BESBES, M

Bienstman, Peter

HUGONIN, JP

LALANNE, P

English

Ghent University Academic Bibliography

CORRESPONDENCE792 nature physics | VOL 2 | DECEMBER 2006 | www.nature.com/naturephysicsTHE RESPONSE OF NANOSTRUCTURED SURFACES IN THE NEAR FIELDARISING FROM: P. LALANNE & J. P. HUGONIN, NATURE PHYS. 2, 551–558 (2006)To the Editors — Th e authors of ref. 1 state that their numerical calculation of the transmission intensity dependence of very simple subwavelength planar structures in a silver fi lm agrees well with an earlier-developed model2, but both model and numerical simulation show signifi cant disagreement with the experimental results of ref. 3. Th e authors1 speculate that the silver surfaces of the subwavelength structures used in ref. 3 were contaminated by an 11 nm overlayer of silver sulphide, because such a layer would bring the reported experimental results and their calculations into better agreement.We have analysed the physical–chemical surface properties of the single-slit, single-groove subwavelength-structured silver fi lms used in the experiments with high-resolution transmission electron microscopy (HRTEM), and we have calculated fully vectorial numerical solutions to Maxwell’s equations for the relevant structures using the fi nite-diff erence-time-domain (FDTD) technique4. Th e HRTEM analysis shows that the silver fi lms are free of detectable contaminants with a detection limit orders of magnitude below the 11 nm layer suggested by ref. 1. Furthermore, the FDTD calculations are in excellent agreement with experiment (Fig. 1a), showing a rapid fringe amplitude decrease in the near-zone (slit–groove distance out to 3–4 wavelengths). Extended FDTD calculations to slit–groove distances beyond the near-zone (Fig. 1b) show that the surface wave evolves to the expected bound surface plasmon polariton (SPP). Th e key fi nding is that a surface wave in the near-zone consists of a distribution of transient surface modes adjacent and in addition to the bound SPP. Beyond the near-zone the results confi rm that the transients dissipate with only the bound SPP mode surviving. Th is result has important implications for the interpretation of light transmission through arrays of subwavelength structures with subwavelength pitch. Th e common assumption that only the SPP mode is populated over the entire surface is not justifi ed in the near-zone.REFERENCES1. Lalanne, P. & Hugonin, J. P. Nature Phys. 2, 551–558 (2006).2. Lalanne, P., Hugonin, J. P. & Rodier, J. C. Phys. Rev. Lett. 95, 263902 (2005).3. Gay, G. et al. Nature Phys. 2, 262–267 (2006).4. Gay, G. et al. Preprint at <http://arxiv.org/physics/0608116> (2006).G. Gay1, O. Alloschery1, J. Weiner1*, H. J. Lezec2,3, C. O’Dwyer4, M. Sukharev5 & T. Seideman51IRSAMC/LCAR Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France.2Applied Physics, Caltech, Pasadena, California 91125, USA.3CNRS, 75794 Paris, France.4Tyndall National Institute, University College Cork, Cork, Ireland.5Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA.*e-mail: jweiner@irsamc.ups-tlse.frAuthors’ reponse — Because Maxwell’s equations for linear dielectric materials are exact, computation plays a crucial role in the analysis of light scattering by subwavelength structures. In ref. 1, two of the present authors use a fully vectorial method to analyse the normalized coupled power |S|2/|S0|2 into the fundamental propagating slit mode of a slit–groove geometry in a silver fi lm previously studied in ref. 2, see Fig. 1a. In agreement with the experimental results2, |S|2/|S0|2 exhibits an oscillatory behaviour as a function of the slit–groove distance d (Fig. 1b). However, the theoretical oscillation frequency, which perfectly matches the propagation constant kSP = k0(εAg/(εAg+1))1/2 of the Ag–air surface plasmon polariton (SPP), signifi cantly diff ers from the experimental one. Th us, an SPP-mediated interaction mechanism is promoted in ref 1, leading to an interpretation very diff erent from that in ref. 2.1.00.80.60.40.214 161210864202 3 4 5 6 70 1Slit–groove distance (μm)Slit–groove distance (μm)0.20.40.60.81.0Normalized intensityNormalized intemsityabFigure 1 Comparison of FDTD simulation and experiment. a, The green points are experimental data taken from ref. 3. The blue curve shows our FDTD result. b, The blue curve plots the same