Abstract

Nonlinear nanophotonics is a rapidly developing field of research with many potential applications for the design of nonlinear nanoantennas, light sources, nanolasers, and ultrafast miniature metadevices. A tight confinement of the local electromagnetic fields in resonant photonic nanostructures can boost nonlinear optical effects, thus offering versatile opportunities for the subwavelength control of light. To achieve the desired functionalities, it is essential to gain flexible control over the near- and far-field properties of nanostructures. To engineer nonlinear scattering from resonant nanoscale elements, both modal and multipolar control of the nonlinear response are widely exploited for enhancing the near-field interaction and optimizing the radiation directionality. Motivated by the recent progress of all-dielectric nanophotonics, where the electric and magnetic multipolar contributions may become comparable, here we review the advances in the recently emerged field of multipolar nonlinear nanophotonics, starting from earlier relevant studies of metallic and metal–dielectric structures supporting localized plasmonic resonances to then discussing the latest results for all-dielectric nanostructures driven by Mie-type multipolar resonances and optically induced magnetic response. These recent developments suggest intriguing opportunities for a design of nonlinear subwavelength light sources with reconfigurable radiation characteristics and engineering large effective optical nonlinearities at the nanoscale, which could have important implications for novel nonlinear photonic devices operating beyond the diffraction limit.

© 2016 Optical Society of America

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2016 (19)

D. A. Smirnova, A. B. Khanikaev, L. A. Smirnov, and Y. S. Kivshar, “Multipolar third-harmonic generation driven by optically induced magnetic resonances,” ACS Photon. 3, 1468–1476 (2016).
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J. Butet and O. J. F. Martin, “Evaluation of the nonlinear response of plasmonic metasurfaces: Miller’s rule, nonlinear effective susceptibility method, and full-wave computation,” J. Opt. Soc. Am. B 33, A8–A15 (2016).
[Crossref]

G. Bautista and M. Kauranen, “Vector-field nonlinear microscopy of nanostructures,” ACS Photon. 3, 1351–1370 (2016).
[Crossref]

G. D. Bernasconi, J. Butet, and O. J. F. Martin, “Mode analysis of second-harmonic generation in plasmonic nanostructures,” J. Opt. Soc. Am. B 33, 768–779 (2016).
[Crossref]

Y. Huang, A. E. Miroshnichenko, and L. Gao, “Low-threshold optical bistability of graphene-wrapped dielectric composite,” Sci. Rep. 6, 23354 (2016).
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A. V. Krasavin, P. Ginzburg, G. A. Wurtz, and A. V. Zayats, “Nonlocality-driven supercontinuum white light generation in plasmonic nanostructures,” Nat. Commun. 7, 11497 (2016).
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S.-D. Liu, E. S. P. Leong, G.-C. Li, Y. Hou, J. Deng, J. H. Teng, H. C. Ong, and D. Y. Lei, “Polarization-independent multiple Fano resonances in plasmonic nonamers for multimode-matching enhanced multiband second-harmonic generation,” ACS Nano 10, 1442–1453 (2016).
[Crossref]

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U. Zywietz, M. K. Schmidt, A. B. Evlyukhin, C. Reinhardt, J. Aizpurua, and B. N. Chichkov, “Electromagnetic resonances of silicon nanoparticle dimers in the visible,” ACS Photon. 2, 913–920 (2015).
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2014 (25)

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A. E. Krasnok, C. R. Simovski, P. A. Belov, and Y. S. Kivshar, “Superdirective dielectric nanoantennas,” Nanoscale 6, 7354–7361 (2014).
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D. A. Smirnova, I. V. Shadrivov, A. E. Miroshnichenko, A. I. Smirnov, and Y. S. Kivshar, “Second-harmonic generation by a graphene nanoparticle,” Phys. Rev. B 90, 035412 (2014).
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B. Metzger, M. Hentschel, T. Schumacher, M. Lippitz, X. Ye, C. B. Murray, B. Knabe, K. Buse, and H. Giessen, “Doubling the efficiency of third harmonic generation by positioning ITO nanocrystals into the hot-spot of plasmonic gap-antennas,” Nano Lett. 14, 2867–2872 (2014).
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J. Butet and O. J. F. Martin, “Nonlinear plasmonic nanorulers,” ACS Nano 8, 4931–4939 (2014).
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P. Albella, R. A. de la Osa, F. Moreno, and S. A. Maier, “Electric and magnetic field enhancement with ultralow heat radiation dielectric nanoantennas: considerations for surface-enhanced spectroscopies,” ACS Photon. 1, 524–529 (2014).
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M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14, 6488–6492 (2014).
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R. Sanatinia, S. Anand, and M. Swillo, “Modal engineering of second-harmonic generation in single GaP nanopillars,” Nano Lett. 14, 5376–5381 (2014).
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S. Liu, M. B. Sinclair, T. S. Mahony, Y. C. Jun, S. Campione, J. Ginn, D. A. Bender, J. R. Wendt, J. F. Ihlefeld, P. G. Clem, J. B. Wright, and I. Brener, “Optical magnetic mirrors without metals,” Optica 1, 250–256 (2014).
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L. Lu, J. D. Joannopoulos, and M. Soljacic, “Topological photonics,” Nat. Photonics 8, 821–829 (2014).
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2013 (17)

