Letter pubs.acs.org/NanoLett
Nonlinear Fano-Resonant Dielectric Metasurfaces Yuanmu Yang,†,⊥ Wenyi Wang,‡ Abdelaziz Boulesbaa,§ Ivan I. Kravchenko,§ Dayrl P. Briggs,§ Alexander Puretzky,§ David Geohegan,§ and Jason Valentine*,∥ †
Interdisciplinary Materials Science Program, Vanderbilt University, Nashville, Tennessee 37212, United States Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, Tennessee 37212, United States § Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ∥ Department of Mechanical Engineering, Vanderbilt University, Nashville, Tennessee 37212, United States ‡
Nano Lett. 2015.15:7388-7393. Downloaded from pubs.acs.org by UNIV OF SUNDERLAND on 09/20/18. For personal use only.
S Supporting Information *
ABSTRACT: Strong nonlinear light−matter interaction is highly sought-after for a variety of applications including lasing and all-optical light modulation. Recently, resonant plasmonic structures have been considered promising candidates for enhancing nonlinear optical processes due to their ability to greatly enhance the optical near-field; however, their small mode volumes prevent the inherently large nonlinear susceptibility of the metal from being efficiently exploited. Here, we present an alternative approach that utilizes a Fano-resonant silicon metasurface. The metasurface results in strong near-field enhancement within the volume of the silicon resonator while minimizing two photon absorption. We measure a third harmonic generation enhancement factor of 1.5 × 105 with respect to an unpatterned silicon film and an absolute conversion efficiency of 1.2 × 10−6 with a peak pump intensity of 3.2 GW cm−2. The enhanced nonlinearity, combined with a sharp linear transmittance spectrum, results in transmission modulation with a modulation depth of 36%. The modulation mechanism is studied by pump−probe experiments. KEYWORDS: Metamaterial, dielectric antenna, Fano resonance, third harmonic generation subwavelength scale.6−10 However, since the field maxima in plasmonic structures occurs at the boundary of the metal/ dielectric interface, the intrinsic nonlinearity of the metal cannot be efficiently exploited. One way to mitigate this issue is to place nonlinear materials in the vicinity of the plasmonic “hot-spots”;11−13 though the small modal volume of plasmonic resonances will still limit the overall generation efficiency. Furthermore, plasmonic nanostructures generally suffer from a low damage threshold due to large optical absorption and the low melting temperature of metals compared to dielectrics. As an alternative, low-loss dielectric structures such as silicon nanodisks14 and oligomers15 exhibiting Mie resonances have recently been studied for enhancing third harmonic generation (THG) but achieving intense near-field enhancements, and therefore high THG efficiencies, has remained challenging due to the leaky nature of the optical modes.16−18 On-chip photonic structures such as ring-resonators and slow light waveguides have also been proposed for THG due to their ability to achieve large quality factors (Q-factor) and/or long photon residence times.19,20 In these cases the conversion efficiencies are limited due to two-photon absorption (TPA)21 of the fundamental
N
onlinear optics forms the basis for a number of useful processes including light generation in parametric upand down-conversion tunable lasers,1 generation of entangled photons for quantum optics,2 and the nonlinear Kerr effect for ultrafast all-optical light modulation.3−5 However, the nonlinear optical response of materials is intrinsically weak and thus a long interaction length and/or high intensity is needed for efficient nonlinear light interaction. When dealing with bulk crystals, the common method to boost nonlinear conversion is to employ phase-matching between the fundamental and generated waves1 though this still requires a relatively long sample interaction length, which is problematic for compact integrated devices. A different approach is to employ resonance-induced electromagnetic field enhancement. When employed in nanoscale films, this approach does not require phase matching and takes advantage of the fact that the nth order harmonic generation is proportional to the integration of induced electric dipoles over the volume of a nanostructure unit cell p(n) ∝
∫V χ (n) (r)[E loc(r, ω)]n dV
(1)
where χ is the intrinsic nth order nonlinear susceptibility of the material, Eloc(r, ω) is the local electric field, and V is the volume of a unit cell. As an example, localized surface plasmon resonances can be utilized to substantially enhance Eloc(r, ω) by efficiently funneling light from the far-field to a deep (n)
© 2015 American Chemical Society
Received: July 15, 2015 Revised: October 16, 2015 Published: October 26, 2015 7388
DOI: 10.1021/acs.nanolett.5b02802 Nano Lett. 2015, 15, 7388−7393
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Figure 1. (a) Schematic of three photon up-conversion with the Fano-resonant silicon metasurface. The blue bar resonators represent the “bright” mode, and the red disk resonators represent the “dark” mode. (b) Diagram of one unit cell of the metasurface. The geometrical parameters are a = 200 nm, b = 700 nm, r = 210 nm, g = 60 nm, t = 120 nm, p1 = 750 nm, and p2 = 750 nm. (c), Schematic of the Fano interference between the bright and dark mode resonators. (d) An SEM image of the fabricated metasurface. (e) Simulated (blue) and experimentally measured (red) transmittance spectra of the metasurface.
