Letter pubs.acs.org/NanoLett
Efficient Second-Harmonic Generation in Nanocrystalline Silicon Nanoparticles Sergey V. Makarov,*,† Mihail I. Petrov,† Urs Zywietz,‡ Valentin Milichko,† Dmitry Zuev,† Natalia Lopanitsyna,¶,§ Alexey Kuksin,¶,§ Ivan Mukhin,† George Zograf,† Evgeniy Ubyivovk,∥ Daria A. Smirnova,⊥ Sergey Starikov,¶,§ Boris N. Chichkov,‡ and Yuri S. Kivshar†,⊥ †
Department of Nanophotonics and Metamaterials, ITMO University, St. Petersburg 197101, Russia Nanotechnology Department, Laser Zentrum Hannover e.V., Hannover D-30419, Germany ¶ Laboratory of Chemical Thermodynamics, Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow 125412, Russia § Moscow Institute of Physics and Technology, Moscow 141701 Russia ∥ St. Petersburg State University, St. Petersburg 199034, Russia ⊥ Nonlinear Physics Centre, Australian National University, Canberra ACT 2601, Australia ‡
S Supporting Information *
ABSTRACT: Recent trends to employ high-index dielectric particles in nanophotonics are motivated by their reduced dissipative losses and large resonant enhancement of nonlinear effects at the nanoscale. Because silicon is a centrosymmetric material, the studies of nonlinear optical properties of silicon nanoparticles have been targeting primarily the third-harmonic generation effects. Here we demonstrate, both experimentally and theoretically, that resonantly excited nanocrystalline silicon nanoparticles fabricated by an optimized laser printing technique can exhibit strong second-harmonic generation (SHG) effects. We attribute an unexpectedly high yield of the nonlinear conversion to a nanocrystalline structure of nanoparticles supporting the Mie resonances. The demonstrated efficient SHG at green light from a single silicon nanoparticle is 2 orders of magnitude higher than that from unstructured silicon films. This efficiency is significantly higher than that of many plasmonic nanostructures and small silicon nanoparticles in the visible range, and it can be useful for a design of nonlinear nanoantennas and silicon-based integrated light sources. KEYWORDS: Nonlinear nanophotonics, second-harmonic generation, crystallization kinetics, silicon nanoparticles, dielectric nanoantennas, Mie scattering, magnetic dipole resonance
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The most promising material for implementation of alldielectric resonant nanophotonics is silicon (Si) due to its complementary metal oxide semiconductor compatibility and nonlinear optical properties.12,13 In particular, enhanced thirdharmonic generation (THG) in silicon-on-insulator nanoantennas3−7 and self-organized resonant Si nanostructures8 have been demonstrated recently. By using an array of Si
ptical response of high-index dielectric nanoparticles exhibits negligible dissipative losses, high heat resistance, and strong magnetic multipolar resonances in the visible and near-infrared regions of the electromagnetic spectrum. 1 Compared to metallic nanoparticles where the electric field is strongly confined near metal−dielectric interfaces, the electric field of the resonant modes in dielectric nanoparticles penetrates deep inside their volume, strongly enhancing lightmatter interactions and multipolar effects.2 This fact encourages the use of all-dielectric nanoantennas for strengthening the nonlinear optical response.3−11 © 2017 American Chemical Society
Received: January 28, 2017 Revised: April 4, 2017 Published: April 14, 2017 3047
DOI: 10.1021/acs.nanolett.7b00392 Nano Lett. 2017, 17, 3047−3053
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Nano Letters
Figure 1. Schematic of laser printing and enhanced SHG from Si nanoparticles. Inset: dark-field image of an array of the laser-printed Si nanoparticles.
Figure 2. Scattering spectra of isolated Si nanoparticles. (a) Experimentally measured and (b) numerically calculated spectra for nanoparticles with diameters of 220, 250, 300, and 350 nm, from bottom to top, respectively. Insets show the geometries employed for measurements and modeling, respectively.
nanoparticles, the THG conversion efficiency up to 10−5 was demonstrated, which is the highest value reported for THG at nanoscale using comparable pump energies.5,6 To generate the second-harmonic (SH) light, different designs of all-dielectric nanoantennas are being developed based mainly on the III−V semiconductor platform,14−17 while Si nanoparticles are traditionally left out in these studies because of the inhibited second-order nonlinearity in Si due to its centrosymmetric crystalline structure.18
In this Letter, in a sharp contrast to a common trend to use noncentrosymmetric materials we demonstrate experimentally efficient SHG from spherical Si nanoparticles fabricated by an optimized laser printing method. We explain this effect theoretically by analyzing the enhancement of local electromagnetic fields inside the nanoparticles near the magnetic dipole Mie resonance3−8 and by a composite multigrain structure of the Si nanoparticles that induces the secondorder nonlinearity originating from quadrupolar volume and dipolar surface sources induced at interfaces between the grains 3048
DOI: 10.1021/acs.nanolett.7b00392 Nano Lett. 2017, 17, 3047−3053
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Nano Letters
Figure 3. Experimental SHG results. (a) Experimental SH spectra from an isolated Si nanoparticle with diameter 350 nm and a-Si:H film at intensity 30 GW/cm2. Left inset: TEM image of Si nanoparticle. Scale bar is 20 nm. Right inset: simulated grain structure of Si nanoparticle cooled at K = 0.25 K/ps. (b) Measured efficiency of SHG for the Si nanoparticle with diameter 350 nm. Left inset: optical image of the Si nanoparticle emitting SH. Right inset: a sketch of the SHG experiment.
