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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 14 — Jul. 10, 2006
  • pp: 6586–6587
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Analytical model of the optical response of periodically structured metallic films: Reply

Abdelkrim Benabbas, Valérie Halté, and Jean-Yves Bigot  »View Author Affiliations


Optics Express, Vol. 14, Issue 14, pp. 6586-6587 (2006)
http://dx.doi.org/10.1364/OE.14.006586


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Abstract

Some remarks are made on the validity of a commonly used analytical model based on the rigorous coupled wave analysis to describe the optical response of one-dimensional metallic gratings.

© 2006 Optical Society of America

The purpose of this comment is to reply the one of E. Popov and M. Nevière [1

1. E. Popov and M. Nevière, “Analytical model of the optical response of periodically structured metallic films: Comment,” Opt. Express14, (2006). [CrossRef] [PubMed]

] regarding our recent modeling of the optical response of periodically structured metallic films [2

2. A. Benabbas, V. Halté, and J.-Y. Bigot, “Analytical model of the optical response of periodically structured metallic films,” Opt. Express 13, 8730–8745 (2005). [CrossRef] [PubMed]

] and to precise the conditions of validity of this model. Several remarks are raised by these authors who used a rigorous numerical approach to determine the applicability of the truncated rigorous coupled wave (RCW) theory that we used. Let us first dissipate any misunderstanding by making a semantic remark. Prior to our work several other recent articles [3

3. S. A. Damanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003). [CrossRef]

,4

4. S. A. Damanyan, M. Nevière, and A. V. Zayats, “Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes,” Phys. Rev. B 70, 075103 (2004). [CrossRef]

], including one published by M. Nevière [4

4. S. A. Damanyan, M. Nevière, and A. V. Zayats, “Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes,” Phys. Rev. B 70, 075103 (2004). [CrossRef]

], have qualified as “analytical” the theory consisting in extracting expressions of the diffraction efficiencies of TM polarized electromagnetic waves illuminating a one dimensional grating. Strictly speaking the word analytical can be somehow misleading since the theory used relies on a truncation of the Fourier series of the periodic dielectric function of the structure as well as of the electromagnetic fields in the different media (metal, substrate and surrounding). Therefore it should rather be named approximate analytical method. To go along with the previously named studies we have also used this terminology.

Regarding the limitations of the truncated RCW model, we fully agree that it is not suited for treating the diffraction of light by periodic slits in metallic films. That was not the purpose of our work. Indeed, as specified at the beginning of Section 2 in ref. [2

2. A. Benabbas, V. Halté, and J.-Y. Bigot, “Analytical model of the optical response of periodically structured metallic films,” Opt. Express 13, 8730–8745 (2005). [CrossRef] [PubMed]

] and second sentence of the abstract, we did not consider the case of a lamellar grating but rather the case of a one-dimensional grating surrounded by two different dielectric media. In addition, it is correct that the two approximations consisting in using a sinusoidal modulation for the dielectric function of the nanostructure and in truncating the expansions to first order also have strong limitations. This has been unambiguously stated by S. Darmanyan and A.V. Zayats in section IV of Ref. [3

3. S. A. Damanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003). [CrossRef]

] or clearly observed for example in the recent experimental work of K. G. Lee et al. [5

5. K G. Lee and Q-Han Park, “Coupling of surface plasmons polaritons and light in metallic nanoslits”, Phys. Rev. Lett. 95, 103902 (2005). [CrossRef] [PubMed]

].

More importantly, the spirit of our article is not to predict the exact positions and amplitudes of the nanostructure resonance. It rather serves the two following purposes. First, it is a simple tractable model which allows giving a physical picture of important features associated to surface plasmon polaritons like: the Fano line shape of the transmission, the coupling between the two surface plasmons as well as the non-reciprocity of the reflectivity upon excitation from each side of the nanostructure. Second, it allows going further in the description of metallic nanostructures designed such that the spectral positions of the resonances lie close to the interband transition of the metal. Indeed, in the case of arrays of holes in noble metals, it turns out that the role of the interband transitions (d-EFermi) is essential to obtain the positions of the surface plasmon-polariton resonances [6

6. V. Halté, A. Benabbas, and J.-Y. Bigot, “Optical response of periodically modulated nanostructures near the interband transition threshold of noble metal,” Opt. Express 14, 2909–2920 (2006). [CrossRef] [PubMed]

]. In that work we show the important role played by the dielectric function of the metal for the static response of the nanostructure. It is also crucial when the dynamics of the electrons at the Fermi level is involved. This is notably the case when modeling time resolved femtosecond experiments [7

7. V. Halté, A. Benabbas, L. Guidoni, and J.-Y. Bigot,“Femtosecond dynamics of the transmission of gold arrays of subwavelength holes,” Phys. Stat. Sol. B 242, 1872–1876 (2005). [CrossRef]

].

