Abstract

We compare the numerical results obtained by the Finite Element Method (FEM) and the Finite Difference Time Domain Method (FDTD) for near-field spectroscopic studies and intensity map computations. We evaluate their respective efficiencies and we show that an accurate description of the dispersion and of the geometry of the material must be included for a realistic modeling. In particular for the nano-objects, we show that a grid size around �??�?a �?? 4�?a/λ (expressed in λ units) as well as a Drude-Lorentz�?? model of dispersion for FDTD should be used in order to describe more accurately the confinement of the light around the nanostructures (i.e. the high gradients of the electromagnetic field) and to assure the convergence to the physical solution.

© 2005 Optical Society of America

PDF Article

References

  • View by:
  • |

  1. D. Barchiesi, C. Girard, O.J.F. Martin, D. Van Labeke, and D. Courjon, �??Computing the optical near-field distributions around complex subwavelength surface structures: A comparative study of different methods,�?? Phys. Rev. E 54, 4285-4292 (1996).
    [CrossRef]
  2. B. Guizal, D. Barchiesi, and D. Felbacq, �??Electromagnetic beam diffraction by a finite lamellar structure,�?? J. Opt. Soc. Am. A 20, 2274-2280 (2003).
  3. A. Taflove, and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, 2000).
  4. W.A. Challener, I.K. Sendur, and C. Peng, �??Scattered field formulation of finite difference time domain for a focused light beam in dense media with lossy material,�?? Opt. Express 11, 3160-3170 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-23-3160">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-23-3160</a>
  5. R. Fikri, D. Barchiesi, F. H�??Dhili, R. Bachelot, A. Vial, and P. Royer, �??Modeling recent experiments of apertureless near-field optical microscopy using 2D finite element method,�?? Opt. Commun. 221, 13-22 (2003).
  6. R. Fikri, T. Grosges, and D. Barchiesi, �??Apertureless scanning near-field optical microscopy : On the need of the tip vibration modelling,�?? Opt. Lett. 28, 2147-2149 (2003).
  7. R. Fikri, T. Grosges, and D. Barchiesi, �??Apertureless scanning near-field optical microscopy: Numerical modeling of the lock-in detection,�?? Opt. Commun. 232, 15-23 (2004).
    [CrossRef]
  8. A. Vial, A.S. Grimault, D. Mac´ýas, D. Barchiesi, and M. Lamy de la Chapelle, �??Improved analytical fit of gold dispersion: application to the modelling of extinction spectra with the FDTD method,�?? Phys. Rev. B 71, 085416- 085422 (2005).
    [CrossRef]
  9. G. Mie, �??Beitr¨age zur Optik tr¨uber Medien, speziell kolloidaler Metall¨osungen,�?? Ann. Phys. 25, 377-445 (1908).
  10. C. Gr´ehan, G. Gouesbet, and F. Guilloteau, �??Comparison of the diffraction theory and the generalized lorenz-mie theory for a sphere arbitrarily located into a laser beam,�?? Opt. Commun. 90, 1-6 (1992).
    [CrossRef]
  11. H. Du, �??Mie-scattering calculation,�?? Appl. Opt. 43, 1951-1956 (2004).
    [CrossRef]
  12. H. Xu, �??Calculation of the near field of aggregates of arbitrary spheres,�?? J. Opt. Soc. Am. A 21, 804-809 (2004).
    [CrossRef]
  13. C.F. Bohren, and D.R. Huffman, Absorption and scattering of light by small particles (John Wiley and Sons, New York, 1983).
  14. M. Born, and E.Wolf, Principle of Optics (Pergamon Press, Oxford, 1993).
  15. J. Jin, The Finite Element Method in Electromagnetics (John Wiley and Sons, New York, 1993).
