Abstract

Fitting optical properties of metals is of great interest for numerical methods in electromagnetism, especially finite difference time domain (FDTD). However, this is a tedious task given that theoretical models used usually fail to interlink perfectly with the experimental data. However, in this paper, we propose a method for fitting the relative permittivity of metals by a sum of Drude-Lorentz or a sum of partial-fraction models. We use the particle swarm optimization (PSO) hybridized either with Nelder-Mead downhill simplex, or with gradient method. The main electronic transitions in metals help to guide the fitting process toward the solution. The method is automatic and applied blindly to silver, gold, copper, aluminum, chromium, platinum, and titanium.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Optical dielectric constants of single crystalline silver films in the long wavelength range

Junho Choi, Fei Cheng, Justin W. Cleary, Liuyang Sun, Chandriker Kavir Dass, Joshua R. Hendrickson, Chun-Yuan Wang, Shangjr Gwo, Chih-Kang Shih, and Xiaoqin Li
Opt. Mater. Express 10(2) 693-703 (2020)

On a causal dispersion model for the optical properties of metals

J. Orosco and C. F. M. Coimbra
Appl. Opt. 57(19) 5333-5347 (2018)

Effect of microstructure on the optical properties of sputtered iridium thin films

Nicole A. Pfiester, Kevin A. Grossklaus, Margaret A. Stevens, and Thomas E. Vandervelde
Opt. Mater. Express 10(4) 1120-1128 (2020)

References

  • View by:
  • |
  • |
  • |

  1. L. G. Shultz, “The optical constants of silver, gold, copper and aluminum. I. the absorption coefficient k,” J. Opt. Soc. Am. 44(5), 357–362 (1954).
    [Crossref]
  2. L. G. Shultz and F. R. Tangherlini, “The optical constants of silver, gold, copper and aluminum. II. the index of refraction n,” J. Opt. Soc. Am. 44(5), 362–368 (1954).
    [Crossref]
  3. J. J. E. Nestell and R. W. Christy, “Derivation of optical constants of metals from thin-film measurements at oblique incidence,” Appl. Opt. 11(3), 643–651 (1972).
    [Crossref]
  4. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [Crossref]
  5. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–1118 (1983).
    [Crossref]
  6. W. S. M. Werner, K. Glantschnig, and C. Ambrosch-Draxl, “Optical constants and inelastic electron-scattering data for 17 elemental metals,” J. Phys. Chem. 38(4), 1013–1092 (2009).
    [Crossref]
  7. L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films 520(1), 501–509 (2011).
    [Crossref]
  8. S. Babar and J. H. Weaver, “Optical constants of Cu, Ag, and Au revisited,” Appl. Opt. 54(3), 477–481 (2015).
    [Crossref]
  9. E. D. Palik, Handbook of Optical Constants (Academic Press Inc., 1985).
  10. https://refractiveindex.info (2016).
  11. “Optical data from Sopra SA,” http://www.sspectra.com/sopra.html .
  12. J. B. Schneider, “Understanding the finite-difference time-domain method,” https://www.eecs.wsu.edu/schneidj/ufdtd/ (request data: 29.11. 2019) (2010).
  13. L. Han, D. Zhou, K. Li, l. Xun, and W.-P. Huang, “A Rational-Fraction dispersion model for efficient simulation of dispersive material in FDTD method,” J. Lightwave Technol. 30(13), 2216–2225 (2012).
    [Crossref]
  14. 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]
  15. D. Liu and K. Michalski, “Comparative study of bio-inspired optimization algorithms and their application to dielectric function fitting,” J. Electromagn. Waves Appl. 30(14), 1885–1894 (2016).
    [Crossref]
  16. H. Sehmi, W. Langbein, and E. Muljarov, “Optimizing the Drude-Lorentz model for material permittivity: Method, program, and examples for gold, silver, and copper,” Phys. Rev. B 95(11), 115444 (2017).
    [Crossref]
  17. M. Gilliot, “Errors in ellipsometry data fitting,” Opt. Commun. 427, 477–484 (2018).
    [Crossref]
  18. V. Kravets, P. Y. Kurioz, and L. Poperenko, “Spectral dependence of the magnetic modulation of surface plasmon polaritons in permalloy/noble metal films,” J. Opt. Soc. Am. B 31(8), 1836–1844 (2014).
    [Crossref]
  19. M. Garcia, “Surface plasmons in metallic nanoparticles: Fundamentals and applications,” J. Phys. D: Appl. Phys. 44(28), 283001 (2011).
    [Crossref]
  20. C. Sharma, G. S. Rathore, and V. Dubey, “Determination of optical constants of SnO2 thin film for display application,” Adv. Phys. Lett. 1, 38–42 (2014).
  21. D. Barchiesi and T. Grosges, “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 089996 (2015).
    [Crossref]
  22. C. Grosse, “A program for the fitting of Debye, Cole–Cole, Cole–Davidson, and Havriliak–Negami dispersions to dielectric data,” J. Colloid Interface Sci. 419, 102–106 (2014).
    [Crossref]
  23. J. Kennedy and R. Eberhart, “Particle swarm optimization," in IEEE International Conference on Neural Networks (Vol. IV) (IEEE, 1995), pp. 1942–1948.
  24. E. Rachid, H. Hachimi, and A. ELHami, “A new hybrid genetic algorithm and particle swarm optimization,” Key Eng. Mater. 35(8), 3905–3917 (2011).
    [Crossref]
  25. V. Selvi and R. Umarani, “Comparative analysis of ant colony and particle swarm optimization techniques,” Int. J. Comput. Appl. 5(4), 1–6 (2010).
    [Crossref]
  26. P. Drude, “Zur elektrontheorie des metalle,” Ann. Phys. 306(3), 566–613 (1900).
    [Crossref]
  27. I. Almog, M. S. Bradley, and V. Bulović, “The Lorentz oscillator and its applications,” https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-007-electromagnetic-energy-from-motors-to-lasers-spring-2011/readings/MIT6_007S11_lorentz.pdf .
  28. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998).
    [Crossref]
  29. K. A. Michalski, “On the low-order partial-fraction fitting of dielectric functions at optical wavelengths,” IEEE Trans. Antennas Propag. 61(12), 6128–6135 (2013).
    [Crossref]
  30. 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]
  31. A. Deinega and S. John, “Effective optical response of silicon to sunlight in the finite-difference time-domain method,” Opt. Lett. 37(1), 112–114 (2012).
    [Crossref]
  32. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005), 3rd ed.
  33. A. Vial, “Implementation of the critical points model in the recursive convolution method for modeling dispersive media with the finite-difference time domain method,” J. Opt. A: Pure Appl. Opt. 9(7), 745–748 (2007).
    [Crossref]
  34. J. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7(4), 308–313 (1965).
    [Crossref]
  35. Y. Shi and R. Eberhart, “A modified particle swarm optimizer," 1998 IEEE International Conference on Evolutionary Computation Proceedings, IEEE World Congress On Computational Intelligence (Cat. No. 98TH8360), (IEEE, 1998), pp. 69–73.
  36. S. Xu and Y. Rahmat-Samii, “Boundary conditions in particle swarm optimization revisited,” IEEE Trans. Antennas Propag. 55(3), 760–765 (2007).
    [Crossref]
  37. S. Chatterjee, D. Goswami, S. Mukherjee, and S. Das, “Behavioral analysis of the leader particle during stagnation in a particle swarm optimization algorithm,” Inf. Sci. 279, 18–36 (2014).
    [Crossref]
  38. D. Barchiesi and T. Grosges, “Propagation of uncertainties and applications in numerical modeling: tutorial,” J. Opt. Soc. Am. A 34(9), 1602–1619 (2017).
    [Crossref]
  39. A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy 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(8), 085416 (2005).
    [Crossref]
  40. D. Barchiesi and T. Grosges, “Errata fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 089996 (2015).
    [Crossref]
  41. R. Lässer and N. Smith, “Interband optical transitions in gold in the photon energy range 2–25 eV,” Solid State Commun. 37(6), 507–509 (1981).
    [Crossref]
  42. H. Aouani, J. Wenger, D. Gérard, H. Rigneault, E. Devaux, T. W. Ebbesen, F. Mahdavi, T. Xu, and S. Blair, “Crucial role of the adhesion layer on the plasmonic fluorescence enhancement,” ACS Nano 3(7), 2043–2048 (2009).
    [Crossref]
  43. S. Kessentini and D. Barchiesi, Nanostructured Biosensors Influence of Adhesion Layer, Roughness and Size on the LSPR A Parametric Study (INTECH Open Access, 2013), chap. 12, pp. 311–330.
  44. F. Colas, D. Barchiesi, S. Kessentini, T. Toury, and M. Lamy de la Chapelle, “Comparison of adhesion layers of gold on silicate glasses for SERS detection,” J. Opt. 17(11), 114010 (2015).
    [Crossref]
  45. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998).
    [Crossref]
  46. H. Ehrenreich, H. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev. 132(5), 1918–1928 (1963).
    [Crossref]
  47. D. Barchiesi and A. Otto, “Excitations of surface plasmon polaritons by attenuated total reflection, revisited,” Riv. Nuovo Cimento 36(5), 173–209 (2013).
    [Crossref]
  48. D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics the plasmon localization,” J. Microsc. 229(3), 525–532 (2008).
    [Crossref]
  49. C. Kittel, Introduction To Solid State Physics (Wiley, 2005), 8th ed.
  50. S. Onur, S. A. Güngör, F. Tümer, and M. Tümer, “The color, photophysical and electrochemical properties of azo-imine ligands and their copper (ii) and platinium (ii) complexes,” J. Mol. Struct. 1200, 127135 (2020).
    [Crossref]
  51. S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203(3-6), 283–288 (2002).
    [Crossref]
  52. D. W. Lynch, C. Olson, and J. Weaver, “Optical properties of Ti, Zr, and Hf from 0.15 to 30 eV,” Phys. Rev. B 11(10), 3617–3624 (1975).
    [Crossref]
  53. M. Guerrisi, R. Rosei, and P. Winsemius, “Splitting of the interband absorption edge in Au,” Phys. Rev. B 12(2), 557–563 (1975).
    [Crossref]
  54. M. Kadi, A. Smaali, and R. Outemzabet, “Analysis of optical and related properties of tin oxide thin films determined by Drude-Lorentz model,” Surf. Coat. Technol. 211, 45–49 (2012).
    [Crossref]
  55. 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]
  56. K. E. Oughstun and N. A. Cartwright, “On the Lorentz-Lorenz formula and the Lorentz model of dielectric dispersion,” Opt. Express 11(13), 1541–1546 (2003).
    [Crossref]