relies on the collective oscillation of the resonators for the suppression of radiative loss.28 The interference between the collective “bright” and “dark” modes forms a typical three-level Fano-resonant system, as illustrated in Figure 1c. Polycrystalline silicon (Poly-Si) was chosen as the resonator material due to its large linear refractive index (n ≈ 3.7) and large intrinsic third-order susceptibility and nonlinear index −18 m2·V−2, n2(Si) ≈ 2.7 × 10−18 m2·W−1) in (χ(3) Si ≈ 2.79 × 10 the near-infrared band.29 In order to fabricate the structures, a 120 nm thick poly-Si layer was first deposited on a quartz substrate using low-pressure chemical vapor deposition (LPCVD). The resonators were then defined using electron beam lithography (EBL) followed by reactive-ion etching (RIE) (see Supporting Information Section 1, for further details). A scanning electron microscope (SEM) image of the fabricated sample is shown in Figure 1d. The experimentally measured transmittance, plotted in Figure 1e, was acquired by illuminating the sample with normal-incident white light with the electric field oriented along the long axis of the bar resonator. Numerical simulations of the structure were also carried out using a commercially available software (CST Microwave Studio) using the finite-integration frequencydomain (FIFD) solver (see Supporting Information Section 3 for details). A sharp peak in the transmittance curve is observed at a wavelength of 1348 nm with an experimental Q-factor of 466, as determined by fitting the dark mode resonance to a Fano line shape. The measured linear transmittance spectrum line-shape agrees well with the simulation, though the Q-factor and peak transmittance are reduced, which is expected due to imperfections with the fabricated sample. Accompanying the narrow transmittance curve, the metasurface also possesses a large electric field enhancement within the disk resonator corresponding to the excitation of the magnetic dipole mode, as shown in Figure 2a. The simulated field
wave within silicon (Si), a result of the long optical path length of the bus waveguides. In this letter, we report a Fano-resonant22−24 Si-based metasurface possessing large third-order nonlinearity for use in THG. The enhanced nonlinearity is due to a high Q-factor Fano resonance that in turn strongly enhances the local electric field within Si, thus resulting in large effective χ(3). Unlike ring resonators and other chip-based devices, there is no bus waveguide, and thus, TPA is greatly reduced while the volumetric nature of the modes allows better overlap with the χ(3) material compared to plasmonic implementations. This results in a metasurface with a THG enhancement of more than 5 orders of magnitude and a conversion efficiency on the order of 10−6 with a peak pump intensity of 3.2 GW cm−2, which is the highest value reported to date in micro- or nanostructured films at comparable pump energies,6,25 despite the fact that the excitation pulse has not yet been fully utilized due to the large spectral width of the laser compared with the width of the Fano resonance. Furthermore, by combining the large nonlinearity with the high Q-factor resonance, we experimentally demonstrate how the metasurface can be used for all-optical modulation. The Fano-resonant metasurface is illustrated in Figure 1a,b and consists of a periodic lattice of coupled rectangular bar and disk resonators formed from Si. The rectangular bar resonator supports a “bright” electric dipole resonance that is excited when the incident electric field is along the x-axis. The disk supports a “dark” magnetic dipole resonance in which the electric field is directed along the azimuthal direction, rotating around the disk’s axis. The out-of-plane magnetic dipole in the disk cannot be directly excited by normal incident light, but can instead be excited through near-field interaction with the bright mode bar resonator. Similar to past demonstrations of coherent plasmonic metamaterials,26,27 this dielectric metasurface also 7389
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Figure 2. (a) Simulated electric field amplitude at the Fano resonance peak wavelength of 1350 nm in both the x−y and y−z plane. The choice of cut-plane is represented with the white dashed lines. (b) Third harmonic spectra of the metasurface with the incident electric field polarized along the x-axis and y-axis, respectively. (c) Third harmonic spectra of an unpatterned Si film and a bare quartz substrate, respectively (average pump power of 25 mW; peak pump intensity of 1.6 GW cm−2).