  16. K.S. Yee, �??Numerical solution of initial boundary value problems involving Maxwell�??s equations in isotropic media,�?? IEEE Trans. Antennas Propag. 16, 302-307 (1966).
  17. K. Kunz, and R. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, 1993).
  18. A. Taflove, Advances in Computational Electrodynamics, the Finite-Difference Time-Domain Method (Artech House, Norwood, 1998).
  19. W.M. Saj, �??FDTD simulations of 2D plasmon waveguide on silver nanorods in hexagonal lattice,�?? Opt. Express 13, 4818-4827 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-13-4818">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-13-4818</a>
    [CrossRef]
  20. M.C. Beard, and C.A. Schmuttenmaer, �??Using the finite-difference time-domain pulse propagation method to simulate time-resolved the experiments,�?? J. Chem. Phys. 114, 2903-2909 (2001).
    [CrossRef]
  21. F.L. Teixeira, W.C. Chew, M. Straka, M.L. Oristaglio, and T. Wang, �??Finite-difference time-domain simulation of ground penetrating radar on dispersive, inhomogeneous, and conductive soils,�?? IEEE Trans. Geosci. Remote Sens. 36, 1928-1937 (1998).
  22. S.K. Gray, and T. Kupka, �??Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders,�?? Phys. Rev. B 68, 045415-045425 (2003).
    [CrossRef]
  23. M. Futamata, Y. Maruyama, and M. Ishikawa, �??Local electric field and scattering cross section of Ag nanoparticles under surface plasmon resonance by finite difference time domain method,�?? J. Phys. Chem. B 107, 7607- 7617 (2003).
    [CrossRef]
  24. J.T. Krug II, E.J. Sanchez, and X.S. Xie, �??Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,�?? J. Chem. Phys. 116, 10895-10901 (2002).
    [CrossRef]
  25. N. F´elidj, J. Aubard, G. L´evi, J.R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F.R. Aussenegg, �??Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,�?? Phys. Rev. B 65, 075419-075427 (2002).
    [CrossRef]
  26. J. Grand, S. Kostcheev, J.L. Bijeon, M. Lamy de la Chapelle, P.M. Adam, A. Rumyantseva, G. L´erondel, and P. Royer, �??Optimization of SERS-active substrates for near-field raman spectroscopy,�?? Syn. Metals 139, 621-624 (2003).
  27. T.O. K¨orner, and W. Fichtner, �??Auxiliary differential equation: efficient implementation in the finite-difference time-domain method,�?? Opt. Lett. 22, 1586-1588 (1997).
  28. P. Johnson and R. Christy, �??Optical constants of the noble metals,�?? Phys. Rev. 6, 4370-4379 (1972).
  29. T. Laroche, F.I. Baida and D. Van Labeke, �??Three-dimensional time-difference time-domain study of enhanced second harmonic generation at the end of a apertureless scanning near-field optical microscope metal tip,�?? J. Opt. Soc. Am. B 22, 1045-1051 (2005).
    [CrossRef]
  30. S. Dey, and R. Mittra, �??A conformal finite-difference time-domain technique for modeling cylindrical dielectric resonators,�?? IEEE Trans. Microwave Theory Tech. 47, 1737-1739 (1999).
  31. W.H. Yu, and R. Mittra, �??A conformal finite difference time domain technique for modeling curved dielectric surfaces,�?? IEEE Microw. Wirel. Compon. Lett. 11, 25-27 (2001).
    [CrossRef]
  32. C. Ropers, D.J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D.S. Kim, and C. Lienau, �??Femtosecond Light Transmission and Subradiant Damping in Plasmonic Crystals,�?? Phys. Rev. Lett. 94, 113901-4 (2005).
    [CrossRef]
  33. T.A. Davis and I.S. Duff, �??A combined unifrontal multifrontal method for unsymmetric sparse matrices,�?? ACM T. Math Software 25, 1-20 (1999).

