Abstract

A generalized auxiliary differential equation (ADE) finite-difference time-domain (FDTD) dispersive scheme is introduced for the rigorous simulation of wave propagation in metallic structures at optical frequencies, where material dispersion is described via an arbitrary number of Drude and critical point terms. The implementation of an efficient perfectly matched layer for the termination of such media is also discussed and demonstrated. The model's validity is directly compared with both analytical and numerical results that employ known dispersion schemes, for the case of two benchmark examples, transmission through a thin metal film and scattering from a metallic nanocylinder. Furthermore, the accuracy of the proposed method is also demonstrated in the study of the optical properties of Ag and Au metal-insulator-metal waveguides, filters, and resonators, which also involve dielectrics whose material dispersion is described by the Sellmeier model.

© 2013 IEEE

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  2. M. I. Stockman, "Nanoplasmonics: Past, present, and glimpse into future," Opt. Exp. 19, 22 029-22 106 (2011).
  3. E. Le Ru, P. Etchegoin, Principles of Surface Enhanced Raman Spectroscopy and Related Plasmonic Effects (Elsevier, 2009).
  4. D. K. Gramotnev, S. I. Bozhevolnyi, "Plasmonics beyond the diffraction limit," Nat. Photonics 4, 83-91 (2010).
  5. A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
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  7. A. C. Tasolamprou, D. C. Zografopoulos, E. E. Kriezis, "Liquid crystal-based dielectric loaded surface plasmon polariton optical switches," J. Appl. Phys. 110, (2011) art. no. 093102.
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  10. A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, M. L. de la Chapelle, "Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, (2005) art. no. 085416.
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  19. J. Lu, Y. Change, "Implementation of an efficient dielectric function into the finite difference time domain method for simulating the coupling between localized surface plasmons of nanostrustures," Superlattice. Microst. 47, 60-65 (2010).
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  27. D. Popovic, M. Okoniewski, "Effective permittivity at the interface of dispersive dielectrics in FDTD," IEEE Microw. Guided Wave Lett. 12, 401-403 (2003).
  28. A. Mohammadi, M. Agio, "Dispersive contour-path finite-difference time-domain algorithm for modelling surface plasmon polaritons at flat interfaces," Opt. Exp. 14, 11 330-11 338 (2006).
  29. Y. Zhao, Y. Hao, "Finite-difference time-domain study of guided modes in nano-plasmonic waveguides," IEEE Trans. Antennas Propag. 55, 3070-3077 (2007).
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  33. A. Zhao, J. Juntunen, A. Raisanen, "Generalized material-independent PML absorbers for the FDTD simulation of electromagnetic waves in arbitrary anisotropic dielectric and magnetic media," IEEE Microw. Guided Wave Lett. 8, 52-54 (1998).
  34. O. Ramadan, "Auxiliary differential equation formulation: An efficient implementation of the perfectly matched layer," IEEE Microw. Wireless Compon. Lett. 13, 69-71 (2003).
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  36. Z. Lin, Y. Fang, J. Hu, C. Zhang, "On the FDTD formulations for modeling wideband Lorentzian media," IEEE Trans. Antennas Propag. 59, 1338-1346 (2011).
  37. M. C. Beard, C. A. Schmuttenmaer, "Using the finite-difference time-domain pulse propagation method to simulate time-resolved THz experiments," J. Chem. Phys. 114, 2903-2909 (2001).
  38. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2007).
  39. J.-Y. Lu, K.-P. Chiu, H.-Y. Chao, Y.-H. Chang, "Multiple metallic-shell nanocylinders for surface-enhanced spectroscopes," Nanoscale Res. Lett. 6, 173- (2011).
  40. S. A. Maier, "Plasmonics: Metal nanostructures for subwavelength photonic devices," IEEE J. Sel. Top. Quantum Electron. 12, 1214-1220 (2006).
  41. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, (2006) art. no. 035407.
  42. I. Udagedara, M. Premaratne, I. D. Rukhlenko, H. T. Hattori, G. P. Agrawal, "Unified perfectly matched layer for finite-difference time-domain modeling of dispersive optical materials," Opt. Exp. 17, 21 179-21 190 (2009).
  43. S. R. Mirnaziry, A. Setayesh, M. S. Abrishamian, "Design and analysis of plasmonic filters based on stubs," J. Opt. Soc. Amer. B 28, 1300-1307 (2011).
  44. COMSOL Multiphysics v4.3a http://www.comsol.com.
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  46. PMMA Datasheet, MicroChem Corp. http://www.microchem.com.

