Origin of third harmonic generation in plasmonic nanoantennas

Transcription

1 Vol. 7, No. 5 1 May 217 OPTICAL MATERIALS EXPRESS 1575 Origin of third harmonic generation in plasmonic nanoantennas A NTONINO C ALÀ L ESINA, 1,* P IERRE B ERINI, 1,2 R AMUNNO 1,3 AND L ORA 1 Department of Physics and Centre for Research in Photonics, University of Ottawa, Ottawa, Canada School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Canada 3 lora.ramunno@uottawa.ca 2 * antonino.calalesina@uottawa.ca Abstract: Plasmonic nanoantennas have been recently proposed to boost nonlinear optical processes. In a metal dipole nanoantenna with a dielectric nanoparticle placed in the gap, the linear field enhancement can be exploited to enhance third harmonic emission. Since both metals and dielectrics exhibit nonlinearity, the nonlinear far-field contains contributions from each, and the difficulty of measuring these contributions separately has led to seemingly contradictory interpretations about the origin of the nonlinear emission. We determine that the origin of the third harmonic from metal-dielectric dipole nanoantennas depends on nanoantenna design, and in particular, the width. We find that the emission from gold dominates in thin threadlike nanoantennas, whereas the emission from the gap material dominates in wider nanoantennas. We also find that the nonlinear emission from gold in dipole nanoantennas is lower than monopoles of comparable dimensions, but that placing a highly nonlinear material in their gaps makes the nonlinear emission from the gap material dominate over gold. 217 Optical Society of America OCIS codes: (1919) Nonlinear optics; (25.543) Plasmonics; (1962) Harmonic generation and mixing; (16.433) Nonlinear optical materials; (19.327) Kerr effect; ( ) Subwavelength structures, nanostructures. References and links 1. M. Kauranen and A. V. Zayats, Nonlinear plasmonics, Nat. Photonics 6, (212). 2. P.-Y. Chen, C. Argyropoulos, G. D Aguanno, and A. Alù, Enhanced second-harmonic generation by metasurface nanomixer and nanocavity, ACS Photonics 2, 1 16 (215). 3. J. B. Lassiter, X. Chen, X. Liu, C. Ciracì, T. B. Hoang, S. Larouche, S. H. Oh, M. H. Mikkelsen, and D. R. Smith, Third-harmonic generation enhancement by film-coupled plasmonic stripe resonators, ACS Photonics 1, (214). 4. B. Jin and C. Argyropoulos, Enhanced four-wave mixing with nonlinear plasmonic metasurfaces, Sci. Rep. 6, (216). 5. P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings, Nano Lett. 1, (21). 6. A. Calà Lesina, L. Ramunno, and P. Berini, Dual-polarization plasmonic metasurface for nonlinear optics, Opt. Lett. 4, 2874 (215). 7. T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, Towards the origin of the nonlinear response in hybrid plasmonic systems, Phys. Rev. Lett. 16, (211). 8. H. Aouani, M. Rahmani, M. Navarro-Cía, and S. A. Maier, Third-harmonic-upconversion enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna, Nat. Nanotechnol. 9, (214). 9. 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, (214). 1. H. Linnenbank, Y. Grynko, J. Förstner, and S. Linden, Second harmonic generation spectroscopy on hybrid plasmonic/dielectric nanoantennas, Light Sci. Appl. 5, e1613 (216). 11. C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, Origin of second-harmonic generation enhancement in optical split-ring resonators, Phys. Rev. B 85, 2143 (212). 12. G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, Continuous control of the nonlinearity phase for harmonic generations, Nat. Mater. 14, (215). 13. K. O Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, Predicting nonlinear properties of metamaterials from the linear response, Nat. Mater. 14, (215). 14. A. Calà Lesina, A. Vaccari, P. Berini, and L. Ramunno, On the convergence and accuracy of the FDTD method for nanoplasmonics, Opt. Express 23, 1481 (215). # Journal Received 27 Feb 217; revised 5 Apr 217; accepted 5 Apr 217; published 11 Apr 217

