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  regarding our recent modeling of the optical response of periodically structured metallic films  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 [3,4], including one published by M. Nevière , 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.  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.  or clearly observed for example in the recent experimental work of K. G. Lee et al. .
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 . 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 .
In conclusion, in agreement with previously reported works [3, 4] the truncated one-dimensional RCW method, which we used in our work , 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.
We acknowledge fruitful email exchange with Prof. M. Nevière during the course of writing this comment.
References and links
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]
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]