ACM T. Math Software (1)

T.A. Davis and I.S. Duff, �??A combined unifrontal multifrontal method for unsymmetric sparse matrices,�?? ACM T. Math Software 25, 1-20 (1999).

Ann. Phys. (1)

G. Mie, �??Beitr¨age zur Optik tr¨uber Medien, speziell kolloidaler Metall¨osungen,�?? Ann. Phys. 25, 377-445 (1908).

Appl. Opt. (1)

IEEE Microw. Wirel. Compon. Lett. (1)

W.H. Yu, and R. Mittra, �??A conformal finite difference time domain technique for modeling curved dielectric surfaces,�?? IEEE Microw. Wirel. Compon. Lett. 11, 25-27 (2001).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K.S. Yee, �??Numerical solution of initial boundary value problems involving Maxwell�??s equations in isotropic media,�?? IEEE Trans. Antennas Propag. 16, 302-307 (1966).

IEEE Trans. Geosci. Remote Sens. (1)

F.L. Teixeira, W.C. Chew, M. Straka, M.L. Oristaglio, and T. Wang, �??Finite-difference time-domain simulation of ground penetrating radar on dispersive, inhomogeneous, and conductive soils,�?? IEEE Trans. Geosci. Remote Sens. 36, 1928-1937 (1998).

IEEE Trans. Microwave Theory Tech. (1)

S. Dey, and R. Mittra, �??A conformal finite-difference time-domain technique for modeling cylindrical dielectric resonators,�?? IEEE Trans. Microwave Theory Tech. 47, 1737-1739 (1999).

J. Chem. Phys. (2)

M.C. Beard, and C.A. Schmuttenmaer, �??Using the finite-difference time-domain pulse propagation method to simulate time-resolved the experiments,�?? J. Chem. Phys. 114, 2903-2909 (2001).
[CrossRef]

J.T. Krug II, E.J. Sanchez, and X.S. Xie, �??Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,�?? J. Chem. Phys. 116, 10895-10901 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

J. Phys. Chem. B (1)

M. Futamata, Y. Maruyama, and M. Ishikawa, �??Local electric field and scattering cross section of Ag nanoparticles under surface plasmon resonance by finite difference time domain method,�?? J. Phys. Chem. B 107, 7607- 7617 (2003).
[CrossRef]

Opt. Commun. (3)

C. Gr´ehan, G. Gouesbet, and F. Guilloteau, �??Comparison of the diffraction theory and the generalized lorenz-mie theory for a sphere arbitrarily located into a laser beam,�?? Opt. Commun. 90, 1-6 (1992).
[CrossRef]

R. Fikri, T. Grosges, and D. Barchiesi, �??Apertureless scanning near-field optical microscopy: Numerical modeling of the lock-in detection,�?? Opt. Commun. 232, 15-23 (2004).
[CrossRef]

R. Fikri, D. Barchiesi, F. H�??Dhili, R. Bachelot, A. Vial, and P. Royer, �??Modeling recent experiments of apertureless near-field optical microscopy using 2D finite element method,�?? Opt. Commun. 221, 13-22 (2003).

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. (1)

P. Johnson and R. Christy, �??Optical constants of the noble metals,�?? Phys. Rev. 6, 4370-4379 (1972).

Phys. Rev. B (3)

A. Vial, A.S. Grimault, D. Mac´ýas, D. Barchiesi, and M. Lamy de la Chapelle, �??Improved analytical fit of gold dispersion: application to the modelling of extinction spectra with the FDTD method,�?? Phys. Rev. B 71, 085416- 085422 (2005).
[CrossRef]

S.K. Gray, and T. Kupka, �??Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders,�?? Phys. Rev. B 68, 045415-045425 (2003).
[CrossRef]

N. F´elidj, J. Aubard, G. L´evi, J.R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F.R. Aussenegg, �??Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,�?? Phys. Rev. B 65, 075419-075427 (2002).
[CrossRef]

Phys. Rev. E (1)

D. Barchiesi, C. Girard, O.J.F. Martin, D. Van Labeke, and D. Courjon, �??Computing the optical near-field distributions around complex subwavelength surface structures: A comparative study of different methods,�?? Phys. Rev. E 54, 4285-4292 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

C. Ropers, D.J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D.S. Kim, and C. Lienau, �??Femtosecond Light Transmission and Subradiant Damping in Plasmonic Crystals,�?? Phys. Rev. Lett. 94, 113901-4 (2005).
[CrossRef]

Syn. Metals (1)

J. Grand, S. Kostcheev, J.L. Bijeon, M. Lamy de la Chapelle, P.M. Adam, A. Rumyantseva, G. L´erondel, and P. Royer, �??Optimization of SERS-active substrates for near-field raman spectroscopy,�?? Syn. Metals 139, 621-624 (2003).

Other (6)

C.F. Bohren, and D.R. Huffman, Absorption and scattering of light by small particles (John Wiley and Sons, New York, 1983).

M. Born, and E.Wolf, Principle of Optics (Pergamon Press, Oxford, 1993).

J. Jin, The Finite Element Method in Electromagnetics (John Wiley and Sons, New York, 1993).

K. Kunz, and R. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, 1993).

A. Taflove, Advances in Computational Electrodynamics, the Finite-Difference Time-Domain Method (Artech House, Norwood, 1998).

A. Taflove, and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, 2000).

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.


Metrics