J. van de Groep and A. Polman, “Designing dielectric resonators on substrates: combining magnetic and electric resonances,” Opt. Express 21, 26285–26302 (2013).
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H. Shen, N. Nguyen, D. Gachet, V. Maillard, T. Toury, and S. Brasselet, “Nanoscale optical properties of metal nanoparticles probed by second-harmonic generation microscopy,” Opt. Express 21, 12318–12326 (2013).
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J. Butet, K. Thyagarajan, and O. J. F. Martin, “Ultrasensitive optical shape characterization of gold nanoantennas using second harmonic generation,” Nano Lett. 13, 1787–1792 (2013).
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K. Thyagarajan, J. Butet, and O. J. F. Martin, “Augmenting second harmonic generation using Fano resonances in plasmonic systems,” Nano Lett. 13, 1847–1851 (2013).
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G. F. Walsh and L. D. Negro, “Enhanced second harmonic generation by photonic-plasmonic Fano-type coupling in nanoplasmonic arrays,” Nano Lett. 13, 3111–3117 (2013).
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E. Poutrina, A. Rose, D. Brown, A. Urbas, and D. R. Smith, “Forward and backward unidirectional scattering from plasmonic coupled wires,” Opt. Express 21, 31138–31154 (2013).
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A. E. Krasnok, I. S. Maksymov, A. I. Denisyuk, P. A. Belov, A. E. Miroshnichenko, C. R. Simovski, and Y. S. Kivshar, “Optical nanoantennas,” Phys.-Usp. 56, 539–564 (2013).
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K. Thyagarajan, S. Rivier, A. Lovera, and O. J. Martin, “Enhanced second-harmonic generation from double resonant plasmonic antennae,” Opt. Express 20, 12860–12865 (2012).
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M. Navarro-Cia and S. A. Maier, “Broad-band near-infrared plasmonic nanoantennas for higher harmonic generation,” ACS Nano 6, 3537–3544 (2012).
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Figures (6)

