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Supplementary Information An actively ultrafast tunable giant slow-light effect in ultra-thin nonlinear metasurfaces Cuicui Lu,† Xiaoyong Hu,†,‡,* Kebin Shi,†,‡ Qin Hu,† Rui Zhu,†,‡ Hong Yang,† and Qihuang Gong†,‡ † State Key Laboratory for Mesoscopic Physics & Department of Physics, Peking University, Beijing 100871, People’s Republic of China ‡ Collaborative Innovation Center of Quantum Matter, Beijing 100871, People’s Republic of China 1 The supplementary information includes: I. Discussion of selecting structure parameters of the metasurface II. Sample fabrication III. Micro-spectroscopy measurement system IV. Calculation methods for group index ng V. Calculated linear transmission spectra of the metasurface with different structural parameters VI. Optical interference experiment setup and measurement process VII. Femtosecond pump-probe experiment setup and measurement process VIII. Closed-aperture Z-scan measurements and discussion of nonlinearity VIIII. AFM images for ZnO nanoparticles on ITO nanograin film and gold film 2 I. Discussion of selecting structure parameters of the metasurface 1). The reason for selecting the equilateral triangle structure The choice for the equilateral triangle structure comes from the following aspects. Firstly, we want to achieve giant slow light effect. Gold rectangles have been investigated in many papers, and the group index for gold rectangles is not large. While, few works of slow light effect on triangle are found, and the curiosity on triangles encouraged us to investigate. Secondly, we want to achieve large optical nonlinearity to reduce the pump power for ultrafast optical tunability. Gold triangles have stronger surface plasmon polariton resonances according to our previous work (see Cuicui Lu, et al. Plasmonics, 7, 159 (2011)). Thirdly, it is flexible to use triangle dimer to achieve different slow light effect through changing the gap between the two triangles or the structure parameters. Fourthly, other triangle shapes, such as right triangles, acute triangles or obtuse triangles, also have some similar optical properties, however, all of these triangle shapes include at least one sharp angle which is very difficult for nano-fabrications, so equilateral is a trade-off choice. 2) The reason for selecting the gold nanoprism thickness of 40 nm The choice of the effective thickness of 40 nm for gold nanoprisms is based on the following considerations. Firstly, the penetration depth of gold in the near-infrared range has an order of 20 nm, the effective thickness should be larger than the penetration depth in order to obtain obvious metamaterial induced transparency effect, and avoid the transmission of the probe light directly. This results in a larger thickness for gold nanoprisms. Secondly, from the aspect of the practical nano-fabrication, it is very difficult to maintain the perfect structure parameters of gold nanoprisms for a large gold thickness. The larger of the gold thickness, the more obtuse of the corners will be. Then, the triangles will be deformed seriously. This requires that the gold 3 thickness should be as thin as possible. Considering the above factors, we have to select 40 nm as the gold thickness. 4 II. Sample fabrication High-conductivity ITO layer was deposited on SiO2 substrate by using radio frequency sputtering in an oxygen/argon plasma with a mixing ratio of 1:140 at a temperature of 500 °C. The resistance was about 8 Ω/square for the high-conductivity ITO layer. The single layer graphene was fabricated using the chemical vapor deposition (CVD) method.S1 An electron-beam lithography system (Model Raith E-line, Raith Company, Germany) was used to prepare the periodic patterns of the metasurface. The gold film was fabricated by using a laser molecular beam epitaxy (LMBE) growth system (Model LMBE 450, SKY Company, China). The beam (with a wavelength of 248 nm and a pulse repetition rate of 5 Hz) output from an excimer laser system (Model COMPexPro 205, Coherent Company, USA) was used as the excitation light source. The beam was focused onto a gold target mounted on a rotating holder, 15-mm away from the substrate. The typical energy density of the excitation laser was about 500 mJ/cm2. The growth rate measured by a film thickness/rate monitor was about 0.01 nm/pulse. The growth process was conducted under a pressure of 6.5×10-4 Pa for gold films. The ZnO nanoparticles were synthesized by zinc acetate dihydrate and potassium hydroxide in methanol according to the literature procedures.S2,S3 The resulting ZnO nanoparticles were washed twice with methanol. Finally, chloroform, ethylalcohol