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3 Vol. 7, No. 5 1 May 217 OPTICAL MATERIALS EXPRESS 1577 contributes to the third harmonic emission. We consider THG because it requires less complex structures, e.g., a monopole nanoantenna, which is not suitable for SHG [11, 12]. Furthermore, the third order nonlinear susceptibility can be derived from the linear properties of the medium based on Miller s rule, whereas the application of this rule is not straightforward for SHG in nanostructures and metamaterials [13]. The design space of a metal monopole nanoantenna is also explored to show when this simpler structure should be preferred for THG. 2. Simulations and discussion We simulate gold nanostructures on a semi-infinite SiO 2 substrate (Fig. 1(a)) by using the finitedifference time-domain (FDTD) method in 3D [14]. The thickness of all nanostructures was t = 5 nm, the width was chosen among the set w = {3, 5, 7} nm, and the gap of the dipole nanoantennas among the set g = {1, 2, 3} nm filled by a dielectric nanoparticle of length g and width w. We simulate nine dipole nanoantennas (each combination of w and g) and three monopole nanoantennas (each w value), one at a time, without periodic boundary conditions. The nanoantennas are oriented along the z-direction on an xz-plane, and the simulation domain is discretized with 1 nm resolution. A z-polarized and y-propagating plane wave excitation at ω (λ = 9 nm), implemented as a sinusoidal signal modulated by a Gaussian pulse, is introduced from air. Plane wave excitation of a single nanoantenna is a good approximation to experiments performed with loosely focused beams. The lengths of the dipole nanoantennas (L d ) and the monopole nanoantennas (L m ) were selected such that each nanoantenna is resonant at λ, resulting in 255 L d 324 nm and 174 L m 198 nm. This was determined by linear extrapolation because the resonance wavelength shifts linearly with the nanoantenna length [15]. To monitor the nonlinear far-field, we use a large simulation domain of (8 nm) 3. The analytical Kirchhoff near-to-far field transformation cannot be applied because the nanoantenna is not embedded in a homogeneous medium. The corners and edges of the metal nanostructures are rounded by r = 1 nm curvature radius to reduce numerical artifacts and to neglect nonlocal effects [16]. Linear dispersion is modelled by the Drude+2CP, Lorentz, and Drude models for gold (Johnson and Christy data) [17], SiO 2 [18], and ITO [19], respectively. We use an isotropic third order nonlinearity (instantaneous Kerr effect) as in [2]. The simulation of the linear and nonlinear responses run at the same time, naturally taking into account pump depletion. We use χ = m 2 /V 2 [21] and neglect nonlinearity in the substrate. The gap dielectric is a fictitious material with the linear properties of ITO and variable χ g to explore the design space. We seek the value of χ g for which the emission from the gap material and gold is the same. The excitation at λ = 9 nm allows us to exploit plasmonic field confinement in gold and to use a real valued χ (complex values are reported in [21] for λ < 63 nm). At 3ω, gold behaves as a lossy dielectric, such that the radiation from the nonlinear source is unaffected by plasmonic resonances [2]. Furthermore, working at λ allows us to keep the study general by avoiding the ITO absorption resonance ( 25 nm) and its epsilon-near-zero (ENZ) region ( 14 nm) where the transition to the metallic regime occurs. This regime has been recently exploited to enhance the nonlinear emission in hybrid nanostructures due to two nested plasmonic resonances [22]. To isolate the contributions to the overall THG emission, we consider the dipole nanoantennas in the following cases: (I) emission only from the gap material ( χ g, χ = ), (II) emission only from gold ( χ g =, χ ), (III) emission from the gap material and gold ( χ g, χ ). We also consider (IV) emission from gold in monopole nanoantennas ( χ ). We quantify the nonlinear emission by calculating the THG scattered power at 3ω as the integral of the normal component of the Poynting vector through a closed surface in the far-field. We report the relative THG efficiency η THG by normalizing with respect to the nanostructure with the largest THG emission, which is the monopole nanoantenna with w = 3 nm.

