Errata

Errata: Fitting the optical constants of gold, silver, chromium, titanium and aluminum in the visible bandwidth

[+] Author Affiliations
Dominique Barchiesi, Thomas Grosges

Institut National de Recherche en Informatique et Automatisme (INRIA), University of Technology of Troyes (UTT), Automatic Mesh Generation and Advanced Methods (GAMMA3), 12 rue Marie Curie, CS 42060, 10004 TROYES CEDEX

J. Nanophoton. 8(1), 089996 (Jan 09, 2015). doi:10.1117/1.JNP.8.089996
History:
Text Size: A A A

Open Access Open Access

Abstract.  This paper [J. Nanophoton. 8(1), 083097 (2014)] was published on 6 January 2014. Thanks to a question by Yoann Brûlé from the Fresnel institute (Marseille, France), we found that the values of γL and γD were swapped in tables in Ref. 1. The problem comes from a bug in the automatic extraction of data from optimization method. Fortunately the curves in Ref. 1 are correct. This erratum gives a more readily available formulation of fitting for all considered metals and the corresponding criteria.

The Combination of Drude and Lorentz Models

The function of fit ϵDL of the relative permittivity of metal is written as the sum of the Drude and the Lorentz models: Display Formula

ϵDL(ω)=ϵωD2ω(ω+iγD)ΔϵωL2ω2ωL2+iγLω.(1)

In the following the angular frequency ω(rad/s) that is used in formula falls within the visible domain [2.354e15;4.709e15]rad/s, corresponding to wavelengths in [400; 800] nm and photon energy in [1.55, 3.10] eV. Outside this domain, the quality of fitting can be impaired. This erratum gives us the opportunity to give better solutions to this hard problem of fitting, by investigating a wider space of search. The values of σR and σI are calculated according formula (8-9) in1, including the number of data used to compute the fitting equation.

Gold (Johnson & Christy2)

Display Formula

ϵDLAuJC(ω)=6.15991.8160E32ω2+i7.2096E13ω4.5011E31ω22.1732E31+i1.6694E15ω,(2)
Display Formula
C=0.99995,F=0.55,σR=0.40,σI=0.38.

Gold (Palik3)

Display Formula

ϵDLAuP(ω)=0.68881.5817E33ω2+i7.3731E15ω+9.3582E32ω25.5354E30+i4.9327E15ω,(3)
Display Formula
C=0.24646,F=1.08,σR=0.95,σI=0.51.

Silver (Palik3)

Display Formula

ϵDLAgP(ω)=0.00675261.7584E32ω2+i1.0444E14ω9.9267E32ω22.6509E32+i7.3068E15ω,(4)
Display Formula
C=0.80656,F=0.07154,σR=0.053,σI=0.048.

Aluminum (Palik3)

Display Formula

ϵDLAlP(ω)=0.133139.0588E32ω2+i3.1083E15ω+5.6526E32ω21.2718E31+i6.4539E15ω,(5)
Display Formula
C=0.996,F=2.98,σR=2.49,σI=1.64.

Chromium (Palik3)

Display Formula

ϵDLCr(ω)=2.77672.5306E32ω2+i2.9966E15ω1.4736E32ω21.1087E31+i2.5764E15ω,(6)
Display Formula
C=0.9998,F=0.947,σR=0.63,σI=0.71.

Titanium (Palik3)

Display Formula

ϵDL(ω)=5.4742E73.4555E32ω2+i5.1502E15ω9.3068E54ω21.7001E47+i3.2120E24ω,(7)
Display Formula
C=0.9665,F=0.57,σR=0.47,σI=0.33.

The proposed results of fitting of relative permittivities of metals are more accurate than those proposed in a previous paper4 and verify the criterion of compatibility with FDTD use. They can be used directly for any spectroscopic simulation5,6 and especially in FDTD codes, and for plasmonics7 and optimization where accurate positions of resonances should be found. The proposed method of fitting under constraint is a combination of PSO and Nelder-mead simplex methods appears to be efficient, even if the solution of the problem of fitting is not unique.