and 2-ethoxyethanol were added to disperse the ZnO nanoparticles and reach a concentration of 0.7 mg/ml. The ZnO nanoparticles were prepared by spin coating the ZnO dispersion solution onto the ITO substrate at 3,000 r/min for 20 s. The spincoating method was adopted for the fabrication of the multilayer sheets of graphene by using the graphene dispersion solution in ethanol with a concentration of 0.2 mg/ml. The spin-coating speed and the time were 1500 r/min and 30 s. 5 III. Micro-spectroscopy measurement system Micro-spectroscopy measurement experimental setup is shown in Fig. S1. A wideband white light source ranging from 880 nm to 1760 nm (Model HL-2000, Ocean Optics) was normally incident on the sample with a Y-polarized direction, i.e. the electric field is parallel to the ydirection of the structure in Figure.1c. The beam radius was focused to 100 μm. The transmission light was collected by a long working distance objective (Mitutoyo 20, NA = 0.58) and then detected using a fiber monochromator (Model NIR-512, Ocean Optics, USA) with a resolution of 0.74 nm, the output signal of which was collected and analyzed by a computer. The final obtained tranmission spectrum was normalized with respect to a 40-nm-thick gold film coated on a 180nm-thick ITO film on SiO2 substrate, which is the standard method to study the transmission properties of photonic metamaterials. Beam Splitter Figure S1. Micro-spectroscopy measurement experimental setup. 6 IV. Calculation methods for group index ng Numerical simulations were performed by using the commercial finite element method (FEM) solver of COMSOL Multiphysics. The permittivity of the gold was calculated as a function of the wavelength using interpolation fitting and was taken from Ref. S4. Here, the three-dimensional frequency domain module was used. The calculation of group refractive index is based on the formula (1) and (2). n c x t (1) dn d (2) ng n where φ is the phase of the electric field, n is the phase refractive index. The phase change can be extracted through COMSOL software, and then the group refractive index ng can be calculated through formulae (1) and (2). From formula (1), for the output and input planes, we can obtain n c x (3) so we obtain n c x (4) where Δx is the thickness of the metasurface, Δφ is the phase change, is incident light frequency, c is the light velocity in the vacuum. From foumula (2), we can obtain 7 ng d (n ) d (5) Substituting fomula (4) into fomula (5), we obtain ng c d ( ) x d (6) Δφ can be given by the numerical calculation result using the software of COMSOL Multiphysics. In the COMSOL software, we wrote the expression “arg(emw.Ey)” to calculate the phase for each plane under Y-polarized incident light. According to the above calculations, we obtain the numeical simulation result of group index for each frequency. 8 V. Calculated linear transmission spectra of the metasurface with different structural parameters Using the commercial finite element method (FEM) solver of COMSOL Multiphysics, we calculated the linear transmission spectra of the metasurface with different structure parameters. The linear transmission spectra of the metasurface was defined as the quotient between the output power flow of the metasurface with gold periodic nanostructures to that of the metasurface without gold periodic nanostructures. 1) For different gold dimer periods Figure S2 shows the calculated linear transmission spectra of the metasurface with different gold dimer periods. With the increase of the period of the gold dimer, the transparency window center of the metamaterial-induced transparency also has an obvious red-shift, and the left valley (i.e. in the shorter wavelength) adjacent to the transparency peak becomes shallow. Because the left valley is mainly contributed by the outer corners of the gold dimmer interaction (see Fig. 2c); while the right valley is mainly caused by the inner corners of the gold dimmers interaction (see Fig. 2e). 9 1.0 0.5 0.0 1.0 900 nm 0.5 Transmission 0.0 1.0 950 nm 0.5 0.0 1.0 1000 nm 0.5 0.0 1.0 1050 nm 0.5 0.0 1.0 1100 nm 0.5 0.0 1150 nm 1200 1400 Wavelength (nm) 1600 Figure S2. Calculated linear transmission spectra of the metasurface with different gold dimer periods. The blue, red, green, purple and yellow lines correspond to the period of 900 nm, 950 nm, 1000 nm, 1050 nm, and 1100 nm for the unit cell, respectively. 10 2) For different lateral lengths of gold nanoprisms Figure S3 shows the calculated transmission spectra of the metasurface with different lateral lengths of gold nanoprisms. With increase of the lateral length, the metamaterial-induced transparency peak has a little red-shift. 