2012 (2)

A. Deinega, S. John, "Effective optical response of silicon to sunlight in the finite-difference time-domain method," Opt. Lett. 37, 112-114 (2012).

P. Neutens, L. Lagae, G. Borghs, P. Van Dorpe, "Plasmon filters and resonators in metal-insulator-metal waveguides," Opt. Exp. 20, 3408-3423 (2012).

2011 (9)

S. R. Mirnaziry, A. Setayesh, M. S. Abrishamian, "Design and analysis of plasmonic filters based on stubs," J. Opt. Soc. Amer. B 28, 1300-1307 (2011).

M. I. Stockman, "Nanoplasmonics: Past, present, and glimpse into future," Opt. Exp. 19, 22 029-22 106 (2011).

A. C. Tasolamprou, D. C. Zografopoulos, E. E. Kriezis, "Liquid crystal-based dielectric loaded surface plasmon polariton optical switches," J. Appl. Phys. 110, (2011) art. no. 093102.

A. Vial, T. Laroche, M. Dridi, L. Le Cunff, "A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method," Appl. Phys. A: Mater. 103, 849-853 (2011).

L. J. Prokopeva, J. D. Borneman, A. V. Kildishev, "Optical dispersion models for time-domain modeling of metal-dielectric nanostructures," IEEE Trans. Magn. 47, 1150-1153 (2011).

Y. Ren, J. K. Chen, Y. Zhang, "Optical properties and thermal response of copper films induced by ultrashort-pulsed lasers," J. Appl. Phys. 110, (2011) art. no. 113102.

M. Hamidi, F. I. Baida, A. Belkhir, O. Lamrous, "Implementation of the critical points model in a SFM-FDTD code working in oblique incidence," J. Phys. D: Appl. Phys. 44, (2011) art. no. 245101.

Z. Lin, Y. Fang, J. Hu, C. Zhang, "On the FDTD formulations for modeling wideband Lorentzian media," IEEE Trans. Antennas Propag. 59, 1338-1346 (2011).

J.-Y. Lu, K.-P. Chiu, H.-Y. Chao, Y.-H. Chang, "Multiple metallic-shell nanocylinders for surface-enhanced spectroscopes," Nanoscale Res. Lett. 6, 173- (2011).

2010 (2)

J. Lu, Y. Change, "Implementation of an efficient dielectric function into the finite difference time domain method for simulating the coupling between localized surface plasmons of nanostrustures," Superlattice. Microst. 47, 60-65 (2010).

D. K. Gramotnev, S. I. Bozhevolnyi, "Plasmonics beyond the diffraction limit," Nat. Photonics 4, 83-91 (2010).

2009 (1)

I. Udagedara, M. Premaratne, I. D. Rukhlenko, H. T. Hattori, G. P. Agrawal, "Unified perfectly matched layer for finite-difference time-domain modeling of dispersive optical materials," Opt. Exp. 17, 21 179-21 190 (2009).

2008 (3)

T. W. Ebbesen, C. Genet, S. I. Bozhevolnyi, "Surface-plasmon circuitry," Phys. Today 44-50 (2008).

T. J. A. Mohammadi, M. Agio, "Dispersive contour-path algorithm for the two-dimensional finite-difference time-domain method," Opt. Exp. 16, 7397-7406 (2008).

K. P. Prokopidis, "On the development of efficient FDTD-PML formulations for general dispersive media," Int. J. Numer. Model. 21, 394-411 (2008).