4 Vol. 7, No. 5 1 May 217 OPTICAL MATERIALS EXPRESS 1578 (b) 5. gap only gold dominates gap dominates gold only gap + gold = xc χg /χ ηthg (a) ηthg (c) w =3 nm g =1 nm g =2 nmg =3 nm w =5 nm.1 w =7 nm χg /χ 2 Fig. 1. (a) Sketch of dipole and monopole nanoantennas. (b) ηthg for a dipole nanoantenna (w = 3 nm, g = 1 nm). (c) ηthg for the nine dipole nanoantennas (, ) and the three monopole nanoantennas (dashed lines): w = 3 nm (red), w = 5 nm (green), and w = 7 nm (blue), g = 1 nm (dark shade), g = 2 nm (medium shade), g = 3 nm (light shade). In Figs. 1(b) and 1(c), we demonstrate that there are three regimes in hybrid plasmonic/dielectric nanoantennas for THG emission: a gold dominated regime, a gap dominated regime, and a regime where the emission from gold and gap are comparable. In Fig. 1(b), we plot ηthg vs χ g / χ for cases (I) (III) for the dipole nanoantenna (w = 3 nm, g = 1 nm) with the highest ηthg. The dashed line is for emission from the gap material only case study (I) and shows a quadratic behavior with χ g / χ. The solid line is for emission from gold only case study (II) which is horizontal since we are considering a single value for χ. The cross point ( χ g / χ = x c ) between dashed and solid lines red circle ( ) identifies the value such that the nonlinear emission from gold equals that from the gap material. The white squares are for emission from gold and gap case study (III) and they show an asymptotic behavior, approaching the gold only regime on the left and the gap only regime on the right. The red square ( ) identifies the case study (III) for χ g = x c χ. For χ g / χ >> x c emission from the gap material dominates, while for χ g / χ << x c the emission from gold dominates. The red circle and square in Fig. 1(b) are sufficient to identify the boundary between gold and gap dominated regimes, as well as ηthg at the cross point x c. Thus, only these two points are shown in Fig. 1(c) for each of the nine dipole nanoantennas. For comparison, dashed lines are used to indicate ηthg of the three monopoles case study (IV). For the dipole nanoantenna, by changing w and g we observe the variation of four parameters: ηthg, x c, the horizontal spacing between circles (d h ), and the vertical spacing between circle and square (d v ). Increasing w produces a strong decrease in ηthg, a decrease in x c and a decrease in d h. Increasing g produces a slight decrease in ηthg, an increase in x c, and a decrease in d v. A high ηthg means that the baseline emission from gold is high. A high x c means that the emission from gold is more prone to dominate over the emission from the gap material. The lower d h for the largest width indicates that a larger gap volume compensates the lower field enhancement. The smaller d v for the largest gap size means that the gap material s contribution to ηthg is small. The dipole nanoantennas have a lower nonlinear emission from gold than a monopole nanoantenna with the same w, since a continuous structure supports a less damped linear harmonic oscillation, which is a cause of strong nonlinear emission [23]. Our simulations show that nonlinear emission

5 Vol. 7, No. 5 1 May 217 OPTICAL MATERIALS EXPRESS 1579 (a) 4 Ez (3ω ) 35 z [nm] z [nm] 4 (b) Ez (3ω ) (c) Ez (3ω ) [rad] Ez (3ω ) [rad] Ez (3ω ) (d) Ez (3ω ) [rad] Ez (3ω ) Ez (3ω ) [rad] Fig. 2. Absolute value (top) and phase (bottom) of Ez (3ω ): emission from (a) gap only (Visualization 1), (b) gold only (Visualization 2), (c) gap material and gold (Visualization 3) in a dipole nanoantenna; (d) gold in a monopole nanoantenna (Visualization 4). from gold depends strongly on w, preferring threadlike rather than bulky shapes, as reported in [24]. Considering ITO ( χ g = m2 /V 2 [25]) for the dipole nanoantenna in Fig. 1(b), we obtain ηthg 4 13 by quadratic extrapolation, falling within the gap dominated regime. Nonlocal effects due to surface roughness can increase the effective χ and make gold more prone to dominate over the gap material [26]. In the linear regime, the spectral peak of the field enhancement in the gap is slightly red-shifted with respect to the peak of the extinction spectrum [27]. Since the nonlinear emission by the gap material is driven by the linear field enhancement in the gap, and the nonlinear emission from gold is linked to the linear extinction, our simulations show that the nonlinear spectra for the emission from the gap and for the emission from gold exhibit a shift in wavelength, as confirmed in [28]. We use the linear extinction spectrum to determine the nanoantenna lengths required for resonance at λ. This corresponds to maximizing the nonlinear emission from gold. Thus, the nonlinear emission from the gap is not