2020 (1)

S. Onur, S. A. Güngör, F. Tümer, and M. Tümer, “The color, photophysical and electrochemical properties of azo-imine ligands and their copper (ii) and platinium (ii) complexes,” J. Mol. Struct. 1200, 127135 (2020).
[Crossref]

2018 (1)

M. Gilliot, “Errors in ellipsometry data fitting,” Opt. Commun. 427, 477–484 (2018).
[Crossref]

2017 (2)

H. Sehmi, W. Langbein, and E. Muljarov, “Optimizing the Drude-Lorentz model for material permittivity: Method, program, and examples for gold, silver, and copper,” Phys. Rev. B 95(11), 115444 (2017).
[Crossref]

D. Barchiesi and T. Grosges, “Propagation of uncertainties and applications in numerical modeling: tutorial,” J. Opt. Soc. Am. A 34(9), 1602–1619 (2017).
[Crossref]

2016 (1)

D. Liu and K. Michalski, “Comparative study of bio-inspired optimization algorithms and their application to dielectric function fitting,” J. Electromagn. Waves Appl. 30(14), 1885–1894 (2016).
[Crossref]

2015 (4)

D. Barchiesi and T. Grosges, “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 089996 (2015).
[Crossref]

S. Babar and J. H. Weaver, “Optical constants of Cu, Ag, and Au revisited,” Appl. Opt. 54(3), 477–481 (2015).
[Crossref]

D. Barchiesi and T. Grosges, “Errata fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 089996 (2015).
[Crossref]

F. Colas, D. Barchiesi, S. Kessentini, T. Toury, and M. Lamy de la Chapelle, “Comparison of adhesion layers of gold on silicate glasses for SERS detection,” J. Opt. 17(11), 114010 (2015).
[Crossref]

2014 (4)

S. Chatterjee, D. Goswami, S. Mukherjee, and S. Das, “Behavioral analysis of the leader particle during stagnation in a particle swarm optimization algorithm,” Inf. Sci. 279, 18–36 (2014).
[Crossref]

C. Sharma, G. S. Rathore, and V. Dubey, “Determination of optical constants of SnO2 thin film for display application,” Adv. Phys. Lett. 1, 38–42 (2014).