Barchiesi  D., Grosges  T., “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophoton.. 8, (1 ), 083097  (2014). 1934-2608 CrossRef
Johnson  P. B., Christy  R. W., “Optical constants of the noble metals,” Phys. Rev. B. 6, (12 ), 4370 –4379 (1972). 0163-1829 CrossRef
Palik  E. D., Handbook of Optical Constants. ,  Academic Press Inc. ,  San Diego USA  (1985).
Vial  A., Grimault  A.-S., Macias  D., Barchiesi  D., de la Chapelle  M. Lamy, “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 –085423 (2005). 0163-1829 CrossRef
Grosges  T., Barchiesi  D., Toury  T., Gréhan  G., “Design of nanostructures for imaging and biomedical applications by plasmonic optimization,” Opt. Lett.. 33, (23 ), 2812 –2814 (2008). 0146-9592 CrossRef
Barchiesi  D., Kessentini  S., Guillot  N., de la Chapelle  M. Lamy, Grosges  T., “Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties,” Opt. Express. 21, (2 ), 2245 –2262 (2013). 1094-4087 CrossRef
Barchiesi  D., Kremer  E., Mai  V. P., Grosges  T., “A Poincaré’s approach for plasmonics: The plasmon localization,” J. Microscopy. 229, (3 ), 525 –532 (2008). 0022-2720 CrossRef

© 2014 Society of Photo-Optical Instrumentation Engineers

Citation

Dominique Barchiesi and Thomas Grosges
"Errata: Fitting the optical constants of gold, silver, chromium, titanium and aluminum in the visible bandwidth", J. Nanophoton. 8(1), 089996 (Jan 09, 2015). ; http://dx.doi.org/10.1117/1.JNP.8.089996


Figures

Tables

References

Barchiesi  D., Grosges  T., “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophoton.. 8, (1 ), 083097  (2014). 1934-2608 CrossRef
Johnson  P. B., Christy  R. W., “Optical constants of the noble metals,” Phys. Rev. B. 6, (12 ), 4370 –4379 (1972). 0163-1829 CrossRef
Palik  E. D., Handbook of Optical Constants. ,  Academic Press Inc. ,  San Diego USA  (1985).
Vial  A., Grimault  A.-S., Macias  D., Barchiesi  D., de la Chapelle  M. Lamy, “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 –085423 (2005). 0163-1829 CrossRef
Grosges  T., Barchiesi  D., Toury  T., Gréhan  G., “Design of nanostructures for imaging and biomedical applications by plasmonic optimization,” Opt. Lett.. 33, (23 ), 2812 –2814 (2008). 0146-9592 CrossRef
Barchiesi  D., Kessentini  S., Guillot  N., de la Chapelle  M. Lamy, Grosges  T., “Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties,” Opt. Express. 21, (2 ), 2245 –2262 (2013). 1094-4087 CrossRef
Barchiesi  D., Kremer  E., Mai  V. P., Grosges  T., “A Poincaré’s approach for plasmonics: The plasmon localization,” J. Microscopy. 229, (3 ), 525 –532 (2008). 0022-2720 CrossRef

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging & repositioning the boxes below.

Related Book Chapters

Topic Collections

Advertisement
  • Don't have an account?
  • Subscribe to the SPIE Digital Library
  • Create a FREE account to sign up for Digital Library content alerts and gain access to institutional subscriptions remotely.
Access This Article
Sign in or Create a personal account to Buy this article ($20 for members, $25 for non-members).
Access This Proceeding
Sign in or Create a personal account to Buy this article ($15 for members, $18 for non-members).
Access This Chapter

Access to SPIE eBooks is limited to subscribing institutions and is not available as part of a personal subscription. Print or electronic versions of individual SPIE books may be purchased via SPIE.org.