Abstract

A novel rational-fraction dispersion model is proposed for simulation of optical properties of arbitrary linear dispersive media over a wide wavelength range. A generally applicable method is proposed for estimating the parameters of this model. It is demonstrated that the rational-fraction dispersion model can fit the relative permittivity data of a material accurately and efficiently in a wide wavelength range. The new model is implemented in the finite-difference time-domain method and is applied as a powerful and computationally efficient tool for simulating nano-particles of dispersive materials in a wide wavelength range of light.

© 2012 IEEE

PDF Article

References

  • View by:
  • |
  • |

  1. A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  2. S. H. Chang, S. Gray, G. Schatz, "Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films," Opt. Exp. 13, 3150-3165 (2005).
  3. T. W. Lee, S. Gray, "Subwavelength light bending by metal slit structures," Opt. Exp. 13, 9652-9659 (2005).
  4. 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, 085416 (2005).
  5. D. F. Kelley, R. J. Luebbers, "Piecewise linear recursive convolution for dispersive media using FDTD," IEEE Trans. Antennas Propag. 44, 792-797 (1996).
  6. T. Laroche, C. Girard, "Near-field optical properties of single plasmonic nanowires," Appl. Phys. Lett. 89, 233119 (2006).
  7. J. M. McMahon, J. Henzie, T. W. Odom, G. C. Schatz, S. K. Gray, "Tailoring the sensing capabilities of nanohole arrays in gold films with Rayleigh anomaly-surface plasmon polaritons," Opt. Exp. 15, 18119-18129 (2007).
  8. S. K. Gray, T. Kupka, "Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders," Phys. Rev. B 68, 045415 (2003).
  9. A. D. Rakic, A. B. Djurisic, J. M. Elazar, M. L. Majewski, "Optical properties of metallic films for vertical-cavity optoelectronic devices," Appl. Opt. 37, 5271-5283 (1998).
  10. F. Hao, P. Nordlander, "Efficient dielectric function for FDTD simulation of the optical properties of silver and gold nanoparticles," Phys. Chem. Lett. 446, 115-118 (2007).
  11. A. Vial, T. Laroche, "Comparison of gold and silver dispersion laws suitable for FDTD simulations," Appli. Phys. B: Lasers Opt. 93, 139-143 (2008).
  12. K. Y. Jung, F. L. Teixeira, "Multispecies ADI-FDTD algorithm for nanoscale three-dimensional photonic metallic structures," IEEE Photon. Technol. Lett. 19, 586-588 (2007).
  13. K. H. Lee, I. Ahmed, R. S. M. Goh, E. H. Khoo, E. P. Li, T. G. G. Hung, "Implementation of the FDTD method based on Lorentz-Drude dispersive model on GPU for plasmonics applications," Progr. Electromagn. Res. 116, 441-456 (2011).
  14. M. Han, R. W. Dutton, S. Fan, "Model dispersive media in finite-difference time-domain method with complex-conjugate pole-residue pairs," IEEE Microw. Wireless Comp. Lett. 16, 119-121 (2006).
  15. 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, 21179-21190 (2009).
  16. P. Etchegoin, E. Le Ru, M. Meyer, "An analytic model for the optical properties of gold," J. Chem. Phys. 125, 164705 (2006).
  17. N. Okada, J. B. Cole, "Effective permittivity for FDTD calculation of plasmonic materials," Micromachines 3, 168-179 (2012).
  18. 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 (2007).
  19. M. Hamidi, F. 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, 245101 (2011).
  20. B. Gustavsen, A. Semlyen, "Rational approximation of frequency domain responses by vector fitting," IEEE Trans. Power Del. 14, 1052-1061 (1999).
  21. R. X. Zeng, J. H. Sinsky, "Modified rational function modeling technique for high speed circuits," pp. 1951-1954 (2006).
  22. M. H. Richardson, D. L. Formenti, "Parameter estimation from frequency response measurements using rational fraction polynomials," pp. 167-186 (1982).
  23. S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, "Optimization by simulated annealing," Sci. 220, 671 (1983).
  24. P. B. Johnson, R. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370 (1972).
  25. S. Foteinopoulou, J. Vigneron, C. Vandenbem, "Optical near-field excitations on plasmonic nanoparticle-based structures," Opt. Exp. 15, 4253-4267 (2007).
  26. W. Pernice, F. Payne, D. Gallagher, "Simulation of metallic nano-structures by using a hybrid FDTD-ADI subgridding method," Proc. Int. Conf. Electromag. Adv. Applicat. (ICEAA 2007) (2007) pp. 633-636.
  27. J. A. Roden, S. D. Gedney, "Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media," Microw. Opt. Tech. Lett. 27, 334-338 (2000).