C. Grosse, “A program for the fitting of Debye, Cole–Cole, Cole–Davidson, and Havriliak–Negami dispersions to dielectric data,” J. Colloid Interface Sci. 419, 102–106 (2014).
[Crossref]

V. Kravets, P. Y. Kurioz, and L. Poperenko, “Spectral dependence of the magnetic modulation of surface plasmon polaritons in permalloy/noble metal films,” J. Opt. Soc. Am. B 31(8), 1836–1844 (2014).
[Crossref]

2013 (3)

K. A. Michalski, “On the low-order partial-fraction fitting of dielectric functions at optical wavelengths,” IEEE Trans. Antennas Propag. 61(12), 6128–6135 (2013).
[Crossref]

D. Barchiesi and A. Otto, “Excitations of surface plasmon polaritons by attenuated total reflection, revisited,” Riv. Nuovo Cimento 36(5), 173–209 (2013).
[Crossref]

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]

2012 (3)

2011 (3)

M. Garcia, “Surface plasmons in metallic nanoparticles: Fundamentals and applications,” J. Phys. D: Appl. Phys. 44(28), 283001 (2011).
[Crossref]

L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films 520(1), 501–509 (2011).
[Crossref]

E. Rachid, H. Hachimi, and A. ELHami, “A new hybrid genetic algorithm and particle swarm optimization,” Key Eng. Mater. 35(8), 3905–3917 (2011).
[Crossref]

2010 (1)

V. Selvi and R. Umarani, “Comparative analysis of ant colony and particle swarm optimization techniques,” Int. J. Comput. Appl. 5(4), 1–6 (2010).
[Crossref]

2009 (2)

W. S. M. Werner, K. Glantschnig, and C. Ambrosch-Draxl, “Optical constants and inelastic electron-scattering data for 17 elemental metals,” J. Phys. Chem. 38(4), 1013–1092 (2009).
[Crossref]

H. Aouani, J. Wenger, D. Gérard, H. Rigneault, E. Devaux, T. W. Ebbesen, F. Mahdavi, T. Xu, and S. Blair, “Crucial role of the adhesion layer on the plasmonic fluorescence enhancement,” ACS Nano 3(7), 2043–2048 (2009).
[Crossref]

2008 (1)

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics the plasmon localization,” J. Microsc. 229(3), 525–532 (2008).
[Crossref]

2007 (4)

A. Vial, “Implementation of the critical points model in the recursive convolution method for modeling dispersive media with the finite-difference time domain method,” J. Opt. A: Pure Appl. Opt. 9(7), 745–748 (2007).
[Crossref]

S. Xu and Y. Rahmat-Samii, “Boundary conditions in particle swarm optimization revisited,” IEEE Trans. Antennas Propag. 55(3), 760–765 (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]

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]

2005 (1)

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy 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(8), 085416 (2005).
[Crossref]

2003 (1)

2002 (1)

S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203(3-6), 283–288 (2002).
[Crossref]

1998 (2)

1983 (1)

1981 (1)

R. Lässer and N. Smith, “Interband optical transitions in gold in the photon energy range 2–25 eV,” Solid State Commun. 37(6), 507–509 (1981).
[Crossref]

1975 (2)

D. W. Lynch, C. Olson, and J. Weaver, “Optical properties of Ti, Zr, and Hf from 0.15 to 30 eV,” Phys. Rev. B 11(10), 3617–3624 (1975).
[Crossref]

M. Guerrisi, R. Rosei, and P. Winsemius, “Splitting of the interband absorption edge in Au,” Phys. Rev. B 12(2), 557–563 (1975).
[Crossref]

1972 (2)

1965 (1)

J. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7(4), 308–313 (1965).
[Crossref]

1963 (1)

H. Ehrenreich, H. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev. 132(5), 1918–1928 (1963).
[Crossref]

1954 (2)

1900 (1)

P. Drude, “Zur elektrontheorie des metalle,” Ann. Phys. 306(3), 566–613 (1900).
[Crossref]

Alexander, R. W.

Almog, I.

I. Almog, M. S. Bradley, and V. Bulović, “The Lorentz oscillator and its applications,” https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-007-electromagnetic-energy-from-motors-to-lasers-spring-2011/readings/MIT6_007S11_lorentz.pdf .

Ambrosch-Draxl, C.

W. S. M. Werner, K. Glantschnig, and C. Ambrosch-Draxl, “Optical constants and inelastic electron-scattering data for 17 elemental metals,” J. Phys. Chem. 38(4), 1013–1092 (2009).
[Crossref]

Aouani, H.

H. Aouani, J. Wenger, D. Gérard, H. Rigneault, E. Devaux, T. W. Ebbesen, F. Mahdavi, T. Xu, and S. Blair, “Crucial role of the adhesion layer on the plasmonic fluorescence enhancement,” ACS Nano 3(7), 2043–2048 (2009).
[Crossref]

Babar, S.

Barchiesi, D.

D. Barchiesi and T. Grosges, “Propagation of uncertainties and applications in numerical modeling: tutorial,” J. Opt. Soc. Am. A 34(9), 1602–1619 (2017).
[Crossref]

D. Barchiesi and T. Grosges, “Errata fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 089996 (2015).
[Crossref]

F. Colas, D. Barchiesi, S. Kessentini, T. Toury, and M. Lamy de la Chapelle, “Comparison of adhesion layers of gold on silicate glasses for SERS detection,” J. Opt. 17(11), 114010 (2015).
[Crossref]

D. Barchiesi and T. Grosges, “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 089996 (2015).
[Crossref]

D. Barchiesi and A. Otto, “Excitations of surface plasmon polaritons by attenuated total reflection, revisited,” Riv. Nuovo Cimento 36(5), 173–209 (2013).
[Crossref]

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics the plasmon localization,” J. Microsc. 229(3), 525–532 (2008).
[Crossref]

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy 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(8), 085416 (2005).
[Crossref]

S. Kessentini and D. Barchiesi, Nanostructured Biosensors Influence of Adhesion Layer, Roughness and Size on the LSPR A Parametric Study (INTECH Open Access, 2013), chap. 12, pp. 311–330.

Bell, R. J.

Bell, R. R.

Bell, S. E.

Blair, S.

H. Aouani, J. Wenger, D. Gérard, H. Rigneault, E. Devaux, T. W. Ebbesen, F. Mahdavi, T. Xu, and S. Blair, “Crucial role of the adhesion layer on the plasmonic fluorescence enhancement,” ACS Nano 3(7), 2043–2048 (2009).
[Crossref]

Bradley, M. S.

I. Almog, M. S. Bradley, and V. Bulović, “The Lorentz oscillator and its applications,” https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-007-electromagnetic-energy-from-motors-to-lasers-spring-2011/readings/MIT6_007S11_lorentz.pdf .

Bulovic, V.

I. Almog, M. S. Bradley, and V. Bulović, “The Lorentz oscillator and its applications,” https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-007-electromagnetic-energy-from-motors-to-lasers-spring-2011/readings/MIT6_007S11_lorentz.pdf .

Cartwright, N. A.

Chatterjee, S.

S. Chatterjee, D. Goswami, S. Mukherjee, and S. Das, “Behavioral analysis of the leader particle during stagnation in a particle swarm optimization algorithm,” Inf. Sci. 279, 18–36 (2014).
[Crossref]

Christy, R. W.

Colas, F.

