Optical resonances in the scattering of light from a nanostructured metal surface: A three-dimensional numerical study

T. V. Teperik and A. G. Borisov

Phys. Rev. B 79, 245409 – Published 8 June 2009

Abstract

We present the full three-dimensional numerical study of the scattering of light by the gold substrate composed of square periodic array of inverted pyramidal pits. The time-dependent wave-packet-propagation approach was used to extract the complete scattering matrix as well as the near fields. The role of the pit-localized and surface-supported plasmonic modes in resonant reflection spectra and field enhancement is revealed. We show that the resonances in the specular reflection arise because of the excitation of the pit-localized plasmons while resonant absorption is linked with excitation of the surface-plasmon polaritons. For certain structure parameters absorption can reach 100%. Our theoretical results are in a good agreement with recently published experimental data [N. M. B. Perney et al., Opt. Express 14, 847 (2006); Phys. Rev. B 76, 035426 (2007)]. We also show that present structure allows one to obtain zero specular reflection where all scattered intensity is redirected into the grazing beams.

Received 5 March 2009

DOI:https://doi.org/10.1103/PhysRevB.79.245409

Authors & Affiliations

T. V. Teperik^1,2,* and A. G. Borisov^2,3

¹Laboratoire Charles Fabry de l’Institut d’Optique, CNRS, Université Paris-Sud, Campus Polytechnique, RD 128, 91127 Palaiseau Cedex, France
²Donostia International Physics Center (DIPC), P. Manuel de Lardizabal 4, San Sebastián 20018, Spain
³Laboratoire des Collisions Atomiques et Moléculaires, UMR CNRS-Université Paris-Sud 8625, Bât. 351, Université Paris-Sud, 91405 Orsay Cedex, France

^*Corresponding author; tatiana.teperik@institutoptique.fr

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Issue

Vol. 79, Iss. 24 — 15 June 2009

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Images

Figure 1
(Color online) Schematic representation of the surface with square array of the inverted square pyramidal pits. Upper panel shows the cross section of the array by the $(x z)$ plane perpendicular to the surface and containing the apex of the pit. $D$ is the period of the structure, $A$ is the pit aperture, $h$ is the pit depth, and $α$ is a pit apex angle. Lower panel defines the coordinate frame. The radiation is incident along the normal to the surface (the $z$ direction).Reuse & Permissions
Figure 2
(Color online) Reflectivity of the metal surface with square array of pyramidal pits. Normal incidence. The results are shown as a function of the wavelength of the incident radiation. Panels of the figure correspond to the arrays characterized by the same period $D = 2000 nm$ and different pit aperture $A$ as indicated in the insets. Red solid line shows the calculated specular-reflection coefficient $R_{00}$ and black dashed line shows the calculated total-reflection coefficient $R$ . Experimental data from Ref. 46 is plotted with blue dots. The labeled structures correspond to localized plasmon resonances (P1 and P2) and resonances pinned to the diffraction thresholds (D1 and D2) as discussed in the text.Reuse & Permissions
Figure 3
(Color online) Same as Fig. 2, but for the pyramidal pit arrays characterized by the same pit aperture $A = 940 nm$ and different periods $D$ as indicated in the insets of each panel.Reuse & Permissions
Figure 4
(Color online) Intensity of the electromagnetic field $I = {| E_{x} |}^{2} + {| E_{y} |}^{2} + {| E_{z} |}^{2}$ as a function of the $z$ and $x$ coordinates. Results are presented in the $(x, z)$ plane perpendicular to the surface and containing the apex of the pit (see Fig. 1 for definition of the coordinate system). The metal surface is shown with white line. Different panels show the results obtained for the pit arrays characterized by the same period $D = 2000 nm$ and pit aperture $A$ indicated in the insets (in nm). The fields are extracted from the WPP calculations at the wavelengths corresponding to the diffraction (D1 and D2) and pit-localized plasmon (P1 and P2) resonances indicated in Fig. 2. The framed inset shows the intensity of the field of the P1 resonance in immediate vicinity of the metal face of the pit with $A = 1450 nm$ . L is a bisector of the pyramidal face.Reuse & Permissions
Figure 5
(Color online) $E_{z}$ component of the near field corresponding to the excitation of the pit-localized plasmons P1 and P2 for the pyramidal pit array characterized by $D = 2000 nm$ and aperture size $A = 1450 nm$ . Results are presented as a function of the $z$ and $x$ coordinates in the $(x, z)$ plane perpendicular to the surface and containing the apex of the pit (see Fig. 1 for definition of the coordinate system).Reuse & Permissions

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