2012

N. Okada, J. B. Cole, "Effective permittivity for FDTD calculation of plasmonic materials," Micromachines 3, 168-179 (2012).

2011

K. H. Lee, I. Ahmed, R. S. M. Goh, E. H. Khoo, E. P. Li, T. G. G. Hung, "Implementation of the FDTD method based on Lorentz-Drude dispersive model on GPU for plasmonics applications," Progr. Electromagn. Res. 116, 441-456 (2011).

M. Hamidi, F. 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, 245101 (2011).

2009

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, 21179-21190 (2009).

2008

A. Vial, T. Laroche, "Comparison of gold and silver dispersion laws suitable for FDTD simulations," Appli. Phys. B: Lasers Opt. 93, 139-143 (2008).

2007

K. Y. Jung, F. L. Teixeira, "Multispecies ADI-FDTD algorithm for nanoscale three-dimensional photonic metallic structures," IEEE Photon. Technol. Lett. 19, 586-588 (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 (2007).

J. M. McMahon, J. Henzie, T. W. Odom, G. C. Schatz, S. K. Gray, "Tailoring the sensing capabilities of nanohole arrays in gold films with Rayleigh anomaly-surface plasmon polaritons," Opt. Exp. 15, 18119-18129 (2007).

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

S. Foteinopoulou, J. Vigneron, C. Vandenbem, "Optical near-field excitations on plasmonic nanoparticle-based structures," Opt. Exp. 15, 4253-4267 (2007).

2006

T. Laroche, C. Girard, "Near-field optical properties of single plasmonic nanowires," Appl. Phys. Lett. 89, 233119 (2006).

P. Etchegoin, E. Le Ru, M. Meyer, "An analytic model for the optical properties of gold," J. Chem. Phys. 125, 164705 (2006).

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

2005

S. H. Chang, S. Gray, G. Schatz, "Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films," Opt. Exp. 13, 3150-3165 (2005).

T. W. Lee, S. Gray, "Subwavelength light bending by metal slit structures," Opt. Exp. 13, 9652-9659 (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, 085416 (2005).

2003

S. K. Gray, T. Kupka, "Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders," Phys. Rev. B 68, 045415 (2003).

2000

J. A. Roden, S. D. Gedney, "Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media," Microw. Opt. Tech. Lett. 27, 334-338 (2000).

1999

B. Gustavsen, A. Semlyen, "Rational approximation of frequency domain responses by vector fitting," IEEE Trans. Power Del. 14, 1052-1061 (1999).

1998

A. D. Rakic, A. B. Djurisic, J. M. Elazar, M. L. Majewski, "Optical properties of metallic films for vertical-cavity optoelectronic devices," Appl. Opt. 37, 5271-5283 (1998).

1996

D. F. Kelley, R. J. Luebbers, "Piecewise linear recursive convolution for dispersive media using FDTD," IEEE Trans. Antennas Propag. 44, 792-797 (1996).

1983

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, "Optimization by simulated annealing," Sci. 220, 671 (1983).

1972

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

Appl. Opt.

A. D. Rakic, A. B. Djurisic, J. M. Elazar, M. L. Majewski, "Optical properties of metallic films for vertical-cavity optoelectronic devices," Appl. Opt. 37, 5271-5283 (1998).