FDTD calculation as in a but extended to 16 μm slit–groove distance.nphys473 Weiner Correspondence.indd   792 21/11/06   3:52:19 pmNature Publishing Group ©2006CORRESPONDENCEnature physics | VOL 2 | DECEMBER 2006 | www.nature.com/naturephysics 793In the above comment, the authors provide FDTD computational results that nicely agree with the experimental results in ref. 2, and state that high-resolution TEM images show that their silver samples are basically free of detectable contaminants. Th is seems to question (1) the accuracy of the numerical results in ref. 1, and (2) the validity of the SPP-driven mechanism proposed in ref. 1.In Fig. 1b, we show computational results for the slit–groove geometry obtained with three diff erent fully vectorial frequency-domain methods. Th e black curve has been obtained with a Fourier modal method that relies on a supercell approach incorporating a complex nonlinear coordinate transform along the x coordinate3. It is the same as that in Fig. 1 in ref. 1. We have used 601 Fourier harmonics for the computation. A fi nite-element method in a commercial soft ware package4 has been used to obtain the red curve by using a space discretization with second-order nodal Whitney elements, and a refi ned mesh at the groove and slit edges and at the Ag–air interface. Th e blue curve was obtained with a local-eigenmode modal method CAMFR5. Th e method is similar to the Fourier modal method, except that the fi eld expansion uses the local eigenmodes, whose propagation constants are obtained by solving for the roots of a transcendental equation. Th e numerical results have been obtained with 300 modes and with perfectly matched layers implemented as a complex stretching6. Th e predicted oscillation amplitudes diff er from one curve to another, but remarkably in the present context, all results exactly show the same oscillation frequency kSP. To summarize, computational results obtained with three totally diff erent methods do not corroborate the FDTD results in the above comment, although the same permittivity and the same geometrical parameters have been used in all calculations. Th ese consistent data therefore question the accuracy of the FDTD results. Additionally, they convincingly support our initial statement that the oscillations observed in ref. 2 are essentially due to the Ag–air SPP, even for short distances. Concerning the possibility of a contamination of silver, experimental data with a gold metal are currently under progress in our laboratory.REFERENCES1. Lalanne, P. & Hugonin, J. P. Nature Phys. 2, 551–558 (2006).2. Gay, G. et al. Nature Phys. 2, 262–267 (2006).3. Silberstein, E., Lalanne, P., Hugonin, J. P. & Cao, Q. J. Opt. Soc. Am. A 18, 2865–2875 (2005).4. COMSOL Multiphysic (Electromagnetic Module); <http://www.comsol.com>.5. Bienstman, P. & Baets, R. Opt. Quant. Electron. 33, 327–341 (2001); available at <http://camfr.sourceforge.net>.6. Chew, W. C. & Weedon, W. H. Microwave Opt. Technol. Lett. 7, 599–604 (1994).P. Lalanne1*, J.P. Hugonin1, M. Besbes1 and P. Bienstman21Laboratoire Charles Fabry de l’Institut d’Optique, CNRS, Univ Paris-Sud, Campus Polytechnique, RD128, 91127 Palaiseau cedex, France.2Ghent University, Dept. of Information Technology, Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium.*e-mail: philippe.lalanne@institutoptique.fr0.61.01.41.82.2λSdab0 2 4 6d (µm)IS/S0I2Figure 1 Three totally different methods provide the same oscillation frequency for the slit–groove scattering problem and for all distances. a, Geometry under consideration. b, The black curve (same as that in Fig. 1 in ref. 1), and the red and blue curves are computational data obtained with the methods of refs 3, 4 and 5, respectively. The green crosses are experimental data from ref. 2. All computations have been obtained for εAg = –33.22 + 1.1700i as in ref. 2, for λ = 852 nm, for a groove depth and width of 100 nm. For the sake of frequency comparison, the dotted vertical lines indicate the black curve extrema.nphys473 Weiner Correspondence.indd   793 21/11/06   3:52:23 pmNature Publishing Group ©2006

The response of nanostructured surfaces in the near field - Response

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The response of nanostructured surfaces in the near field - Response

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