In conclusion, in agreement with previously reported works [3

3. S. A. Damanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003). [CrossRef]

, 4

4. S. A. Damanyan, M. Nevière, and A. V. Zayats, “Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes,” Phys. Rev. B 70, 075103 (2004). [CrossRef]

] the truncated one-dimensional RCW method, which we used in our work [2

2. A. Benabbas, V. Halté, and J.-Y. Bigot, “Analytical model of the optical response of periodically structured metallic films,” Opt. Express 13, 8730–8745 (2005). [CrossRef] [PubMed]

], provides a convenient and simple way to predict some features of the light transmission through periodically structured metallic films as long as some precautions are taken. In addition, it becomes particularly useful when one needs to get physical insights into the new features associated to the specific electronic structure of the metal or to dynamical effects resulting from strong perturbations of the electron gas induced by ultrashort optical pulses.

Acknowledgements

We acknowledge fruitful email exchange with Prof. M. Nevière during the course of writing this comment.

References and links

1.

E. Popov and M. Nevière, “Analytical model of the optical response of periodically structured metallic films: Comment,” Opt. Express14, (2006). [CrossRef] [PubMed]

2.

A. Benabbas, V. Halté, and J.-Y. Bigot, “Analytical model of the optical response of periodically structured metallic films,” Opt. Express 13, 8730–8745 (2005). [CrossRef] [PubMed]

3.

S. A. Damanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003). [CrossRef]

4.

S. A. Damanyan, M. Nevière, and A. V. Zayats, “Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes,” Phys. Rev. B 70, 075103 (2004). [CrossRef]

5.

K G. Lee and Q-Han Park, “Coupling of surface plasmons polaritons and light in metallic nanoslits”, Phys. Rev. Lett. 95, 103902 (2005). [CrossRef] [PubMed]

6.

V. Halté, A. Benabbas, and J.-Y. Bigot, “Optical response of periodically modulated nanostructures near the interband transition threshold of noble metal,” Opt. Express 14, 2909–2920 (2006). [CrossRef] [PubMed]

7.

V. Halté, A. Benabbas, L. Guidoni, and J.-Y. Bigot,“Femtosecond dynamics of the transmission of gold arrays of subwavelength holes,” Phys. Stat. Sol. B 242, 1872–1876 (2005). [CrossRef]

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(240.0240) Optics at surfaces : Optics at surfaces
(240.6680) Optics at surfaces : Surface plasmons
(240.7040) Optics at surfaces : Tunneling

ToC Category:
Comment and Reply

History
Original Manuscript: March 1, 2006
Manuscript Accepted: April 14, 2006
Published: July 10, 2006

Citation
Abdelkrim Benabbas, Valérie Halté, and Jean-Yves Bigot, "Analytical model of the optical response of periodically structured metallic films: Reply," Opt. Express 14, 6586-6587 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-14-6586


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References

  1. E. Popov, and M. Nevière, "Analytical model of the optical response of periodically structured metallic films: Comment," Opt. Express 14, (2006). [CrossRef] [PubMed]
  2. A. Benabbas, V. Halté, and J.-Y. Bigot, "Analytical model of the optical response of periodically structured metallic films," Opt. Express 13,8730-8745 (2005). [CrossRef] [PubMed]
  3. S. A. Damanyan and A. V. Zayats, "Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study," Phys. Rev. B 67, 035424 (2003). [CrossRef]
  4. S. A. Damanyan, M. Nevière, and A. V. Zayats, "Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes," Phys. Rev. B 70, 075103 (2004). [CrossRef]
  5. K G. Lee, and Q-Han Park, "Coupling of surface plasmons polaritons and light in metallic nanoslits", Phys. Rev. Lett. 95, 103902 (2005). [CrossRef] [PubMed]
  6. V. Halté, A. Benabbas, and J.-Y. Bigot, "Optical response of periodically modulated nanostructures near the interband transition threshold of noble metal," Opt. Express 14,2909-2920 (2006). [CrossRef] [PubMed]
  7. V. Halté, A. Benabbas, L. Guidoni and J.-Y. Bigot,"Femtosecond dynamics of the transmission of gold arrays of subwavelength holes," Phys. Stat. Sol. B 242, 1872-1876 (2005). [CrossRef]

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