where the inversion symmetry of bulk Si is broken.19−22 Moreover, for the first time to our knowledge we employ a modified high-throughput method of laser printing23,24 to control and engineer the fabrication of nanoparticles with highly efficient second-order nonlinear response. We optimize the effect of the polycrystalline structure by choosing specific laser printing conditions supported by rigorous molecular dynamics simulations of the crystallization kinetics, whereas we achieve the additional near-field enhancement via a control of the nanoparticles size to support a magnetic dipole Mie resonance. Our finding may open novel prospects for a design of nonlinear subwavelength light sources with exceptional characteristics fully integrated in Si-based nanoscale photonic circuits. For all experiments, nanoparticles are printed by employing a femtosecond laser23 (in a single-shot regime) from a smooth surface of a-Si:H film in the forward-transfer geometry (see Figure 1), when the receiving substrate is placed under the film with the spacing of 15 ± 2 μm. This printing geometry allows fabricating a controllable array of resonant Si nanoparticles (see the inset in Figure 1), and it has an advantage over the backtransfer geometry owing to the possibility of the nanoparticles transfer onto a wide variety of substrates, including opaque and structured samples.24 Moreover, there is one important difference between our current approach and the techniques applied previously. Specifically, in the earlier method23 Si nanoparticles were formed in an amorphous state, and in ref 24 Si nanoparticles were formed in the crystalline state, owing to different distances between the substrates. According to our polarization-resolved scattering spectra measurements in a dark-field geometry (Figure 2a) and its comparison with the corresponding numerical modeling (Figure 2b), we observe that the scattering spectra can be described effectively by using dispersion for crystalline silicon.25 Indeed, the numerical modeling that takes into account the presence of a silica substrate and finite aperture of a collecting objective (for details, see Supporting Information), reveals the excitation of dipole, quadrupole, and even octupole Mieresonant modes of magnetic and electric types in the printed nanoparticles. It means that these nanoparticles allow for matching of optical resonances both for pump and emission frequencies separated by one octave, which is useful for the generation of optical harmonics. However, SHG requires symmetry breaking in crystalline structure of nanoparticles material, which can be fulfilled at interfaces between the nanoparticle material and surrounding medium, or between
grains of the material. Figure 3a (inset) shows that the printed Si nanoparticle has a polycrystalline structure, caused by specific cooling conditions in our experiment. Atomistic numerical simulations provide a reconstruction of the crystallization kinetics during the cooling process (see details in Methods). The atomistic modeling results agree well with our experimental data (see the insets in Figure 3a), yielding cooling rate about 0.25 K/ps for crystallization. If a Si liquid drop moves in air, the crystallization can take place prior to its deposition on the glass surface. For instance, the distance of 15 μm in our experiments corresponds to a decrease of the particle temperature from about 2000 to 500 K (for details of calculations, see Supporting Information), revealing that the cooling rate is less than or equal to about 0.1 K/ps, being lower than 0.25 K/ps and, thus, corresponding to a polycrystalline state of the nanoparticle. Owing to the nanocrystalline structure, the fabricated Si nanoparticles demonstrate strong SHG effects, despite the central symmetry of the Si lattice. Filtered and measured SH signal is detected clearly by a spectrometer (for the details, see Methods), and this excludes a contribution of multiphoton luminescence. In Figure 3a, we show a typical SHG spectrum exhibiting a sharp peak at wavelength 525 nm. Remarkably, the generated SH signal from a 350 nm Si nanoparticle is more than 2 orders of magnitude stronger than that from the donor film (a-Si:H, thickness 50 nm) at similar intensities (I ≈ 30 GW/cm2), as shown in Figure 3a. We use the amorphous silicon film for comparison as the simplest object with welldefined sources of SHG, namely, two flat interfaces where centrosymmetry is broken. We test the samples of different thicknesses (50, 100, 120 nm) and do not observe significant differences in the SHG signal, which validates the model of surface SHG.26 The measurements from the film are carried out at the same experimental conditions (focusing, angle of incidence, and collection) as for the nanoparticles. The SHG intensity shows the effect of the second-order nonlinearity due to a quadratic slope in double-logarithm coordinates (Figure 3b). The maximum conversion efficiency is about 1.5× 10−6 at I ≈ 30 GW/cm2; this is several orders of magnitude larger than the corresponding values for plasmonics27−30 and Si nanocrystalls,31 whereas the volume of our nanoparticle is several orders of magnitude smaller than that of photonic crystalls with comparable SHG efficiency.32,33 The origin of such high values of the SHG conversion efficiency can be attributed to two major physical effects. The first effect is a polycrystalline structure of the nanoparticles, 3049
DOI: 10.1021/acs.nanolett.7b00392 Nano Lett. 2017, 17, 3047−3053
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Figure 4. Experimental versus theoretical SHG results. (a) Numerically modeled energy of the electric field trapped inside a Si nanoparticle upon illumination at pump (red dashed curve) and SH (green solid curve) wavelengths. (b) Numerically modeled near-field distributions for the Si nanoparticles of different sizes corresponding to the magnetic dipole resonance m0 excited at the pump wavelength, and two higher-order Mie resonances m1 and m2 at SH wavelength. (c) Experimental (dots) and numerically (solid curve) calculated SH intensities from individual Si nanoparticles with different diameters. (d) Radiation patterns for SHG (green) with respect to the incident polarization (red): experimental (dots) and numerically modeled (curve) for nanoparticles with diameter 310 nm.