F. Colas, D. Barchiesi, S. Kessentini, T. Toury, and M. Lamy de la Chapelle, “Comparison of adhesion layers of gold on silicate glasses for SERS detection,” J. Opt. 17(11), 114010 (2015).
[Crossref]

Das, S.

S. Chatterjee, D. Goswami, S. Mukherjee, and S. Das, “Behavioral analysis of the leader particle during stagnation in a particle swarm optimization algorithm,” Inf. Sci. 279, 18–36 (2014).
[Crossref]

Deinega, A.

Devaux, E.

H. Aouani, J. Wenger, D. Gérard, H. Rigneault, E. Devaux, T. W. Ebbesen, F. Mahdavi, T. Xu, and S. Blair, “Crucial role of the adhesion layer on the plasmonic fluorescence enhancement,” ACS Nano 3(7), 2043–2048 (2009).
[Crossref]

Djurišic, A. B.

Drude, P.

P. Drude, “Zur elektrontheorie des metalle,” Ann. Phys. 306(3), 566–613 (1900).
[Crossref]

Dubey, V.

C. Sharma, G. S. Rathore, and V. Dubey, “Determination of optical constants of SnO2 thin film for display application,” Adv. Phys. Lett. 1, 38–42 (2014).

Ebbesen, T. W.

H. Aouani, J. Wenger, D. Gérard, H. Rigneault, E. Devaux, T. W. Ebbesen, F. Mahdavi, T. Xu, and S. Blair, “Crucial role of the adhesion layer on the plasmonic fluorescence enhancement,” ACS Nano 3(7), 2043–2048 (2009).
[Crossref]

Eberhart, R.

Y. Shi and R. Eberhart, “A modified particle swarm optimizer," 1998 IEEE International Conference on Evolutionary Computation Proceedings, IEEE World Congress On Computational Intelligence (Cat. No. 98TH8360), (IEEE, 1998), pp. 69–73.

J. Kennedy and R. Eberhart, “Particle swarm optimization," in IEEE International Conference on Neural Networks (Vol. IV) (IEEE, 1995), pp. 1942–1948.

Ehrenreich, H.

H. Ehrenreich, H. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev. 132(5), 1918–1928 (1963).
[Crossref]

Elazar, J. M.

ELHami, A.

E. Rachid, H. Hachimi, and A. ELHami, “A new hybrid genetic algorithm and particle swarm optimization,” Key Eng. Mater. 35(8), 3905–3917 (2011).
[Crossref]

Gao, L.

L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films 520(1), 501–509 (2011).
[Crossref]

Gao, Y.

S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203(3-6), 283–288 (2002).
[Crossref]

Garcia, M.

M. Garcia, “Surface plasmons in metallic nanoparticles: Fundamentals and applications,” J. Phys. D: Appl. Phys. 44(28), 283001 (2011).
[Crossref]

Gérard, D.

H. Aouani, J. Wenger, D. Gérard, H. Rigneault, E. Devaux, T. W. Ebbesen, F. Mahdavi, T. Xu, and S. Blair, “Crucial role of the adhesion layer on the plasmonic fluorescence enhancement,” ACS Nano 3(7), 2043–2048 (2009).
[Crossref]

Gilliot, M.

M. Gilliot, “Errors in ellipsometry data fitting,” Opt. Commun. 427, 477–484 (2018).
[Crossref]

Glantschnig, K.

W. S. M. Werner, K. Glantschnig, and C. Ambrosch-Draxl, “Optical constants and inelastic electron-scattering data for 17 elemental metals,” J. Phys. Chem. 38(4), 1013–1092 (2009).
[Crossref]

Goswami, D.

S. Chatterjee, D. Goswami, S. Mukherjee, and S. Das, “Behavioral analysis of the leader particle during stagnation in a particle swarm optimization algorithm,” Inf. Sci. 279, 18–36 (2014).
[Crossref]

Grimault, A.-S.

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy 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(8), 085416 (2005).
[Crossref]

Grosges, T.

D. Barchiesi and T. Grosges, “Propagation of uncertainties and applications in numerical modeling: tutorial,” J. Opt. Soc. Am. A 34(9), 1602–1619 (2017).
[Crossref]

D. Barchiesi and T. Grosges, “Errata fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 089996 (2015).
[Crossref]

D. Barchiesi and T. Grosges, “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 089996 (2015).
[Crossref]

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics the plasmon localization,” J. Microsc. 229(3), 525–532 (2008).
[Crossref]

Grosse, C.

C. Grosse, “A program for the fitting of Debye, Cole–Cole, Cole–Davidson, and Havriliak–Negami dispersions to dielectric data,” J. Colloid Interface Sci. 419, 102–106 (2014).
[Crossref]

Guerrisi, M.

M. Guerrisi, R. Rosei, and P. Winsemius, “Splitting of the interband absorption edge in Au,” Phys. Rev. B 12(2), 557–563 (1975).
[Crossref]

Güngör, S. A.

S. Onur, S. A. Güngör, F. Tümer, and M. Tümer, “The color, photophysical and electrochemical properties of azo-imine ligands and their copper (ii) and platinium (ii) complexes,” J. Mol. Struct. 1200, 127135 (2020).
[Crossref]

Hachimi, H.

E. Rachid, H. Hachimi, and A. ELHami, “A new hybrid genetic algorithm and particle swarm optimization,” Key Eng. Mater. 35(8), 3905–3917 (2011).
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005), 3rd ed.

Han, L.

Huang, W.-P.

John, S.

Johnson, P. B.

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

Kadi, M.

M. Kadi, A. Smaali, and R. Outemzabet, “Analysis of optical and related properties of tin oxide thin films determined by Drude-Lorentz model,” Surf. Coat. Technol. 211, 45–49 (2012).
[Crossref]

Kennedy, J.

J. Kennedy and R. Eberhart, “Particle swarm optimization," in IEEE International Conference on Neural Networks (Vol. IV) (IEEE, 1995), pp. 1942–1948.

Kessentini, S.

F. Colas, D. Barchiesi, S. Kessentini, T. Toury, and M. Lamy de la Chapelle, “Comparison of adhesion layers of gold on silicate glasses for SERS detection,” J. Opt. 17(11), 114010 (2015).
[Crossref]

S. Kessentini and D. Barchiesi, Nanostructured Biosensors Influence of Adhesion Layer, Roughness and Size on the LSPR A Parametric Study (INTECH Open Access, 2013), chap. 12, pp. 311–330.

Kittel, C.

C. Kittel, Introduction To Solid State Physics (Wiley, 2005), 8th ed.

Kravets, V.

Kremer, E.

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics the plasmon localization,” J. Microsc. 229(3), 525–532 (2008).
[Crossref]

Kurioz, P. Y.

Lamy de la Chapelle, M.

