Models of near-field spectroscopic studies: Comparison between finite-element and finite-difference methods

Optics Express

Volumn 13, Issue 21, 2005, Pages 8483-8497

  Grosges, Thomas ^a   Vial, Alexandre ^a   Barchiesi, Dominique ^a  

^a UNIVERSITÉ DE TECHNOLOGIE DE TROYES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTROMAGNETIC FIELD EFFECTS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; TIME DOMAIN ANALYSIS;

DRUDE-LORENTZ' MODEL OF DISPERSION; FINITE DIFFERENCE TIME DOMAIN METHOD (FDTD); INTENSITY MAP COMPUTATIONS; NEAR-FIELD SPECTROSCOPY;

NANOSTRUCTURED MATERIALS;

EID: 26844453795     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OPEX.13.008483     Document Type: Article

References (33)

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).
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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-23-3160.
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).
8. A. Vial, A.S. Grimault, D. Macias, 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).
9. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallosungen, ” Ann. Phys. 25, 377-445 (1908).
10. C. Grehan, 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).
11. H. Du, “Mie-scattering calculation, ” Appl. Opt. 43, 1951-1956 (2004).
12. H. Xu, “Calculation of the near field of aggregates of arbitrary spheres, ” J. Opt. Soc. Am. A 21, 804-809 (2004).
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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-13-4818.
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).
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).
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).
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).
25. N. Feelidj, J. Aubard, G. Leevi, 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).
26. J. Grand, S. Kostcheev, J.L. Bijeon, M. Lamy de la Chapelle, P.M. Adam, A. Rumyantseva, G. Leerondel, and P. Royer, “Optimization of SERS-active substrates for near-field raman spectroscopy, ” Syn. Metals 139, 621-624 (2003).
27. T. O. Korner, 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).
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).
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).
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).