times inside the nanoparticle (see Figure 4b), whereas two higher-order modes (m1 and m2) are excited at 525 nm (SH) in the nanoparticles with close diameters, specifically, electric octupole at 270 nm and magnetic quadrupole at 315 nm. The near-field distributions at the resonances m1 and m2 are depicted in Figure 4b, demonstrating their good spatial overlaps with the fundamental mode m0. Such spectral and spatial overlapping of the modes supported by the nanoparticles may lead to the multifold enhancement of SH yield as compared to the nonresonant case,2 for example, for diameters less than 270 nm (see Figure 4a). Generally, the second-order polarization in centrosymmetric materials can be written as a superposition of surface dipolar and bulk quadrupolar contributions20−22,34,35
which is clearly seen in Figure 3a. The laser-printed nanoparticles have a developed net of interfaces separating different grains and giving rise to the enhanced second-order optical response, owing to local breaking of inversion symmetry.19−22,31 The second effect contributing to the SHG enhancement is related to the excitation of Mie-type resonances in the Si nanoparticles, that is, a contribution of the localelectric-field enhancement at the pump frequency and stimulated outcoupling of the SH radiation. In order to prove rigorously these two physical mechanisms of the SHG enhancement, we perform full-wave numerical simulations for a spherical Si nanoparticle placed on a fused silica substrate (as shown schematically in the right inset in Figure 3b) by using COMSOL Multiphysics and following the procedure described elsewhere6,7,17 (see Methods). The modes sustained by nanostructures are known to play important role in the analysis of their nonlinear response. Therefore, we first study numerically the peculiarities of linear optical scattering from our Si nanoparticles and analyze supported resonances. Figure 4a shows a multiresonant character of the dependence of the electric field energy accumulated inside Si nanoparticles with different diameters under irradiation by a plane electromagnetic wave at pump and SH wavelengths, being 1050 and 525 nm, respectively. Multipolar decomposition (for details, see Supporting Information) reveals the magnetic dipole nature of the resonance (m0) around the diameter of 280 nm at the pump wavelength, yielding the electric field enhancement up to 3
(2ω) (2ω) P(2ω) = Psurf + Pbulk
(1a)
(2ω) (2) Psurf = ε0δ(r − rs)[n̂ (χ⊥⊥⊥ (En(ω))2 + χ⊥(2) (Eτ(ω))2 ) + 2τ χ̂ (2) E (ω)Eτ(ω)] ⊥ n
(1b) (2ω) Pbulk = ε0[β E(ω)∇·E(ω) + γ ∇(E(ω)·E(ω)) + δ′(E(ω)·∇)E(ω)]
(1c)
which we assume to be appplicable for individual randomly distributed grains in a nanosphere. Here, χ(2), β, γ and δ′ are the material parameters characterizing optical nonlinearity, rs defines the interface surface, and ε0 is the dielectric permittivity of vacuum. Electric field vector E(ω) at the fundamental wavelength can be decomposed near the interfaces onto two unit vectors n̂ and τ̂ with corresponding normal E(ω) and n 3050
DOI: 10.1021/acs.nanolett.7b00392 Nano Lett. 2017, 17, 3047−3053
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pulses are tightly focused into the front side of Si films through a transparent (glass) receiver substrate placed on top of the sample in close contact. For focusing, a microscope objective (Nikon) with 50× magnification and a numerical aperture (NA) of 0.45 is used. The Si nanoparticles are fabricated at laser energies E < 10 nJ. Each laser pulse causes a strongly localized melting in a Si layer. Because of the surface tension, the melted volume contracts to a sphere being ejected toward the receiver substrate. Fabricated nanoparticles are almost spherical,23,24 and their diameters are in the range of 200−350 nm, depending on the energy. Also, we apply higher energies24 to fabricate and study randomly distributed smaller nanoparticles (