2007 (5)

Y. Zhao, Y. Hao, "Finite-difference time-domain study of guided modes in nano-plasmonic waveguides," IEEE Trans. Antennas Propag. 55, 3070-3077 (2007).

K. P. Prokopidis, T. D. Tsiboukis, "Modeling of ground-penetrating radar for detecting buried objects in dispersive soils," Appl. Comput. Electron. 22, 287-294 (2007).

F. Hao, P. Nordlander, "Efficient dielectric function for FDTD simulation of the optical properties of silver and gold nanoparticles," Chem. Phys. Lett. 446, 115-118 (2007).

A. Vial, "Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method," J. Opt. A: Pure Appl. Opt. 9, 745-748 (2007).

A. Vial, T. Laroche, "Description of dispersion 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, 7152-7158 (2007).

2006 (5)

M. Han, R. Dutton, S. Fan, "Model dispersive media in finite-difference time-domain method with complex-conjugate pole-residue pairs," IEEE Microw. Wireless Compon. Lett. 16, 119-121 (2006).

P. G. Etchegoin, E. C, L. Ru, M. Meyer, "An analytic model for the optical properties of gold," J. Chem. Phys. 125, (2006) art. no. 164705.

A. Mohammadi, M. Agio, "Dispersive contour-path finite-difference time-domain algorithm for modelling surface plasmon polaritons at flat interfaces," Opt. Exp. 14, 11 330-11 338 (2006).

S. A. Maier, "Plasmonics: Metal nanostructures for subwavelength photonic devices," IEEE J. Sel. Top. Quantum Electron. 12, 1214-1220 (2006).

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, (2006) art. no. 035407.

2005 (2)

T. Grosges, A. Vial, D. Barchiesi, "Models of near-field spectroscopic studies: Comparison between finite-element and finite-difference methods," Opt. Exp. 13, 8483-8497 (2005).

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, M. L. de la Chapelle, "Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, (2005) art. no. 085416.

2004 (1)

M. Fujii, M. Tahara, I. Sakagami, W. Freude, P. Russer, "High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media," IEEE J. Quantum Electron. 40, 175-182 (2004).

2003 (2)

D. Popovic, M. Okoniewski, "Effective permittivity at the interface of dispersive dielectrics in FDTD," IEEE Microw. Guided Wave Lett. 12, 401-403 (2003).

O. Ramadan, "Auxiliary differential equation formulation: An efficient implementation of the perfectly matched layer," IEEE Microw. Wireless Compon. Lett. 13, 69-71 (2003).

2001 (2)

M. C. Beard, C. A. Schmuttenmaer, "Using the finite-difference time-domain pulse propagation method to simulate time-resolved THz experiments," J. Chem. Phys. 114, 2903-2909 (2001).

J. Pereda, L. Vielva, A. Vegas, A. Prieto, "Analyzing the stability of the FDTD technique by combining the von Neumann method with the Routh-Hurwitz criterion," IEEE Trans. Microw. Theory Tech. 49, 377-381 (2001).

1998 (1)

A. Zhao, J. Juntunen, A. Raisanen, "Generalized material-independent PML absorbers for the FDTD simulation of electromagnetic waves in arbitrary anisotropic dielectric and magnetic media," IEEE Microw. Guided Wave Lett. 8, 52-54 (1998).

1994 (1)

J. P. Bérenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).

1972 (1)

P. B. Johnson, R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).

Appl. Comput. Electron. (1)

K. P. Prokopidis, T. D. Tsiboukis, "Modeling of ground-penetrating radar for detecting buried objects in dispersive soils," Appl. Comput. Electron. 22, 287-294 (2007).

Appl. Phys. A: Mater. (1)

A. Vial, T. Laroche, M. Dridi, L. Le Cunff, "A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method," Appl. Phys. A: Mater. 103, 849-853 (2011).

Chem. Phys. Lett. (1)

F. Hao, P. Nordlander, "Efficient dielectric function for FDTD simulation of the optical properties of silver and gold nanoparticles," Chem. Phys. Lett. 446, 115-118 (2007).