F. Colas, D. Barchiesi, S. Kessentini, T. Toury, and M. Lamy de la Chapelle, “Comparison of adhesion layers of gold on silicate glasses for SERS detection,” J. Opt. 17(11), 114010 (2015).
[Crossref]

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy 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(8), 085416 (2005).
[Crossref]

Langbein, W.

H. Sehmi, W. Langbein, and E. Muljarov, “Optimizing the Drude-Lorentz model for material permittivity: Method, program, and examples for gold, silver, and copper,” Phys. Rev. B 95(11), 115444 (2017).
[Crossref]

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).
[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]

Lässer, R.

R. Lässer and N. Smith, “Interband optical transitions in gold in the photon energy range 2–25 eV,” Solid State Commun. 37(6), 507–509 (1981).
[Crossref]

Lemarchand, F.

L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films 520(1), 501–509 (2011).
[Crossref]

Lequime, M.

L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films 520(1), 501–509 (2011).
[Crossref]

Li, K.

Li, Y.

S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203(3-6), 283–288 (2002).
[Crossref]

Liu, D.

D. Liu and K. Michalski, “Comparative study of bio-inspired optimization algorithms and their application to dielectric function fitting,” J. Electromagn. Waves Appl. 30(14), 1885–1894 (2016).
[Crossref]

Liu, H.

S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203(3-6), 283–288 (2002).
[Crossref]

Liu, S.

S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203(3-6), 283–288 (2002).
[Crossref]

Long, L. L.

Lynch, D. W.

D. W. Lynch, C. Olson, and J. Weaver, “Optical properties of Ti, Zr, and Hf from 0.15 to 30 eV,” Phys. Rev. B 11(10), 3617–3624 (1975).
[Crossref]

Macias, D.

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy 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(8), 085416 (2005).
[Crossref]

Mahdavi, F.

H. Aouani, J. Wenger, D. Gérard, H. Rigneault, E. Devaux, T. W. Ebbesen, F. Mahdavi, T. Xu, and S. Blair, “Crucial role of the adhesion layer on the plasmonic fluorescence enhancement,” ACS Nano 3(7), 2043–2048 (2009).
[Crossref]

Mai, V. P.

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics the plasmon localization,” J. Microsc. 229(3), 525–532 (2008).
[Crossref]

Majewski, M. L.

Mead, R.

J. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7(4), 308–313 (1965).
[Crossref]

Michalski, K.

D. Liu and K. Michalski, “Comparative study of bio-inspired optimization algorithms and their application to dielectric function fitting,” J. Electromagn. Waves Appl. 30(14), 1885–1894 (2016).
[Crossref]

Michalski, K. A.

K. A. Michalski, “On the low-order partial-fraction fitting of dielectric functions at optical wavelengths,” IEEE Trans. Antennas Propag. 61(12), 6128–6135 (2013).
[Crossref]

Mukherjee, S.

S. Chatterjee, D. Goswami, S. Mukherjee, and S. Das, “Behavioral analysis of the leader particle during stagnation in a particle swarm optimization algorithm,” Inf. Sci. 279, 18–36 (2014).
[Crossref]

Muljarov, E.

H. Sehmi, W. Langbein, and E. Muljarov, “Optimizing the Drude-Lorentz model for material permittivity: Method, program, and examples for gold, silver, and copper,” Phys. Rev. B 95(11), 115444 (2017).
[Crossref]

Nelder, J.

J. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7(4), 308–313 (1965).
[Crossref]

Nestell, J. J. E.

Olson, C.

D. W. Lynch, C. Olson, and J. Weaver, “Optical properties of Ti, Zr, and Hf from 0.15 to 30 eV,” Phys. Rev. B 11(10), 3617–3624 (1975).
[Crossref]

Onur, S.

S. Onur, S. A. Güngör, F. Tümer, and M. Tümer, “The color, photophysical and electrochemical properties of azo-imine ligands and their copper (ii) and platinium (ii) complexes,” J. Mol. Struct. 1200, 127135 (2020).
[Crossref]

Ordal, M. A.

Otto, A.

D. Barchiesi and A. Otto, “Excitations of surface plasmon polaritons by attenuated total reflection, revisited,” Riv. Nuovo Cimento 36(5), 173–209 (2013).
[Crossref]

Oughstun, K. E.

Outemzabet, R.

M. Kadi, A. Smaali, and R. Outemzabet, “Analysis of optical and related properties of tin oxide thin films determined by Drude-Lorentz model,” Surf. Coat. Technol. 211, 45–49 (2012).
[Crossref]

Palik, E. D.

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

Philipp, H.

H. Ehrenreich, H. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev. 132(5), 1918–1928 (1963).
[Crossref]

Poperenko, L.

Prokopidis, K. P.

Qu, S.

S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203(3-6), 283–288 (2002).
[Crossref]

Rachid, E.

E. Rachid, H. Hachimi, and A. ELHami, “A new hybrid genetic algorithm and particle swarm optimization,” Key Eng. Mater. 35(8), 3905–3917 (2011).
[Crossref]

Rahmat-Samii, Y.

S. Xu and Y. Rahmat-Samii, “Boundary conditions in particle swarm optimization revisited,” IEEE Trans. Antennas Propag. 55(3), 760–765 (2007).
[Crossref]

Rakic, A. D.

Rathore, G. S.

C. Sharma, G. S. Rathore, and V. Dubey, “Determination of optical constants of SnO2 thin film for display application,” Adv. Phys. Lett. 1, 38–42 (2014).

Rigneault, H.

H. Aouani, J. Wenger, D. Gérard, H. Rigneault, E. Devaux, T. W. Ebbesen, F. Mahdavi, T. Xu, and S. Blair, “Crucial role of the adhesion layer on the plasmonic fluorescence enhancement,” ACS Nano 3(7), 2043–2048 (2009).
[Crossref]

Rosei, R.

M. Guerrisi, R. Rosei, and P. Winsemius, “Splitting of the interband absorption edge in Au,” Phys. Rev. B 12(2), 557–563 (1975).
[Crossref]

Schneider, J. B.

J. B. Schneider, “Understanding the finite-difference time-domain method,” https://www.eecs.wsu.edu/schneidj/ufdtd/ (request data: 29.11. 2019) (2010).

Segall, B.

H. Ehrenreich, H. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev. 132(5), 1918–1928 (1963).
[Crossref]

Sehmi, H.

H. Sehmi, W. Langbein, and E. Muljarov, “Optimizing the Drude-Lorentz model for material permittivity: Method, program, and examples for gold, silver, and copper,” Phys. Rev. B 95(11), 115444 (2017).
[Crossref]

Selvi, V.

V. Selvi and R. Umarani, “Comparative analysis of ant colony and particle swarm optimization techniques,” Int. J. Comput. Appl. 5(4), 1–6 (2010).
[Crossref]

Sharma, C.

C. Sharma, G. S. Rathore, and V. Dubey, “Determination of optical constants of SnO2 thin film for display application,” Adv. Phys. Lett. 1, 38–42 (2014).