Appl. Phys. Lett.

T. Laroche, C. Girard, "Near-field optical properties of single plasmonic nanowires," Appl. Phys. Lett. 89, 233119 (2006).

Appli. Phys. B: Lasers Opt.

A. Vial, T. Laroche, "Comparison of gold and silver dispersion laws suitable for FDTD simulations," Appli. Phys. B: Lasers Opt. 93, 139-143 (2008).

IEEE Trans. Antennas Propag.

D. F. Kelley, R. J. Luebbers, "Piecewise linear recursive convolution for dispersive media using FDTD," IEEE Trans. Antennas Propag. 44, 792-797 (1996).

IEEE Microw. Wireless Comp. Lett.

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

IEEE Photon. Technol. Lett.

K. Y. Jung, F. L. Teixeira, "Multispecies ADI-FDTD algorithm for nanoscale three-dimensional photonic metallic structures," IEEE Photon. Technol. Lett. 19, 586-588 (2007).

IEEE Trans. Power Del.

B. Gustavsen, A. Semlyen, "Rational approximation of frequency domain responses by vector fitting," IEEE Trans. Power Del. 14, 1052-1061 (1999).

J. Opt. A: Pure Appl. Opt.

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 (2007).

J. Phys. D Appl. Phys.

M. Hamidi, F. 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, 245101 (2011).

J. Chem. Phys.

P. Etchegoin, E. Le Ru, M. Meyer, "An analytic model for the optical properties of gold," J. Chem. Phys. 125, 164705 (2006).

Micromachines

N. Okada, J. B. Cole, "Effective permittivity for FDTD calculation of plasmonic materials," Micromachines 3, 168-179 (2012).

Microw. Opt. Tech. Lett.

J. A. Roden, S. D. Gedney, "Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media," Microw. Opt. Tech. Lett. 27, 334-338 (2000).

Opt. Exp.

S. Foteinopoulou, J. Vigneron, C. Vandenbem, "Optical near-field excitations on plasmonic nanoparticle-based structures," Opt. Exp. 15, 4253-4267 (2007).

Opt. Exp.

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, 21179-21190 (2009).

S. H. Chang, S. Gray, G. Schatz, "Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films," Opt. Exp. 13, 3150-3165 (2005).

T. W. Lee, S. Gray, "Subwavelength light bending by metal slit structures," Opt. Exp. 13, 9652-9659 (2005).

J. M. McMahon, J. Henzie, T. W. Odom, G. C. Schatz, S. K. Gray, "Tailoring the sensing capabilities of nanohole arrays in gold films with Rayleigh anomaly-surface plasmon polaritons," Opt. Exp. 15, 18119-18129 (2007).

Phys. Rev. B

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, 085416 (2005).

Phys. Chem. Lett.

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

Phys. Rev. B

S. K. Gray, T. Kupka, "Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders," Phys. Rev. B 68, 045415 (2003).

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

Progr. Electromagn. Res.

K. H. Lee, I. Ahmed, R. S. M. Goh, E. H. Khoo, E. P. Li, T. G. G. Hung, "Implementation of the FDTD method based on Lorentz-Drude dispersive model on GPU for plasmonics applications," Progr. Electromagn. Res. 116, 441-456 (2011).

Sci.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, "Optimization by simulated annealing," Sci. 220, 671 (1983).

Other

R. X. Zeng, J. H. Sinsky, "Modified rational function modeling technique for high speed circuits," pp. 1951-1954 (2006).

M. H. Richardson, D. L. Formenti, "Parameter estimation from frequency response measurements using rational fraction polynomials," pp. 167-186 (1982).

W. Pernice, F. Payne, D. Gallagher, "Simulation of metallic nano-structures by using a hybrid FDTD-ADI subgridding method," Proc. Int. Conf. Electromag. Adv. Applicat. (ICEAA 2007) (2007) pp. 633-636.

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.