1.0 0.5 350 0.0 1.0 Transmission 0.5 0.0 1.0 380 0.5 400 0.0 1.0 0.5 0.0 1.0 420 0.5 0.0 450 1200 1300 1400 Wavelength (nm) 1500 Figure S3. Calculated linear transmission spectra of the metasurface with different lateral lengths of gold nanoprisms. The blue, red, green, purple, and yellow lines corresponds to lateral lengths of gold nanoprisms of 350 nm, 380 nm, 400 nm, 420 nm, and 450 nm for the unit cell, respectively. 11 3) For different gold nanoprism thicknesses Figure S4 shows the calculated transmission spectra of the metasurface with different gold nanoprism thicknesses. When the gold nanoprism thickness is 10 nm, which is less than that of the optical thick, no metamaterial-induced transparency has been obtained. When the gold nanoprism thickness is more than 20 nm, the metamaterial-induced transparency is obtained. With the increase of the gold nanoprism thickness from 20 nm to 100 nm, the metamaterialinduced transparency is insensitive to thickness changes, and it becomes a little narrower with the increase of the thickness, which permits the fabrication process has larger error for the thickness. 1.0 0.5 0.0 1.0 10 Transmission 0.5 0.0 1.0 20 0.5 0.0 1.0 40 0.5 0.0 1.0 60 0.5 0.0 100 1100 1200 1300 1400 Wavelength (nm) 1500 Figure S4. Calculated linear transmission spectra of the metasurface with different gold nanoprism thickness of 20 nm, 40 nm, 60 nm, 80 nm and 100 nm, respectively. 12 4) For different incident polarizations Figure S5 shows the calculated transmission spectra of the metasurface with different incident polarizations. The angles are formed by the electric field of the incident light away from the X axis. For example, the 00 case corresponds to the incident light only possessing Ex component, while 900 case corresponds to the incident light only possessing Ey component. With the increase of the incident light angle away from the X-axis, the transparency window width becomes small and the left valley (adjacent to the transparency peak) becomes deep, while the transparency window peak is invariant. When the polarization angle is 120, the valleys beside the transparency window have near depth. 13 1.0 0.5 0.0 1.0 0 0.5 Transmission 0.0 1.0 30 0.5 0.0 1.0 60 0.5 0.0 1.0 90 0.5 0.0 1.0 120 0.5 0.0 150 1100 1200 1300 1400 1500 1600 Wavelength (nm) Figure S5. Calculated linear transmission spectrum of the metasurface with different incident polarization cases. The angles are formed by the electric field of the incident light away from the X axis. For example, the 00 case corresponds to the incident light only possessing Ex component, while 900 case corresponds to the incident light only possessing Ey component. 14 VI. Optical interference experiment setup and measurements The basic thought for measurement of the time delay is the optical interference, as shown in Figure S6. A beam (with pulse duration of 35 fs and a repetition rate of 1 kHz) from a femtosecond optical parameter amplifier system (model Opera Solo, Coherent Company, USA) was split into two beams with a ratio of 10:1. Both the probe and pump light were Y-polarized waves. The intensity of the probe light was attenuated to be less than 10 W/cm 2, so that the influence of the probe light on the refractive index change of metasurface can be neglected. The weak beam, as the probe light, was split into two beams (B_pro1 and B_pro2), they propagate two ITO glasses, and the optical pathways were tuned to be equal. sA delay line was used to adjust the optical path of B_pro1 and B_pro2 till the interference fringes appeared on the CCD screen. And then one ITO glass in beam B_pro2 was replaced by our sample, the CCD images were recorded at different time by adjusting the delay line till the interference fringes appeared. The strong beam, used as the pump light (B_pum), was also incident on this upper-surface plane and focused with a spot size of about 100 μm. There was a angle of about 30°between the beams B_pum and B_pro2. 15 Figure S6. Slow light measurement experimental setup. 