Shi, Y.

Y. Shi and R. Eberhart, “A modified particle swarm optimizer," 1998 IEEE International Conference on Evolutionary Computation Proceedings, IEEE World Congress On Computational Intelligence (Cat. No. 98TH8360), (IEEE, 1998), pp. 69–73.

Shultz, L. G.

Smaali, A.

M. Kadi, A. Smaali, and R. Outemzabet, “Analysis of optical and related properties of tin oxide thin films determined by Drude-Lorentz model,” Surf. Coat. Technol. 211, 45–49 (2012).
[Crossref]

Smith, N.

R. Lässer and N. Smith, “Interband optical transitions in gold in the photon energy range 2–25 eV,” Solid State Commun. 37(6), 507–509 (1981).
[Crossref]

Song, Y.

S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203(3-6), 283–288 (2002).
[Crossref]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005), 3rd ed.

Tangherlini, F. R.

Toury, T.

F. Colas, D. Barchiesi, S. Kessentini, T. Toury, and M. Lamy de la Chapelle, “Comparison of adhesion layers of gold on silicate glasses for SERS detection,” J. Opt. 17(11), 114010 (2015).
[Crossref]

Tümer, F.

S. Onur, S. A. Güngör, F. Tümer, and M. Tümer, “The color, photophysical and electrochemical properties of azo-imine ligands and their copper (ii) and platinium (ii) complexes,” J. Mol. Struct. 1200, 127135 (2020).
[Crossref]

Tümer, M.

S. Onur, S. A. Güngör, F. Tümer, and M. Tümer, “The color, photophysical and electrochemical properties of azo-imine ligands and their copper (ii) and platinium (ii) complexes,” J. Mol. Struct. 1200, 127135 (2020).
[Crossref]

Umarani, R.

V. Selvi and R. Umarani, “Comparative analysis of ant colony and particle swarm optimization techniques,” Int. J. Comput. Appl. 5(4), 1–6 (2010).
[Crossref]

Vial, A.

A. Vial, “Implementation of the critical points model in the recursive convolution method for modeling dispersive media with the finite-difference time domain method,” J. Opt. A: Pure Appl. Opt. 9(7), 745–748 (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]

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]

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy 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(8), 085416 (2005).
[Crossref]

Wang, Y.

S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203(3-6), 283–288 (2002).
[Crossref]

Ward, C. A.

Weaver, J.

D. W. Lynch, C. Olson, and J. Weaver, “Optical properties of Ti, Zr, and Hf from 0.15 to 30 eV,” Phys. Rev. B 11(10), 3617–3624 (1975).
[Crossref]

Weaver, J. H.

Wenger, J.

H. Aouani, J. Wenger, D. Gérard, H. Rigneault, E. Devaux, T. W. Ebbesen, F. Mahdavi, T. Xu, and S. Blair, “Crucial role of the adhesion layer on the plasmonic fluorescence enhancement,” ACS Nano 3(7), 2043–2048 (2009).
[Crossref]

Werner, W. S. M.

W. S. M. Werner, K. Glantschnig, and C. Ambrosch-Draxl, “Optical constants and inelastic electron-scattering data for 17 elemental metals,” J. Phys. Chem. 38(4), 1013–1092 (2009).
[Crossref]

Winsemius, P.

M. Guerrisi, R. Rosei, and P. Winsemius, “Splitting of the interband absorption edge in Au,” Phys. Rev. B 12(2), 557–563 (1975).
[Crossref]

Xu, S.

S. Xu and Y. Rahmat-Samii, “Boundary conditions in particle swarm optimization revisited,” IEEE Trans. Antennas Propag. 55(3), 760–765 (2007).
[Crossref]

Xu, T.

H. Aouani, J. Wenger, D. Gérard, H. Rigneault, E. Devaux, T. W. Ebbesen, F. Mahdavi, T. Xu, and S. Blair, “Crucial role of the adhesion layer on the plasmonic fluorescence enhancement,” ACS Nano 3(7), 2043–2048 (2009).
[Crossref]

Xun, l.

Zhang, X.

S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203(3-6), 283–288 (2002).
[Crossref]

Zhou, D.

Zhu, D.

S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203(3-6), 283–288 (2002).
[Crossref]

Zografopoulos, D. C.

ACS Nano (1)

H. Aouani, J. Wenger, D. Gérard, H. Rigneault, E. Devaux, T. W. Ebbesen, F. Mahdavi, T. Xu, and S. Blair, “Crucial role of the adhesion layer on the plasmonic fluorescence enhancement,” ACS Nano 3(7), 2043–2048 (2009).
[Crossref]

Adv. Phys. Lett. (1)

C. Sharma, G. S. Rathore, and V. Dubey, “Determination of optical constants of SnO2 thin film for display application,” Adv. Phys. Lett. 1, 38–42 (2014).

Ann. Phys. (1)

P. Drude, “Zur elektrontheorie des metalle,” Ann. Phys. 306(3), 566–613 (1900).
[Crossref]

Appl. Opt. (5)

Comput. J. (1)

J. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7(4), 308–313 (1965).
[Crossref]

IEEE Trans. Antennas Propag. (2)

S. Xu and Y. Rahmat-Samii, “Boundary conditions in particle swarm optimization revisited,” IEEE Trans. Antennas Propag. 55(3), 760–765 (2007).
[Crossref]

K. A. Michalski, “On the low-order partial-fraction fitting of dielectric functions at optical wavelengths,” IEEE Trans. Antennas Propag. 61(12), 6128–6135 (2013).
[Crossref]

Inf. Sci. (1)

S. Chatterjee, D. Goswami, S. Mukherjee, and S. Das, “Behavioral analysis of the leader particle during stagnation in a particle swarm optimization algorithm,” Inf. Sci. 279, 18–36 (2014).
[Crossref]

Int. J. Comput. Appl. (1)

V. Selvi and R. Umarani, “Comparative analysis of ant colony and particle swarm optimization techniques,” Int. J. Comput. Appl. 5(4), 1–6 (2010).
[Crossref]

J. Colloid Interface Sci. (1)

C. Grosse, “A program for the fitting of Debye, Cole–Cole, Cole–Davidson, and Havriliak–Negami dispersions to dielectric data,” J. Colloid Interface Sci. 419, 102–106 (2014).
[Crossref]

J. Electromagn. Waves Appl. (1)

D. Liu and K. Michalski, “Comparative study of bio-inspired optimization algorithms and their application to dielectric function fitting,” J. Electromagn. Waves Appl. 30(14), 1885–1894 (2016).
[Crossref]

J. Lightwave Technol. (2)

J. Microsc. (1)

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics the plasmon localization,” J. Microsc. 229(3), 525–532 (2008).
[Crossref]

