Supplementary information for Stretchable photonic crystal cavity with

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1 Supplementary information for Stretchable photonic crystal cavity with wide frequency tunability Chun L. Yu, 1,, Hyunwoo Kim, 1, Nathalie de Leon, 1,2 Ian W. Frank, 3 Jacob T. Robinson, 1,! Murray McCutcheon, 3," Mingzhao Liu, 1,# Mikhail D. Lukin, 2 Marko Loncar, 3 Hongkun Park, 1,2,* 1 Department of Chemistry and Chemical Biology, 2 Department of Physics, and 3 School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA S1. FDTD simulations Finite-difference time-domain (FDTD) simulations were performed on a commercial package by Lumerical Solutions, Inc. We used the material properties for Si from the simulation package and the refractive index of PDMS was set as 1.4 for all wavelengths. We chose a hexagonal lattice with lattice spacing of 500 nm and a nanowire (NW) radius of 100 nm, resulting in a band gap from 1500 nm to 1900 nm. Because the experimental laser scanning range was from 1480 nm to 1680 nm, we designed the structure dimensions to support high- Q modes in the middle of scanning range. By imposing symmetric or anti-symmetric boundary conditions on the y-z plane at x = 0, two sets of modes were isolated (Table S1). Note that the Q factors here do not take into account the effect of the fiber. The reason that we only observed two modes experimentally is most likely due to the low Q factors of the other modes. S2. Materials and methods To fabricate flexible PCs, a bi-layer ebeam resist (PMMA 495 A2 and PMMA 950 A2) was! "

2 spin-coated onto a single crystalline Si wafer (University Wafer). PC patterns were written with an e-beam writer (Elionix F125) and developed in MIBK:IPA. After development, 40 nm thick Al was evaporated on the wafer and lifted-off in acetone. Reactive ion etching (STS ICP-RIE) was used to etch the Si wafer with C 4 F 8 and SF 6 gases to generate Si NWs. Subsequently, 20 nm SiO 2 was deposited uniformly on the wafer using atomic layer deposition (ALD). A directional SiO 2 etch was performed to remove the oxide on the wafer, while the oxide on the NW surface was intact. The SiO 2 layer on the NWs formed a protective layer for the next etching step. Si nanowires were subsequently undercut with a combination of C 4 F 8, H 2, SF 6 gases. A 4 µm tall window surrounding the PCs was created using photolithography. PDMS was prepared by using Sylgard 184 with a 10:1 ratio, and subsequently poured onto the wafer with PCs. Degassed PDMS was cured in the oven at 70 C for 2 hours. Photoresist on the wafer was dissolved by Remover PG (MicroChem) at 70 C. Finally, the PDMS film was pushed along the silicon wafer surface to peel off the PCs. A tapered fiber was used to optically excite the resonant modes. To extend the evanescent field into the air surrounding the fiber (SMF-28), the fiber was heated with a torch and pulled until the diameter was reduced to ~700 nm. The tapered fiber was then lowered into contact with the cavity using high-precision stages with a resolution of 50 nm/step (Suruga). As shown in Figure 2a, the mesa structure serves as a spacer to separate the tapered fiber from the bulk PDMS substrate. To cover a large excitation bandwidth ( nm) we employed two separate lasers (Santec TSL 510), each covering half of the total bandwidth. Polarization of the light was controlled by an in-line fiber polarization controller (Thorlab, PLC-900). The transmission spectra were obtained by scanning the laser wavelength at fixed polarizations and recording the output intensity using a high-speed fiber-coupled detector (Thorlab, DET01CFC).! #

3 S3. Calculation of strain on PC cavity Our PC is elongated along the stretching axis, while it is shrunk in the other two orthogonal directions. The amount of cavity length elongation is extracted by comparing the optical microscope images of the device at the minimum and maximum strains. Using the line profiles along the cavity, strain is calculated by dividing the change in the PC length by its original length. Figure S1 shows the analysis for mechanical stretching along the line cavity. The analysis for stretching orthogonal to the line cavity is done in the same way. S4. Q analysis When the PDMS is stretched along the line cavity, the Q factor increases and then decreases (Fig. S2a). As shown in Fig. S2b, because the background is not flat, we estimate the fullwidth at half-maximum (FWHM) by taking an average of the background. Beyond the shift of 14 nm, the resonance lineshape is distorted, making Q analysis inaccurate. A second photonic crystal cavity is used when the PDMS is stretched orthogonal to the line defect. The resonant peak exhibits a Fano lineshape (Fig. S2d). Q factor is extracted by performing a Fano fit 1 with the following formula:!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!, where A 0 and F 0 are constant factors, q describes the ratio between resonant and nonresonant transition amplitudes,! 0 is the resonance frequency, and! is the resonance linewidth. So Q =! 0 /!. S4. Mechanical deformation simulations Finite element simulations (COMSOL) were performed in order to investigate the strain! $

4 distribution of the PC cavity embedded in PDMS, which can affect the cavity length. The material parameters of PDMS used in the simulation are as follows: density (965 kg"m -3 ), Young s Modulus (615 kpa), and Poisson ratio (0.495). The PDMS block was stressed in the directions along and perpendicular to the cavity line until the strain in the mesa matched experimentally observed values. Figure S3 shows the percentage of deformation for cross sections along the cavity and shows good deformation uniformity in the area with the Si NWs. Strain is not plotted, as the much stiffer Si NWs are not strained. Note, however, that NWsare still displaced from their zero-stress positions. Therefore, the relevant quantity that is plotted is the amount of deformation from the zero-stress position (Figure S3ii), normalized by the zero-stress value. The simulation confirms uniform strain across the PC for both stretching directions. References 1. Galli, M.; Portalupi, S. L.; Belotti, M.; Andreani, L. C.; O'Faolain, L.; Krauss, T. F. Appl. Phys. Lett. 2009, 94, ! %

5 Table S1. Resonant wavelengths and Q factors for symmetric and anti-symmetric modes.! &

6 Figure S1. Calculation of strain applied to the PC cavity. Optical images of a PC cavity whose resonance frequency is (a) nm, and (b) nm. The overlaid plots show the brightness intensity profile along the white dashed lines. Strain is calculated by dividing the PC length change by the pre-stretching value.! '

7 Figure S2. Q analysis for mechanical stretching. (a) Q factor as a function of resonance shift when PDMS was stretched along the line defect. A representative figure of the resonance peak is shown in (b). (c) Q factors as a function of absolute resonance shift when PDMS was stretched orthogonal to the line defect. A representative figure of the resonance peak is shown in (d). Blue curve is the Fano fit.! (

8 Figure S3. Cross sections of the PDMS mesa along the cavity in the PC. (i) elongated cavity (3% strain) with the stress along the cavity, (ii) cavity without stress, (iii) compressed cavity (-6% strain) with the stress perpendicular to the cavity. The color-map depicts deformation normalized by zero-stress position. The white line along the symmetry plane at the center of the cavity is a simulation artifact where fractional deformation goes to zero; the width of the zero deformation area is determined by the size of the mesh in the simulation.! )