Figure 3. (a) Wavelength-dependent THG intensity of the metasurface when normalized to an unpatterned Si film of the same thickness. The blue points are data taken under 0.8 GW cm−2 peak pump intensity, and the red points are data taken under 1.6 GW cm−2 peak pump intensity. The black dash line indicates the linear Fano resonance peak. (b) Experimental relative change in transmittance as a function of pump intensity at 1348, 1352, and 1356 nm. (c) Relative transmittance of a probe beam through the Fano-resonant metasurface with pump beam turning on and off at different pump intensities and at a fixed negative pump−probe delay time, with a 80 MHz optical parametric oscillator system. (d) Time-resolved pump−probe measurement of the Fano-resonant metasurface with a 1 kHz optical parametric amplifier system.
waveguide-based devices such as a large Q-factor and good modal overlap with the active material, while greatly reducing parasitic losses such as TPA of the pump beam and direct THG absorption in the bus waveguides. In order to quantitatively determine the nonlinear enhancement, we first compare the THG intensity from the metasurface with an unpatterned Si film with the same thickness. In the THG intensity measurement, we use an optical parametric
enhancement is on the same order as state-of-the-art nonlinear plasmonic devices,12,13 although we expect the experimental field enhancement to be lower due to a lower experimental Qfactor. However, the major benefit of the dielectric metasurface, when compared with its plasmonic counterparts, is that the field enhancement occurs within the volume of the dark mode resonator with excellent modal overlap with the nonlinear material (Si). The metasurface possesses the advantages of 7390
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beam. By increasing the pump intensity up to 2 GW cm−2, we observe modulation of the transmission up to 32%. Specifically, the transmittance decreases when the pump is on. The decrease of transmittance when pump is on can be explained by the redshift of the Fano resonance peak due to the thermo-optic effect in silicon and the fact that the phonon relaxation time is greater than the 12.5 ns pulse interval of the laser. In order to examine faster Kerr and TPA nonlinear processes in the films we utilized a 1 kHz optical parametric amplifier (OPA) system for ultrafast time-resolved measurements. The details of the OPA-based pump−probe setup is described in the Supporting Information, Section 2. In such a system, the transmission modulation due to the thermal effect can be largely avoided due to the 1 ms pulse interval. Figure 3d shows the ultrafast optical switching occurs with a pump fluence of ∼60 mJ/cm2. The fast switching component can be attributed to the near-instant Kerr and TPA effects and has a switching time of 490 fs. The modulation depth was measured to be 0.2%, smaller than what one may expect based on the field enhancement shown in Figure 2a. We attribute this small modulation depth to two primary reasons. First, the required degenerate pump and probe beams again force us to separate the pump and probe beam by a ∼10 degree angle (s-polarized incidence), which causes the Fano resonance to widen and undergo a shift in wavelength. Second, we have used a photodiode as the detector, which averages the transmittance over the 8 nm fwhm of the band-pass filters, again reducing the effective modulation depth. We also note that Kerr and TPA effect-based transmission modulation is on the same order of magnitude as has been recently reported in a Si nanodisk-based system.30 The slightly longer switching time for our Fanoresonant metasurface compared to the nanodisk system (490 fs compared with 65 fs) is likely due to the higher Q-factor. Based on the pump arriving at near-normal incidence and a quality factor of 466, as measured in the transmittance measurements presented in Figure 1e, a photon lifetime of τ = Qλ/2πc = 333 fs could be expected, close to the experimental measurement. Following the fast modulation, we also observe a slow tail in the pump−probe trace. This tail can be attributed to the free carrier relaxation process. An exponential fit to the tail, with a pump− probe delay up to 20 ps, gives a relaxation time of 24.5 ps. Finally, the absolute THG efficiency for the Fano-resonant Si-based metasurface was characterized by simultaneously measuring the pump and THG beam power (see Supporting Information Section 2 for details of the measurement). Based on these measurements, a conversion efficiency of 1.2 × 10−6 with an average pump power of 50 mW and a peak pump intensity of 3.2 GW cm−2 was measured, as shown in Figure 4a. These measurements were performed with a pump laser with a line width of ∼15 nm, which is much greater than the line width of the Fano resonance (∼2.9 nm). To further increase the conversion efficiency, a laser with comparable power but longer pulse width could be used. A photograph of the sample under 50 mW average pump power (Figure 4b) clearly shows the third harmonic blue light emission. The nonlinear simulation (see Supporting Information Section 3 for details) reveals that, at a peak pump intensity of 3.2 GW cm−2, a conversion efficiency of 1 × 10−4 can be achieved. However, with a tightly focused pump beam, as is in the case of our experiment, the broad incident angle range still becomes the major limiting factor for us to fully utilize the high Q-factor Fano resonance. Nonetheless, to the best of our knowledge, a third harmonic conversion efficiency of 1.2 × 10−6 is still the
