque, I. M. Hancu, L. Piatkowski, N. F. van Hulst, and M. F. Kling, “Roadmap on plasmonics,” J. Opt. 20(4), 043001 (2018).
[Crossref]

Wang, Z.

S. I. Azzam, J. Fang, J. Liu, Z. Wang, N. Arnold, T. Klar, L. J. Prokopeva, X. Meng, V. M. Shalaev, and A. V. Kildishev, “Time-resolved dynamics of plasmonic systems with gain,” (unpublished).

Werner, D. H.

Werner, P. L.

Werra, J. F. M.

J. F. M. Werra, C. Wolff, C. Matyssek, and K. Busch, “Current sheets in the discontinuous Galerkin time-domain method: an application to graphene,” Proc. SPIE 9502, 95020E (2015).
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Figures (4)

Fig. 1
Fig. 1 Simulation setup of a D2CP film under plane wave illumination. (a) The geometry, source, and probes for the computational domain configuration. (b) Permittivity of gold with D2CP model compared to experimental data [34]. (c) The transient incident wave. (d,e) The transient reflected (d) and transmitted (e) E field at probes 1 and 2, respectively.
Fig. 2
Fig. 2 The reflection and transmission coefficients and their relative errors for different ppf values. (a), (b) Comparison of the reflection and transmission coefficients between the analytical solution and the CDGTD method with a GDM model for gold and ppf = 2. (c), (d) Relative errors of the reflection and transmission coefficients. (e), (f) Ratio of the relative error for ppf/2 to that for ppf.
Fig. 3
Fig. 3 Geometry and mesh of the nanosphere. (a) Geometry of the nanosphere with source and observation points. (b) Tetrahedral mesh of the nanosphere and its surrounding space.
Fig. 4
Fig. 4 Near-field response of the gold nanosphere employing a DCP dispersive model. The numerical results from the CDGTD method with the GDM model are compared to the analytical solutions from Mie theory. (a) The total fields at [-250, −250, −250] nm. (b) The total fields at [-250, −250, 0] nm. (c) The total fields at [-250, −250, 250] nm.

Tables (2)

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Table 1 Parameters of the ADE for Different Dispersion Terms

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Table 2 The Parameters of Drude - 2 Critical Points Model

Equations (20)

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2 J m t 2 + b 1,m J m t + b 0,m J m = a 0,m E t + a 1,m 2 E t 2 , m 1,M ¯ ,
J m = iω ε 0 P m =iω χ m E,
χ m (ω)= a 0,m iω a 1,m ω 2 iω b 1,m + b 0,m
ε(ω)= ε 1 σ iω ε 0 + m a 0,m iω a 1,m ω 2 iω b 1,m + b 0,m
χ De (ω)= Δε/τ iω+1/τ χ D (ω)= ω D 2 iω(iω Γ D ) , χ L (ω)= f L ω L 2 ω 2 iω Γ L + ω L 2 χ c (ω)= f c ω c ( e i ϕ c ω c ωi Γ c + e i ϕ c ω c +ω+i Γ c )=2 f c ω c ω c cos ϕ c +( iω Γ c )sin ϕ c ω 2 2iω Γ c +( ω c 2 + Γ c 2 )
ε 1 E t = c 2 ×B σ ε 0 E J i m=1 M J m ,
B t =×E M i ,
M ee (k) d e (k) dt = C ee (k) e (k) + K eb (k) b (k) + L ee (k) e (k) + L eb (k) b (k) + l L ee (kl) e (l) , + l L eb (kl) b (l) + m D m (k) j m (k) j i (k)
M bb (k) d b (k) dt = C bb (k) b (k) + K be (k) e (k) + L be (k) e (k) + l L bb (k) b (l) + l L be (kl) e (l) m l (k) ,
2 j m (k) t 2 + b 1,m j m (k) t + b 0,m j m (k) = a 0,m e (k) t + a 1,m 2 e (k) t 2 ,
M bb (k) b n+1/2 (k) b n1/2 (k) Δt = C bb (k) b n+1/2 (k) + b n1/2 (k) 2 + K be (k) e n (k) + L bb (k) b n1/2 (k) , + L be (k) e n (k) + l L bb (kl) b n1/2 (l) + l L be (kl) e n (l) m i,m (k)
M ee (k) e n+1 (k) e n (k) Δt = C ee (k) e n+1 (k) + e n (k) 2 + K eb (k) b n1/2 (k) + L ee (k) e n (k) + L eb (k) b n+1/2 (k) + l L ee (kl) e n (l) + l L eb (kl) b n+1/2 (l) + m D m (k) j m,n+1 (k) + j m,n (k) 2 j i,n+1/2 (k) ,
j m,n+1 (k) 2 j m,n (k) + j m,n1 (k) (Δt) 2 + b 1 j m,n+1 (k) j m,n1 (k) 2Δt + b 0 j m,n (k) = a 0 e n+1 (k) e n1 (k) 2Δt + a 1 e n+1 (k) 2 e n (k) + e n1 (k) (Δt) 2
j m,n+1 (k) = α m j m,n1 (k) + β m j m,n1 (k) + γ m e n+1 (k) + ξ m e n (k) + ζ m e n1 (k) ,
α m = [ 1+ b 1 Δt 2 ] 1 [ 2 b 0 (Δt) 2 ], β m = [ 1+ b 1 Δt 2 ] 1 [ b 1 Δt 2 1 ], γ m = [ 1+ b 1 Δt 2 ] 1 [ a 1 + a 0 Δt 2 ], ξ m = [ 1+ b 1 Δt 2 ] 1 ( 2 a 1 ), ζ m = [ 1+ b 1 Δt 2 ] 1 [ a 1 a 0 Δt 2 ].
b n+1/2 (k) = [ M bb (k) Δt 2 C bb (k) ] 1 [ ( M bb (k) + Δt 2 C bb (k) ) b n1/2 (k) +Δt( K be (k) e n (k) + L bb (k) b n1/2 (k) + L be (k) e n (k) + l L bb (kl) b n1/2 (l) + l L be (kl) e n (l) m i,n (k) ) ].
e n+1 (k) = [ M ee (k) Δt C ee (k) 2 Δt m=1 M γ m D m (k) Z sl Z ls 2 ] 1 × { [ M ee (k) Δt C ee (k) 2 Δt m=1 M ξ m D m (k) Z sl Z ls 2 ] } e n (k) +Δt( K eb (k) b n1/2 (k) + L ee (k) e n (k) + L eb (k) b n+1/2 (k) + l L bb (kl) b n1/2 (k) + l L be (kl) e n (l) m i,n (k) ) Δt m=1 M D m (k) ( ξ m 2 Z sl Z ls e n1 (k) + 1+ α m 2 Z sl J m,n (k) + β m 2 Z sl J m,n1 (k) ) }.
j m,n+1 (k) = α m j m,n (k) + β m j m,n1 (k) + Z ls ( γ m e m,n+1 (k) + ξ m e m,n (k) + ζ m e m,n1 (k) ).
E pulse (t)= e ( t t 0 t w ) 2 sin[ ω(t t 0 ) ].
Error of X= | X n (λ) X a (λ) | | X a (λ) | ×100%,

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