Fig. 1.
Fig. 1. (a) Schematic of nonlinear light scattering by an arbitrarily shaped nanoparticle. The formulas delineate the light–matter interaction Hamiltonian (bottom) and the nonlinearly generated field (top) expanded in terms of multipole moments. Illustrations of (b) SHG and (c) THG from a single spherical nanoparticle made of gold and silicon, respectively. Shown are near-field distributions of the electric field magnitude at the fundamental and harmonic frequencies. Nonlinear response of a 150 (600) nm diameter gold (silicon) nanoparticle is driven by ED (MD) mode at wavelength λ0=0.794 (2.15) μm and dominated by the surface (bulk) nonlinear polarization source, characterized by the nonlinear susceptibility tensor χs(2) (χb(3)) of the second (third) order. Polarization of the exciting plane wave is specified by red arrows in caption (b).
Fig. 2.
Fig. 2. (a) SH scattering pattern from Ag nanoparticles in water with four well-resolved quadrupolar lobes. Insets: SH scattering pattern from MG/PS nanoparticles featuring a dominant nonlocally excited electric dipole (top); transmission electron microscopy (TEM) image of Ag nanoparticles (bottom). (b) SH conversion efficiency by individual nanocup scales linearly as a function of the incident laser power and increases with nanocup angle. Inset: scanning electron microscopy (SEM) image of a chemically synthesized nanocup on a glass substrate oriented at 30° to the substrate normal. 120 nm silica nanoparticle is capped with a 35 nm thick Au layer. (c) Coherent control of light scattering from a gold nanowire by two collinear signal and control beams with zero phase delay. (d) Schematic view of a graphene-wrapped nanoparticle placed into an axially symmetric slightly inhomogeneous external field. The SH radiation is predominantly directed into the upper half space. Panels (a–d) are adopted from Refs. [117,120,32], and [36], respectively.
Fig. 3.
Fig. 3. (a) Top left: schematic view of the experiment on SHG with a metasurface of metal–dielectric disk-like nanoparticles made of Au/MgF2/Au layers. Top right: multipole decomposition of SH signal numerically calculated for the TE-polarized pump at the oblique 30° incidence. Bottom left: SEM image of a fabricated metasurface. Bottom right: linear transmission of the metasurface (gray) at normal incidence and second-harmonic spectra for TM- and TE-polarized pump waves (red and blue) measured for the incident angle of 30° (adopted from Ref. [166]). The insets illustrate the electric current distribution in a single composite nanoparticle in ED and MD resonant modes associated with two dips in transmission. (b) Top: schematic of the experiment on the resonantly enhanced THG from a fishnet metamaterial, exhibiting a magnetic response. The inset shows a scanning electron micrograph image of the sample. Bottom left: measured THG (solid blue) and pump (dashed red) spectra, normalized to maxima. Bottom right: back-focal-plane Fourier image of TH radiation (adopted from Ref. [165]).
Fig. 4.
Fig. 4. (a) Left: illustration of THG from silicon nanodisks driven by the magnetic dipolar resonance excited in the disks by the impinging laser light at the fundamental frequency. Superimposed is exemplary near-field distribution of the induced electric field in a disk at MD resonance. Right: photographic image of the eye-visible generated radiation from the nanodisk sample (adopted from Ref. [175]). (b) Left: schematic illustration of the resonant THG from silicon quadrumers of four a-Si:H nanodisks with SEM image of the sample in the bottom left corner. Rotating arrows picture the origin of the magnetic Fano resonance in quadrumers: two coupled magnetic-like modes formed by out-of-plane magnetic dipoles and circulating displacement current produced by in-plane electric dipoles give rise to the Fano interference. For details, see Ref. [204]. Right: THG spectroscopy of a-Si:H quadrumers on a glass substrate. Shown are experimental transmission (black line) and THG (blue dots) spectra of the sample excited by obliquely incident s-polarized radiation at the angle of 45°. TH power is plotted normalized to the spectrum of a bare a-Si:H film (after Ref. [185]). (c) Left: simulated (blue) and experimentally measured (red) transmission spectra of the silicon Fano-resonant metasurface with the Fano peak at the wavelength of 1350 nm. SEM image of the fabricated structure is shown in the inset. Right: third-harmonic spectra of the metasurface excited with the incident electric field polarized along the long (x-) and short (y-) axes of the bars, respectively (adopted from Ref. [179]). (d) Ultrafast all-optical switching in resonant silicon nanodisks. Left: schematic of the experiment; a-Si disk 250 nm in diameter is capable of switching optical pulses at femtosecond rates. Right: measured modulation of the probe pulse transmittance as a function of time delay between the probe and pump pulses at low pump powers (taken from Ref. [178]).
Fig. 5.
Fig. 5. Spectra of the normalized scattered FF (blue) and radiated TH (purple) powers calculated numerically for a spherical dielectric particle of radius 230 nm and refractive index 3.5 excited by a linearly polarized plane wave with electric field directed along the x axis. Labeled are the positions of Mie resonances (MQ, ED, and MD) in the linear scattering. Intensity maps show spatial distributions of the TH field generated near MD resonance in different cross-sections. Bottom: transformations of the TH radiation pattern with switching directionality. Within the broad MD resonance, both magnetic dipole and magnetic octupole contribute to the THG peak that determines predominantly axially symmetric emission profile (right) and a six-petalled TH near-field structure. The xy cuts of radiation patterns for the corresponding pure magnetic dipole l=1 (red) and magnetic octupole l=3 (pink) are depicted in the polar plot. Images are adopted from Ref. [47].
Fig. 6.
Fig. 6. SHG (blue line) and linear scattering (green line) efficiencies as functions of the pump wavelength calculated for a cylindrical AlGaAs nanoantenna with a radius of 225 nm and height of 400 nm in air. Insets show profiles of the electric field amplitude in an E-plane cross-section cut through the center of the cylinder, which correspond to the maxima of two dependencies dominated by MD and EQ modes, respectively (adopted from Refs. [180,183]).

Equations (10)

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Ws=π|E0|22ηk2l=1m=ll(2l+1)(|aE(l,m)|2+|aM(l,m)|2),
dP(θ,ϕ)dΩ=π|E0|22ηk2|l=1m=ll(i)l+1(2l+1)·(ilaM(l,m)Xl,m+il+1aE(l,m)r^×Xl,m)|2,
Esca=EED+EMD+EEQ+=k24πϵ0eikrr{[[r^×p]×r^]1c[r^×m]ik6[[r^×Q(r^)]×r^]+},
P=ϵ0[χ(1)·E+χ(2):EE+χ(3)EEE+],
Hint=p·Em·B[Q]·E,
P(2ω)=Psurf(2ω)+Pbulk(2ω),
Psurf(2ω)=ϵ0χs(2):E(ω)E(ω)δ(rrs)Ps(2ω)δ(rrs),
Pbulk(2ω)=ϵ0χb(2):E(ω)E(ω),
Ps(2ω)=n^(χ(2)EnEn+χ(2)EτEτ)+2χ(2)EnEτ,
Pbulk(2ω)=βE(ω)·E(ω)+γ(E(ω)·E(ω))+δ(E(ω)·)E(ω),

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