We present an experimental and theoretical study of Babinet's principle of complementarity in plasmonics. We have used spatially-resolved electron energy loss spectroscopy and cathodoluminescence to investigate electromagnetic response of elementary plasmonic antenna: gold discs and complementary disc-shaped apertures in a gold layer. We have also calculated their response to the plane wave illumination. While the qualitative validity of Babinet's principle has been confirmed, quantitative differences have been found related to the energy and quality factor of the resonances and the magnitude of related near fields. In particular, apertures were found to exhibit stronger interaction with the electron beam than solid antennas, which makes them a remarkable alternative of the usual plasmonic-antennas design. We also examine the possibility of magnetic near field imaging based on the Babinet's principle.

Central European Institute of Technology Brno University of Technology Purkyňova 123 612 00 Brno Czech Republic

Institute of Physical Engineering Brno University of Technology Technická 2 616 69 Brno Czech Republic

Institute of Scientific Instruments Czech Academy of Sciences Královopolská 147 612 00 Brno Czech Republic

Materials Physics Center CSIC UPV EHU Paseo Manuel de Lardizabal 5 20018 San Sebastián Spain

University Service Centre for Transmission Electron Microscopy TU Wien Wiedner Hauptstraße 8 10 1040 Wien Austria

Zobrazit více v PubMed

Novotny L, van Hulst N. Antennas for light. Nat. Photonics. 2011;5:83. doi: 10.1038/nphoton.2010.237. DOI

Schuller JA, et al. Plasmonics for extreme light concentration and manipulation. Nat. Mater. 2010;9:193. doi: 10.1038/nmat2630. PubMed DOI

Benz F, et al. Single-molecule optomechanics in “picocavities”. Sci. 2016;354:726–729. doi: 10.1126/science.aah5243. PubMed DOI

Kelly KL, Coronado E, Zhao LL, Schatz GC. The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment. The J. Phys. Chem. B. 2003;107:668–677. doi: 10.1021/jp026731y. DOI

Anderson MS. Locally enhanced Raman spectroscopy with an atomic force microscope. Appl. Phys. Lett. 2000;76:3130–3132. doi: 10.1063/1.126546. DOI

Anger P, Bharadwaj P, Novotny L. Enhancement and quenching of single-molecule fluorescence. Phys. Rev. Lett. 2006;96:113002. doi: 10.1103/PhysRevLett.96.113002. PubMed DOI

Atwater HA, Polman A. Plasmonics for improved photovoltaic devices. Nat. Mater. 2010;9:205. doi: 10.1038/nmat2629. PubMed DOI

Farahani JN, Pohl DW, Eisler H-J, Hecht B. Single quantum dot coupled to a scanning optical antenna: A tunable superemitter. Phys. Rev. Lett. 2005;95:017402. doi: 10.1103/PhysRevLett.95.017402. PubMed DOI

Pfeiffer M, et al. Enhancing the optical excitation efficiency of a single self-assembled quantum dot with a plasmonic nanoantenna. Nano Lett. 2010;10:4555–4558. doi: 10.1021/nl102548t. PubMed DOI

Cheng F, et al. Enhanced photoluminescence of monolayer WS2 on Ag films and nanowire-WS2-film composites. ACS Photonics. 2017;4:1421–1430. doi: 10.1021/acsphotonics.7b00152. DOI

Born, M., Wolf, E. & Bhatia, A. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).

Falcone F, et al. Babinet principle applied to the design of metasurfaces and metamaterials. Phys. Rev. Lett. 2004;93:197401. doi: 10.1103/PhysRevLett.93.197401. PubMed DOI

Zentgraf T, et al. Babinet’s principle for optical frequency metamaterials and nanoantennas. Phys. Rev. B. 2007;76:033407. doi: 10.1103/PhysRevB.76.033407. DOI

Chen H-T, et al. Complementary planar terahertz metamaterials. Opt. Express. 2007;15:1084–1095. doi: 10.1364/OE.15.001084. PubMed DOI

Hand TH, Gollub J, Sajuyigbe S, Smith DR, Cummer SA. Characterization of complementary electric field coupled resonant surfaces. Appl. Phys. Lett. 2008;93:212504. doi: 10.1063/1.3037215. DOI

Hentschel M, Weiss T, Bagheri S, Giessen H. Babinet to the half: Coupling of solid and inverse plasmonic structures. Nano Lett. 2013;13:4428–4433. doi: 10.1021/nl402269h. PubMed DOI

Kim J, et al. Babinet-inverted optical Yagi–Uda antenna for unidirectional radiation to free space. Nano Lett. 2014;14:3072–3078. doi: 10.1021/nl500062f. PubMed DOI