IEEE J. Quantum Electron. (1)

M. Fujii, M. Tahara, I. Sakagami, W. Freude, P. Russer, "High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media," IEEE J. Quantum Electron. 40, 175-182 (2004).

IEEE Microw. Guided Wave Lett. (2)

D. Popovic, M. Okoniewski, "Effective permittivity at the interface of dispersive dielectrics in FDTD," IEEE Microw. Guided Wave Lett. 12, 401-403 (2003).

A. Zhao, J. Juntunen, A. Raisanen, "Generalized material-independent PML absorbers for the FDTD simulation of electromagnetic waves in arbitrary anisotropic dielectric and magnetic media," IEEE Microw. Guided Wave Lett. 8, 52-54 (1998).

IEEE J. Sel. Top. Quantum Electron. (1)

S. A. Maier, "Plasmonics: Metal nanostructures for subwavelength photonic devices," IEEE J. Sel. Top. Quantum Electron. 12, 1214-1220 (2006).

IEEE Microw. Wireless Compon. Lett. (2)

O. Ramadan, "Auxiliary differential equation formulation: An efficient implementation of the perfectly matched layer," IEEE Microw. Wireless Compon. Lett. 13, 69-71 (2003).

M. Han, R. Dutton, S. Fan, "Model dispersive media in finite-difference time-domain method with complex-conjugate pole-residue pairs," IEEE Microw. Wireless Compon. Lett. 16, 119-121 (2006).

IEEE Trans. Antennas Propag. (1)

Y. Zhao, Y. Hao, "Finite-difference time-domain study of guided modes in nano-plasmonic waveguides," IEEE Trans. Antennas Propag. 55, 3070-3077 (2007).

IEEE Trans. Antennas Propag. (1)

Z. Lin, Y. Fang, J. Hu, C. Zhang, "On the FDTD formulations for modeling wideband Lorentzian media," IEEE Trans. Antennas Propag. 59, 1338-1346 (2011).

IEEE Trans. Magn. (1)

L. J. Prokopeva, J. D. Borneman, A. V. Kildishev, "Optical dispersion models for time-domain modeling of metal-dielectric nanostructures," IEEE Trans. Magn. 47, 1150-1153 (2011).

IEEE Trans. Microw. Theory Tech. (1)

J. Pereda, L. Vielva, A. Vegas, A. Prieto, "Analyzing the stability of the FDTD technique by combining the von Neumann method with the Routh-Hurwitz criterion," IEEE Trans. Microw. Theory Tech. 49, 377-381 (2001).

Int. J. Numer. Model. (1)

K. P. Prokopidis, "On the development of efficient FDTD-PML formulations for general dispersive media," Int. J. Numer. Model. 21, 394-411 (2008).

J. Appl. Phys. (2)

Y. Ren, J. K. Chen, Y. Zhang, "Optical properties and thermal response of copper films induced by ultrashort-pulsed lasers," J. Appl. Phys. 110, (2011) art. no. 113102.

A. C. Tasolamprou, D. C. Zografopoulos, E. E. Kriezis, "Liquid crystal-based dielectric loaded surface plasmon polariton optical switches," J. Appl. Phys. 110, (2011) art. no. 093102.

J. Comput. Phys. (1)

J. P. Bérenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).

J. Opt. A: Pure Appl. Opt. (1)

A. Vial, "Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method," J. Opt. A: Pure Appl. Opt. 9, 745-748 (2007).

J. Phys. D: Appl. Phys. (1)

A. Vial, T. Laroche, "Description of dispersion 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, 7152-7158 (2007).

J. Chem. Phys. (2)

P. G. Etchegoin, E. C, L. Ru, M. Meyer, "An analytic model for the optical properties of gold," J. Chem. Phys. 125, (2006) art. no. 164705.

M. C. Beard, C. A. Schmuttenmaer, "Using the finite-difference time-domain pulse propagation method to simulate time-resolved THz experiments," J. Chem. Phys. 114, 2903-2909 (2001).