J. Mol. Struct. (1)

S. Onur, S. A. Güngör, F. Tümer, and M. Tümer, “The color, photophysical and electrochemical properties of azo-imine ligands and their copper (ii) and platinium (ii) complexes,” J. Mol. Struct. 1200, 127135 (2020).
[Crossref]

J. Nanophotonics (2)

D. Barchiesi and T. Grosges, “Errata fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 089996 (2015).
[Crossref]

D. Barchiesi and T. Grosges, “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 089996 (2015).
[Crossref]

J. Opt. (1)

F. Colas, D. Barchiesi, S. Kessentini, T. Toury, and M. Lamy de la Chapelle, “Comparison of adhesion layers of gold on silicate glasses for SERS detection,” J. Opt. 17(11), 114010 (2015).
[Crossref]

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

A. Vial, “Implementation of the critical points model in the recursive convolution method for modeling dispersive media with the finite-difference time domain method,” J. Opt. A: Pure Appl. Opt. 9(7), 745–748 (2007).
[Crossref]

J. Opt. Soc. Am. (2)

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

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

J. Phys. Chem. (1)

W. S. M. Werner, K. Glantschnig, and C. Ambrosch-Draxl, “Optical constants and inelastic electron-scattering data for 17 elemental metals,” J. Phys. Chem. 38(4), 1013–1092 (2009).
[Crossref]

J. Phys. D: Appl. Phys. (3)

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]

M. Garcia, “Surface plasmons in metallic nanoparticles: Fundamentals and applications,” J. Phys. D: Appl. Phys. 44(28), 283001 (2011).
[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]

Key Eng. Mater. (1)

E. Rachid, H. Hachimi, and A. ELHami, “A new hybrid genetic algorithm and particle swarm optimization,” Key Eng. Mater. 35(8), 3905–3917 (2011).
[Crossref]

Opt. Commun. (2)

M. Gilliot, “Errors in ellipsometry data fitting,” Opt. Commun. 427, 477–484 (2018).
[Crossref]

S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203(3-6), 283–288 (2002).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. (1)

H. Ehrenreich, H. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev. 132(5), 1918–1928 (1963).
[Crossref]

Phys. Rev. B (5)

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy 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(8), 085416 (2005).
[Crossref]

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

H. Sehmi, W. Langbein, and E. Muljarov, “Optimizing the Drude-Lorentz model for material permittivity: Method, program, and examples for gold, silver, and copper,” Phys. Rev. B 95(11), 115444 (2017).
[Crossref]

D. W. Lynch, C. Olson, and J. Weaver, “Optical properties of Ti, Zr, and Hf from 0.15 to 30 eV,” Phys. Rev. B 11(10), 3617–3624 (1975).
[Crossref]

M. Guerrisi, R. Rosei, and P. Winsemius, “Splitting of the interband absorption edge in Au,” Phys. Rev. B 12(2), 557–563 (1975).
[Crossref]

Riv. Nuovo Cimento (1)

D. Barchiesi and A. Otto, “Excitations of surface plasmon polaritons by attenuated total reflection, revisited,” Riv. Nuovo Cimento 36(5), 173–209 (2013).
[Crossref]

Solid State Commun. (1)

R. Lässer and N. Smith, “Interband optical transitions in gold in the photon energy range 2–25 eV,” Solid State Commun. 37(6), 507–509 (1981).
[Crossref]

Surf. Coat. Technol. (1)

M. Kadi, A. Smaali, and R. Outemzabet, “Analysis of optical and related properties of tin oxide thin films determined by Drude-Lorentz model,” Surf. Coat. Technol. 211, 45–49 (2012).
[Crossref]

Thin Solid Films (1)

L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films 520(1), 501–509 (2011).
[Crossref]

Other (10)

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

https://refractiveindex.info (2016).

“Optical data from Sopra SA,” http://www.sspectra.com/sopra.html .

J. B. Schneider, “Understanding the finite-difference time-domain method,” https://www.eecs.wsu.edu/schneidj/ufdtd/ (request data: 29.11. 2019) (2010).

J. Kennedy and R. Eberhart, “Particle swarm optimization," in IEEE International Conference on Neural Networks (Vol. IV) (IEEE, 1995), pp. 1942–1948.

S. Kessentini and D. Barchiesi, Nanostructured Biosensors Influence of Adhesion Layer, Roughness and Size on the LSPR A Parametric Study (INTECH Open Access, 2013), chap. 12, pp. 311–330.

C. Kittel, Introduction To Solid State Physics (Wiley, 2005), 8th ed.

Y. Shi and R. Eberhart, “A modified particle swarm optimizer," 1998 IEEE International Conference on Evolutionary Computation Proceedings, IEEE World Congress On Computational Intelligence (Cat. No. 98TH8360), (IEEE, 1998), pp. 69–73.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005), 3rd ed.

I. Almog, M. S. Bradley, and V. Bulović, “The Lorentz oscillator and its applications,” https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-007-electromagnetic-energy-from-motors-to-lasers-spring-2011/readings/MIT6_007S11_lorentz.pdf .

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.


Figures (33)