Taminiau TH, Karaveli S, van Hulst NF, Zia R. Quantifying the magnetic nature of light emission. Nat. Commun. 2012;3:979. doi: 10.1038/ncomms1984. PubMed DOI

Feth N, et al. Second-harmonic generation from complementary split-ring resonators. Opt. Lett. 2008;33:1975–1977. doi: 10.1364/OL.33.001975. PubMed DOI

Sannomiya T, Scholder O, Jefimovs K, Hafner C, Dahlin AB. Investigation of plasmon resonances in metal films with nanohole arrays for biosensing applications. Small. 2011;7:1653–1663. doi: 10.1002/smll.201002228. PubMed DOI

Huck C, et al. Plasmonic enhancement of infrared vibrational signals: Nanoslits versus nanorods. ACS Photonics. 2015;2:1489–1497. doi: 10.1021/acsphotonics.5b00390. DOI

Ni X, Ishii S, Kildishev AV, Shalaev VM. Ultra-thin, planar, Babinet-inverted plasmonic metalenses. Light. Sci. Appl. 2013;2:e72. doi: 10.1038/lsa.2013.28. DOI

Arthur Losquin TTAL. Electron microscopy methods for space-, energy-, and time-resolved plasmonics. Front. Phys. 2017;12:127301. doi: 10.1007/s11467-016-0605-2. DOI

García de Abajo FJ. Optical excitations in electron microscopy. Rev. Mod. Phys. 2010;82:209–275. doi: 10.1103/RevModPhys.82.209. DOI

Schnell M, Garcia-Etxarri A, Alkorta J, Aizpurua J, Hillenbrand R. Phase-resolved mapping of the near-field vector and polarization state in nanoscale antenna gaps. Nano Lett. 2010;10:3524–3528. doi: 10.1021/nl101693a. PubMed DOI

Wu Y, Li G, Camden JP. Probing nanoparticle plasmons with electron energy loss spectroscopy. Chem. Rev. 2018;118:2994–3031. doi: 10.1021/acs.chemrev.7b00354. PubMed DOI

Yamamoto N, Araya K, García de Abajo FJ. Photon emission from silver particles induced by a high-energy electron beam. Phys. Rev. B. 2001;64:205419. doi: 10.1103/PhysRevB.64.205419. DOI

Rang M, et al. Optical near-field mapping of plasmonic nanoprisms. Nano Lett. 2008;8:3357–3363. doi: 10.1021/nl801808b. PubMed DOI

Dvořák P, et al. Control and near-field detection of surface plasmon interference patterns. Nano Lett. 2013;13:2558–2563. doi: 10.1021/nl400644r. PubMed DOI

Dvořák P, et al. Imaging of near-field interference patterns by aperture-type SNOM; influence of illumination wavelength and polarization state. Opt. Express. 2017;25:16560–16573. doi: 10.1364/OE.25.016560. PubMed DOI

Bitzer, A., Ortner, A., Merbold, H., Feurer, T. & Walther, M. Terahertz near-field microscopy of complementary planar metamaterials: Babinet’s principle. Opt. Express19, 2537–2545, 10.1364/OE.19.002537 (2011). PubMed

Babocký J, et al. Quantitative 3D phase imaging of plasmonic metasurfaces. ACS Photonics. 2017;4:1389–1397. doi: 10.1021/acsphotonics.7b00022. DOI

von Cube F, et al. Spatio-spectral characterization of photonic meta-atoms with electron energy-loss spectroscopy. Opt. Mater. Express. 2011;1:1009–1018. doi: 10.1364/OME.1.001009. DOI

Mizobata H, Ueno K, Misawa H, Okamoto H, Imura K. Near-field spectroscopic properties of complementary gold nanostructures: applicability of Babinet’s principle in the optical region. Opt. Express. 2017;25:5279–5289. doi: 10.1364/OE.25.005279. PubMed DOI

Rossouw D, Botton GA. Resonant optical excitations in complementary plasmonic nanostructures. Opt. Express. 2012;20:6968–6973. doi: 10.1364/OE.20.006968. PubMed DOI

Yang HU, et al. Accessing the optical magnetic near-field through Babinet’s principle. ACS Photonics. 2014;1:894–899. doi: 10.1021/ph5001988. DOI

Ögüt B, et al. Hybridized metal slit eigenmodes as an illustration of Babinet’s principle. ACS Nano. 2011;5:6701–6706. doi: 10.1021/nn2022414. PubMed DOI

Schmidt F-P, et al. Dark plasmonic breathing modes in silver nanodisks. Nano Lett. 2012;12:5780–5783. doi: 10.1021/nl3030938. PubMed DOI PMC