oscillator (OPO) centered at 1350 nm as the pump and focus the laser beam to a spot with an area of ∼225 μm2 on the metasurface. The THG signal generated in the forward direction is then collected by a high numerical aperture objective and sent to a grating spectrometer with a liquidnitrogen-cooled charge-coupled device (CCD) camera for spectroscopic analysis (see Supporting Information Section 2 for details of the measurement setup). The THG spectra of the metasurface and unpatterned Si film are shown in Figure 2b,c and demonstrate an enhancement factor of 1.5 × 105. Further verifying the origin of the enhancement, the metasurface shows no significant enhancement when illuminated with the electric field orthogonal to the bar resonator, as is shown in Figure 2b. By comparing the third harmonic signal from a Si-on-quartz film and a bare quartz substrate (Figure 2c), we further excluded the effect of THG from the quartz substrate. In addition to THG enhancement, the strong near-field enhancement in the metasurface can also substantially modify the refractive index of Si at the fundamental wavelength via the combination of the nonlinear Kerr and TPA effects, free carrier absorption, and the thermo-optical effect. This index change in turn shifts the Fano resonance peak wavelength leading to alloptical modulation. Experimentally, this is manifest in the third harmonic peak wavelength deviating from λ0/3 where λ0 is the linear Fano resonance peak, as is illustrated in Figure 3a. In the THG enhancement spectrum measurement, we vary the pump wavelength and determine the corresponding THG enhancement by comparing the photon counts at the THG peak of the metasurface and the silicon film, respectively. We demonstrate that the THG peak deviates from the linear Fano resonance peak by 0.93 nm at peak pump intensity of 0.8 GW cm−2. Further increasing the pump intensity to 1.6 GW cm−2 results in a 2.6 nm THG shift, demonstrating the red-shift of THG peak upon increasing the pump intensity. The narrow bandwidth of the linear transmittance spectrum, combined with the various nonlinear effects, can be used to realize ultrathin all-optical modulators. In particular, we show the modulation of transmittance upon increasing the pump power with a normal incident intensity scan (I-scan) measurement. The experimentally measured transmittance modulation is shown in Figure 3b. We observed a red-shift of the transmittance peak upon increasing the pump power, with a modulation depth of 36%. To get a clearer understanding of the modulation mechanism, pump−probe experiments were conducted. The first set of experiments consisted of a pump−probe measurement at a fixed pump−probe delay time of negative 2 ps (the probe beam arrives before the pump beam) using the 80 MHz OPO system. In this scenario modulation of the probe transmittance is isolated to thermo-optical effects in the silicon as all other processes would have decayed prior to the arrival of the probe. The details of the pump−probe setup is described in the Supporting Information, Section 2. One particular challenge in the pump−probe measurement is that the wavelength and polarization of the pump and the probe need to be degenerate (λ = 1350 nm, polarization along the bar). Therefore, to measure the change in the probe transmission, the probe beam is configured to have a 10 degree incident angle, while the pump beam is kept at normal incidence. Note that at 10 degree incidence (p-polarized), the linear Fano peak has shifted to ∼1355 nm, as is discussed in the Supporting Information, Section 3, and in Figure S7. Figure 3c shows the relative transmittance of the sample when we turn on and off the pump 7391
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Letter
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address ⊥
Center for Integrated Nanotechnologies, Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185, USA.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant No. ECCS-1351334 and the Office of Naval Research under Grant No. N00014-14-1-0475. Fabrication of the metasurfaces was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility.
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Figure 4. (a) Log−log plot of the third harmonic power as a function of the pump power and the peak pump intensity with OPO illumination. The red circles indicate the measured data, and the blue line is a numerical fit to the data with a third-order power function. The green circle denotes the pump power at which the photograph in panel b was taken. The inset shows the extracted absolute THG efficiency as a function of the pump power. (b) Photograph taken under ambient room light showing blue light emission from the sample for an incident wavelength at 1350 nm (average pump power of 50 mW, peak pump intensity of 3.2 GW cm−2).
highest reported to date at comparable pump energies for nanoscale thin films. To summarize, utilizing the large near-field enhancements in a Fano-resonant Si-based metasurface, we have demonstrated highly efficient visible (blue) THG and all-optical nonlinear modulation. Such a platform can also be applied for other nonlinear processes such as four-wave mixing,31 enhanced bistability,32 and Raman amplification33 and may even be extended to Si-based coherent lasing.34 By combining the Kerr shift with the narrow bandwidth of the linear transmittance spectrum the dielectric metasurface potentially opens a new route toward the realization of ultracompact optical devices such as saturable absorbers and modulators.
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REFERENCES
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b02802. Sample fabrication, the measurement setup, numerical modeling, and Figures S1−S7 (PDF) 7392
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