Fig. 1.
Fig. 1. Real parts of the permittivity of gold $\epsilon _{Ref}$ [4] (o), [39] (+), [21] ( $\square$ ) and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 12.
Fig. 2.
Fig. 2. Error on the real part of fits [39] (+), [21] ( $\square$ ), $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ).
Fig. 3.
Fig. 3. Imaginary parts of the permittivity of gold $\epsilon _{Ref}$ [4] (o), [39] (+), [21] ( $\square$ ) and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 12.
Fig. 4.
Fig. 4. Error on the imaginary part of fits [39] (+), [21] ( $\square$ ), $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ).
Fig. 5.
Fig. 5. Imaginary parts of the permittivity of gold $\epsilon _{Ref}$ [4] ( $o$ ), and contributions of each Drude-Lorentz term for the best solution obtained at step 2 (- -) and at step 3 (-). The parameters used at step 3 can be found in Table 1 ( $NDL=9$ ).
Fig. 6.
Fig. 6. Real parts of the permittivity of silver $\epsilon _{Ref}$ [11] (o) and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line. The parameters can be found in Tables 34.
Fig. 7.
Fig. 7. Error on fits of the real part of the permittivity of silver $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.
Fig. 8.
Fig. 8. (a) Imaginary parts of the permittivity of silver $\epsilon _{Ref}$ [11] (o) and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line. (b) Error on fits. The parameters can be found in Tables 34.
Fig. 9.
Fig. 9. Error on fits of the imaginary part of the permittivity of silver $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.
Fig. 10.
Fig. 10. Real parts of the permittivity of gold $\epsilon _{Ref}$ [11] (o), and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 56.
Fig. 11.
Fig. 11. Error on fits of the real part of the permittivity of gold $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.
Fig. 12.
Fig. 12. Imaginary parts of the permittivity of gold $\epsilon _{Ref}$ [11] (o), and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 56.
Fig. 13.
Fig. 13. Error on fits of the imaginary part of the permittivity of gold $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.
Fig. 14.
Fig. 14. Real parts of the permittivity of copper $\epsilon _{Ref}$ [11] (o), and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 78.
Fig. 15.
Fig. 15. Error on fits of the real part of the permittivity of copper $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.
Fig. 16.
Fig. 16. Imaginary parts of the permittivity of copper $\epsilon _{Ref}$ [11] (o), and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 78.
Fig. 17.
Fig. 17. Error on fits of the imaginary part of the permittivity of copper $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.
Fig. 18.
Fig. 18. Real parts of the permittivity of aluminum $\epsilon _{Ref}$ [11] (o), and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 910.
Fig. 19.
Fig. 19. Error on fits of the real part of the permittivity of aluminum $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.
Fig. 20.
Fig. 20. Imaginary parts of the permittivity of aluminum $\epsilon _{Ref}$ [11] (o), and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 910.
Fig. 21.
Fig. 21. Error on fits of the imaginary part of the permittivity of aluminum $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.
Fig. 22.
Fig. 22. Real parts of the permittivity of chromium $\epsilon _{Ref}$ [11] (o), and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 1112.
Fig. 23.
Fig. 23. Error on fits of the real part of the permittivity of chromium $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.
Fig. 24.
Fig. 24. Imaginary parts of the permittivity of chromium $\epsilon _{Ref}$ [11] (o), and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 1112.
Fig. 25.
Fig. 25. Error on fits of the imaginary part of the permittivity of chromium $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.
Fig. 26.
Fig. 26. Real parts of the permittivity of platinum $\epsilon _{Ref}$ [11] (o), and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 1314.
Fig. 27.
Fig. 27. Error on fits of the real part of the permittivity of platinum $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.
Fig. 28.
Fig. 28. Imaginary parts of the permittivity of platinum $\epsilon _{Ref}$ [11] (o), and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 1314.
Fig. 29.
Fig. 29. Error on fits of the imaginary part of the permittivity of platinum $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.
Fig. 30.
Fig. 30. Real parts of the permittivity of titanium $\epsilon _{Ref}$ [11] (o), and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 1516.
Fig. 31.
Fig. 31. Error on fits of the real part of the permittivity of titanium $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.
Fig. 32.
Fig. 32. Imaginary parts of the permittivity of titanium $\epsilon _{Ref}$ [11] (o), and best fits for $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and PF (dashed line) ( $NPF=4$ ). The parameters can be found in Tables 1516.
Fig. 33.
Fig. 33. Error on fits of the imaginary part of the permittivity of titanium $\epsilon _{Ref}$ [11] with $NDL=9$ (thick solid line), $NDL=5$ (thin solid line), and $NPF=4$ dashed line.

Tables (17)

Tables Icon

Table 1. Best fits of ϵ A u [4] with N D L = 9 and N D L = 5 terms in the Drude-Lorentz model (Eq. (1)).

Tables Icon

Table 2. Best fit of ϵ A u [4] with 4 terms in the Partial-Fraction model (Eq. (2), N P F = 4 ).

Tables Icon

Table 3. Best fit of ϵ A g [11] with N D L = 9 and 5 terms in the Drude-Lorentz model (Eq. (1)).

Tables Icon

Table 4. Best fit of ϵ A g [11] with 4 terms in the Partial-Fraction model (Eq. (2), N P F = 4 ).

Tables Icon

Table 5. Best fit of ϵ A u [11] with N D L = 9 and 5 terms in the Drude-Lorentz model (Eq. (1)).

Tables Icon

Table 6. Best fit of ϵ A u [11] with 4 terms in the Partial-Fraction model (Eq. (2), N P F = 4 ).

Tables Icon

Table 7. Best fit of ϵ C u [11] with N D L = 9 and 5 terms in the Drude-Lorentz model (Eq. (1)).

Tables Icon

Table 8. Best fit of ϵ C u [11] with 4 terms in the Partial-Fraction model (Eq. (2), N P F = 4 ).

Tables Icon

Table 9. Best fit of ϵ A l [11] with N D L = 9 and 5 terms in the Drude-Lorentz model (Eq. (1)).

Tables Icon

Table 10. Best fit of ϵ A l [11] with 4 terms in the Partial-Fraction model (Eq. (2), N P F = 4 ).

Tables Icon

Table 11. Best fits of ϵ C r [11] with N D L = 9 and 5 terms in the Drude-Lorentz model (Eq. (1)).

Tables Icon

Table 12. Best fit of ϵ C r [11] with 4 terms in the Partial-Fraction model (Eq. (2), N P F = 4 ).

Tables Icon

Table 13. Best fit of ϵ P t [11] with N D L = 9 and 5 terms in the Drude-Lorentz model (Eq. (1)).

Tables Icon

Table 14. Best fit of ϵ P t [11] with 4 terms in the Partial-Fraction model (Eq. (2), N P F = 4 ).

Tables Icon

Table 15. Best fits of ϵ T i [11] with N D L = 9 and 5 terms in the Drude-Lorentz model (Eq. (1)).

Tables Icon

Table 16. Best fit of ϵ T i [11] with 4 terms in the Partial-Fraction model (Eq. (2), N P F = 4 ).

Tables Icon

Table 17. Summary of the results of fits.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

ε D L ( ω ) = ε i = 1 N D L A i 2 ω 2 ω i 2 + ı | Γ i | ω ,
ϵ P F ( ω ) = ϵ + i = 1 N P F c i ı ω p i + c i ı ω p i
Φ ( ω j ) = ε D L ( ω j ) ε R e f ( ω j ) ,
F = C 0 j = 1 N ω | C 1 ( Φ ( ω j ) ) | 2 + | C 2 ( Φ ( ω j ) ) | 2 2 N ω ( D + 1 ) ,
C = | ϵ ϵ + χ 0 | < 1.
χ 0 = ( ω i Γ i ) 2 ( 1 exp ( Γ i Δ t ) ) + ω i 2 Γ D Δ t + i = 1 N D L ( ı η α ı β ( 1 exp ( ( α + ı β ) Δ t ) ) ) .
χ 0 = i = 1 N P L ( 2 c i p i ( 1 exp ( ( ( p i ) + ı ( p i ) ) Δ t ) ) ) .
x i ( t + 1 ) = x i ( t ) + v i ( t + 1 ) ,
v i ( t + 1 ) = ω v i ( t ) + U 1 c 1 ( p i ( t ) x i ( t ) ) + U 2 c 2 ( g ( t ) x i ( t ) ) ,
n r e a l = N 1 ( 0.975 ) 2 / 0.06 2 1000 ,
S ( ω i ) = m ( ω i ) σ ( ω i )

Metrics