Schmidt FP, Ditlbacher H, Hofer F, Krenn JR, Hohenester U. Morphing a plasmonic nanodisk into a nanotriangle. Nano Lett. 2014;14:4810–4815. doi: 10.1021/nl502027r. PubMed DOI PMC

Yankovich AB, et al. Multidimensional hybridization of dark surface plasmons. ACS Nano. 2017;11:4265–4274. doi: 10.1021/acsnano.7b01318. PubMed DOI

Madsen SJ, Esfandyarpour M, Brongersma ML, Sinclair R. Observing plasmon damping due to adhesion layers in gold nanostructures using electron energy loss spectroscopy. ACS Photonics. 2017;4:268–274. doi: 10.1021/acsphotonics.6b00525. PubMed DOI PMC

Rindzevicius T, et al. Nanohole plasmons in optically thin gold films. J. Phys. Chem. C. 2007;111:1207–1212. doi: 10.1021/jp065942q. DOI

Coenen T, Polman A. Optical properties of single plasmonic holes probed with local electron beam excitation. ACS Nano. 2014;8:7350–7358. doi: 10.1021/nn502469r. PubMed DOI

Sannomiya T, Saito H, Junesch J, Yamamoto N. Coupling of plasmonic nanopore pairs: facing dipoles attract each other. Light. Sci. Appl. 2016;5:e16146. doi: 10.1038/lsa.2016.146. PubMed DOI PMC

Schider G, et al. Plasmon dispersion relation of Au and Ag nanowires. Phys. Rev. B. 2003;68:155427. doi: 10.1103/PhysRevB.68.155427. DOI

Schmidt F-P, et al. Universal dispersion of surface plasmons in flat nanostructures. Nat. Commun. 2014;5:3604. doi: 10.1038/ncomms4604. PubMed DOI PMC

Strutt J. On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky. Phil. Magaz. 1899;47:375–394. doi: 10.1080/14786449908621276. DOI

Zhou J, et al. Saturation of the magnetic response of split-ring resonators at optical frequencies. Phys. Rev. Lett. 2005;95:223902. doi: 10.1103/PhysRevLett.95.223902. PubMed DOI

Ritchie RH, Arakawa ET, Cowan JJ, Hamm RN. Surface-plasmon resonance effect in grating diffraction. Phys. Rev. Lett. 1968;21:1530–1533. doi: 10.1103/PhysRevLett.21.1530. DOI

García de Abajo FJ, Kociak M. Probing the photonic local density of states with electron energy loss spectroscopy. Phys. Rev. Lett. 2008;100:106804. doi: 10.1103/PhysRevLett.100.106804. PubMed DOI

Kociak M, Stéphan O. Mapping plasmons at the nanometer scale in an electron microscope. Chem. Soc. Rev. 2014;43:3865–3883. doi: 10.1039/C3CS60478K. PubMed DOI

Hohenester U, Ditlbacher H, Krenn JR. Electron-energy-loss spectra of plasmonic nanoparticles. Phys. Rev. Lett. 2009;103:106801. doi: 10.1103/PhysRevLett.103.106801. PubMed DOI

Egerton, R. F. Electron Energy-Loss Spectroscopy in the Electron Microscope (Springer US, New York, 2011).

Mitchell DRG. Determination of mean free path for energy loss and surface oxide film thickness using convergent beam electron diffraction and thickness mapping: a case study using si and p91 steel. J. Microsc. 2006;224:187–196. doi: 10.1111/j.1365-2818.2006.01690.x. PubMed DOI

Iakoubovskii K, Mitsuishi K, Nakayama Y, Furuya K. Thickness measurements with electron energy loss spectroscopy. Microsc. Res. Tech. 2008;71:626–631. doi: 10.1002/jemt.20597. PubMed DOI

Křápek V, et al. Spatially resolved electron energy loss spectroscopy of crescent-shaped plasmonic antennas. Opt. Express. 2015;23:11855–11867. doi: 10.1364/OE.23.011855. PubMed DOI

Horák M, et al. Comparative study of plasmonic antennas fabricated by electron beam and focused ion beam lithography. Sci. Reports. 2018;8:9640. doi: 10.1038/s41598-018-28037-1. PubMed DOI PMC

Johnson PB, Christy RW. Optical constants of the noble metals. Phys. Rev. B. 1972;6:4370–4379. doi: 10.1103/PhysRevB.6.4370. DOI

Plasmonic sensing using Babinet's principle

Spatio-spectral metrics in electron energy loss spectroscopy as a tool to resolve nearly degenerate plasmon modes in dimer plasmonic antennas