J. Opt. Soc. Amer. B (1)

S. R. Mirnaziry, A. Setayesh, M. S. Abrishamian, "Design and analysis of plasmonic filters based on stubs," J. Opt. Soc. Amer. B 28, 1300-1307 (2011).

J. Phys. D: Appl. Phys. (1)

M. Hamidi, F. I. Baida, A. Belkhir, O. Lamrous, "Implementation of the critical points model in a SFM-FDTD code working in oblique incidence," J. Phys. D: Appl. Phys. 44, (2011) art. no. 245101.

Nanoscale Res. Lett. (1)

J.-Y. Lu, K.-P. Chiu, H.-Y. Chao, Y.-H. Chang, "Multiple metallic-shell nanocylinders for surface-enhanced spectroscopes," Nanoscale Res. Lett. 6, 173- (2011).

Nat. Photonics (1)

D. K. Gramotnev, S. I. Bozhevolnyi, "Plasmonics beyond the diffraction limit," Nat. Photonics 4, 83-91 (2010).

Opt. Exp. (1)

T. J. A. Mohammadi, M. Agio, "Dispersive contour-path algorithm for the two-dimensional finite-difference time-domain method," Opt. Exp. 16, 7397-7406 (2008).

Opt. Lett. (1)

A. Deinega, S. John, "Effective optical response of silicon to sunlight in the finite-difference time-domain method," Opt. Lett. 37, 112-114 (2012).

Opt. Exp. (5)

M. I. Stockman, "Nanoplasmonics: Past, present, and glimpse into future," Opt. Exp. 19, 22 029-22 106 (2011).

A. Mohammadi, M. Agio, "Dispersive contour-path finite-difference time-domain algorithm for modelling surface plasmon polaritons at flat interfaces," Opt. Exp. 14, 11 330-11 338 (2006).

T. Grosges, A. Vial, D. Barchiesi, "Models of near-field spectroscopic studies: Comparison between finite-element and finite-difference methods," Opt. Exp. 13, 8483-8497 (2005).

P. Neutens, L. Lagae, G. Borghs, P. Van Dorpe, "Plasmon filters and resonators in metal-insulator-metal waveguides," Opt. Exp. 20, 3408-3423 (2012).

I. Udagedara, M. Premaratne, I. D. Rukhlenko, H. T. Hattori, G. P. Agrawal, "Unified perfectly matched layer for finite-difference time-domain modeling of dispersive optical materials," Opt. Exp. 17, 21 179-21 190 (2009).

Phys. Rev. B (1)

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, M. L. de la Chapelle, "Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, (2005) art. no. 085416.

Phys. Rev. B (2)

P. B. Johnson, R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, (2006) art. no. 035407.

Phys. Today (1)

T. W. Ebbesen, C. Genet, S. I. Bozhevolnyi, "Surface-plasmon circuitry," Phys. Today 44-50 (2008).

Superlattice. Microst. (1)

J. Lu, Y. Change, "Implementation of an efficient dielectric function into the finite difference time domain method for simulating the coupling between localized surface plasmons of nanostrustures," Superlattice. Microst. 47, 60-65 (2010).

Other (9)

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

E. Le Ru, P. Etchegoin, Principles of Surface Enhanced Raman Spectroscopy and Related Plasmonic Effects (Elsevier, 2009).

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

S. G. Rodrigo, Optical Properties of Nanostructured Metallic Systems (Springer, 2012).

J. Shibayama, K. Watanabe, R. Ando, J. Yamauchi, H. Nakano, "Simple frequency-dependent FDTD algorithm for a Drude-critical points model," Proc. Asia-Pacific Microw.Conf. (2012) pp. WE1D-4.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2007).

M. Born, E. Wolf, Principles of Optics (Pergamon, 1980).

PMMA Datasheet, MicroChem Corp. http://www.microchem.com.

COMSOL Multiphysics v4.3a http://www.comsol.com.

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