optimal. This shift for our dipole nanoantennas in the linear regime ranges from 1 nm (w = 3 nm, g = 1 nm) to 35 nm (w = 7 nm, g = 3 nm). In Fig. 2, we plot the near-fields for the dipole nanoantenna and the monopole nanoantenna with the highest ηthg. We show the absolute value and phase of Ez (3ω ) in the xz plane for cases (I) (IV) in Figs. 2(a) 2(d), respectively, assuming χ g = x c χ. The electric field hot spots show nearly uniform phase and thus can be considered as idealized dipole sources. Visualizations 1 4 show the evolution of the third harmonic electric field in the yz plane for cases (I) (IV), respectively. In the case of THG emission from the gap, as expected, the dipole source is localized in the gap (Fig. 2(a)). More interesting is the emission from gold in the dipole nanoantenna, where we observe one dipole source in each branch of the dipole nanoantenna, and an enhancement of the nonlinear field in the gap (Fig. 2(b)). The electric field distribution when both the gap and gold are emitting (Fig. 2(c)) shows constructive interference in the gap and at the extremes of the dipole nanoantenna, and destructive interference along the dipole nanoantenna branches. The monopole shows a dipole source in the middle (Fig. 2(d)), as also reported in [29], which can be used as an ideal source in metasurfaces for nonlinear beam shaping [2]. In Fig. 3 we show the far-field radiation patterns at 3ω corresponding to the nanoantennas

6 Vol. 7, No. 5 1 May 217 OPTICAL MATERIALS EXPRESS 158 (a) 9 (b) 9 (c) 9 (d) Fig. 3. Radiation pattern at 3ω : emission from (a) gap material only, (b) gold only, and (c) gap material and gold in a dipole nanoantenna; (d) gold in a monopole nanoantenna. in Fig. 2. We consider xy and yz cut planes, where the angle is measured starting from the y-axis. The radiation patterns were calculated by considering a polar coordinate system with the scattering center in the middle of the nanoantenna, and evaluating the normal projection of the Poynting vector through a circle in the far-field. The radiation patterns are normalized with respect to the monopole with highest η THG. The radiation can be seen as produced by a collinear array of phased emitters aligned along z with subwavelength spacing. This produces radiation patterns in the xy plane with the same shape in the four cases in Fig. 3. In all cases, the radiation is observed to be primarily directed through the substrate because it has a larger refractive index than the air above the antennas. The different electric field distributions shown in Fig. 2 play a role only for the radiation patterns in the yz plane. The emission from the gap material only produces a broad radiation pattern (Fig. 3(a)), which can be understood as diffraction by a small aperture; in fact, the broadening decreases as the gap size increases (not shown). In the case of emission from gold only in the dipole nanoantenna (Fig. 3(b)), the two nonlinear dipole sources produce a directive lobe. The simultaneous emission from gold and the gap material produces a hybrid radiation pattern (Fig. 3(c)). When the THG emission from gold and the gap material are comparable (x c region), complex χ and/or χ g values could lower the η THG value due to destructive interference in the far-field. The radiation pattern produced by the monopole nanoantenna (Fig. 3(d)) has the same shape as the one in Fig. 3(b), but is less directive. This is because the central emitter dominates over the sources localized at the extremes of the monopole nanoantenna. Furthermore, we have observed that the forward-to-backward ratio increases with w when the emission comes from the gap, and decreases with w when the emission comes from gold. These radiation properties help to identify the position of the nonlinear emitters, and to understand which emission, whether from the gap material or gold, is dominating in an experiment. 3. Conclusion In conclusion, we investigated third harmonic generation (THG) in hybrid dielectric/metal nanoantennas and found that both nanoantenna design and gap material nonlinear susceptibility determine whether the THG emission is primarily from the gap material, or from gold. In terms of design, nanoantenna width is a primary factor. In addition, THG emission from gold in a dipole is always much lower than that in a monopole of the same width. Due to its fabrication simplicity, the monopole nanoantenna should be preferred, unless the nonlinear permittivity of the gap material is strong enough to make its nonlinear emission much larger than that from gold. Acknowledgments We acknowledge the Canada Research Chairs program, the Southern Ontario Smart Computing Innovation Platform (SOSCIP), and SciNet.