16 VII. Femtosecond pump-probe experiment setup and measurement process The femtosecond pump-probe experiment setup is shown in Fig. S7. A beam (with a pulse duration of 35 fs and a repetition rate of 1 kHz) from a femtosecond optical parameter amplifier system (model Opera Solo, Coherent Company, USA) was split into two beams with a ratio of 10:1. Both the probe and pump light were Y-polarized waves. The intensity of the probe light was attenuated to be less than 10 W/cm2, so that the influence of the probe light on the refractive index change of ZnO/graphene and polycrystalline ITO can be neglected. The weak beam, as the probe light, was incident normal to the upper-surface plane of the metamaterial with a spot size of about 100 μm. The strong beam, used as the pump light, was also incident on this upper-surface plane and focused with a spot size of about 200 μm. There was a small angle of 150 between the pump and probe light. The probe light was in the center of the pump light when propagating through the metamaterial sample. The probe light propagating through the metamaterial was detected using a fiber monochromator (Model NIR-512, Ocean Optics, USA) with a resolution of 0.74 nm, the output signal of which was collected and analyzed by a computer. A delay line was used to adjust the timing between the pump and probe pulses. According to the third-order nonlinear optical Kerr effect, the effective refractive index n of the ZnO-nanograins/graphene micro-sheets can be obtained by the relation n n0 n2 I (7) where n0 and n2 are effective linear and nonlinear refractive indices of the ZnOnanograins/graphene micro-sheets. I is the pump intensity. 17 Femtosecond laser system Figure S7. Optical pump-probe experimental setup. 18 VIII. Closed-aperture Z-scan measurements and discussion of nonlinearity A 35 fs, 1550 nm laser beam from a femtosecond optical parameter amplifier system (model Opera Solo, Coherent Company, USA) with a repetition rate of 1 kHz was used as the light source. The experimental measurement setup was as detailed in Ref. S5. The remarkable peak– valley profile of the curve implies the negative value of the effective nonlinear refractive index n2 of the 180-nm-thick polycrystalline ITO film covered with multilayer-graphene micro-sheets. The normalized transmission can be fitted toS5 T ( z) 1 4x ( x 9)( x 2 1) 2 (8) where T is the normal transmittance, x = z/z0 , z is the longitudinal distance from point, z0 is the Rayleigh range of the laser beam, and ∆φ is the phase change. The effective nonlinear refractive index n2 could be obtained from1 n2 2I 0 (1 e L ) (9) where λ is the laser wavelength in vacuum, α is the linear absorption index, I0 is the peak intensity of the laser beam, and L is the sample thickness. The measured results are shown in Figure S8. The nonlinear refractive index is -7.64×10-10 cm2/W for ITO glass with monolayer graphene on. When the ZnO nanoparticles were coated on the monolayer graphene film, the nonlinear refractive index was increased to -1.07×10-9 cm2/W, the nonlinear improvement of 1.4 times was mainly brought by the quantum confinement. In addition, we also measured the nonlinear refractive index of the multilayer-graphene microsheets on ITO glass using the same Z-scan method; it was -2.06×10-8 cm2/W, so the nonlinearity improvement is obvious (about 27 times compared with that of the monolayer graphene) for the 19 reinforced interaction provided by the multiayer-graphene microsheets. As we know, the final nonlinear refractive index was -8.03×10-7 cm2/W for the complex films in our sample, the 39 times improvement of nonlinearity compared with that of the multilayer-graphene microsheets were mainly contributed from the hot electron injection and surface plasmon polariton resonances. Figure S8. Measured closed-aperture Z-scan curves. (a) SEM image of the ITO film covered with monolayer graphene. (b) Corresponding measured closed-aperture Z-scan curve. (c) SEM image of the ITO film covered with monolayer graphene and ZnO nanoparticles. (d) Corresponding measured closed-aperture Z-scan curve for the film. The red solid curve is the theoretical fit to the data. 20 VIIII. AFM images for ZnO nanoparticles on ITO nanograin film and gold film Both of ZnO and ITO appear nanograin shapes, so can provide strong quantum-size confinement effects, which largely improves the nonlinear refractive index. a b Figure S9. AFM images for ZnO nanoparticles on ITO nanograin film (a) and gold film (b). 21 Supplementary references: S1. Cho J, Gao L, Tian J, Cao H, Wu W, et al. Atomic-scale investigation of graphene grown on cu foil and the effects of thermal annealing. ACS Nano 2011; 5: 3607-3613. S2. Beek WJE, Wienk MM, Kemerink M, Yang X, Janssen RAJ. Hybrid zinc oxide conjugated polymer bulk heterojunction solar cells. J Phys Chem B 2005; 109: 9505-9516. S3. Liu D, Kelly TL. Perovskite solar cells with a planar heterojunction structure prepared using room-temperature solution processing techniques. Nat Photon 2013; 8: 133-138. S4. Johnson PB, Christy RW. Optical constants of the noble metals. Phys Rev B 1972; 6; 43704379. S5. Henari FZ, Cazzini K, El Akkari F, Blau WJ. Beam waist changes in lithium niobate during z-scan measurement. J Appl Phys 1995; 78: 1373-1375. 22