Supporting Information. Ultra-compact pseudowedge plasmonic lasers and laser arrays

Transcription

1 Supporting Information Ultra-compact pseudowedge plasmonic lasers and laser arrays Yu-Hsun Chou 1, Kuo-Bin Hong 1, Chun-Tse Chang 1, Tsu-Chi Chang 1, Zhen-Ting Huang 2, Pi-Ju Cheng 3, Jhen-Hong Yang 4, Meng-Xian Lin 5, Tzy-Rong Lin 2, 6, Kuo Ping Chen 7, Shangjr Gwo 5, 8, and Tien-Chang Lu 1* 1. Department of Photonics, National Chiao Tung University, Hsinchu, Taiwan 2. Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung, Taiwan 3. Academia Sinica, Research Center for Applied Sciences, Taipei 115, Taiwan 4. Institute of Photonic System, National Chiao Tung University, Tainan, Taiwan 5. Department of Physics, National Tsing-Hua University, Hsinchu 30013, Taiwan. 6. Institute of Optoelectronic Sciences, National Taiwan Ocean University, Keelung, Taiwan 7. Imaging and Biomedical Photonics, National Chiao Tung University, Tainan, Taiwan 8. National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan. *Corresponding author address: 1

2 Outline 1. Properties of SPP waves in different metal structures 2. Properties of the colloidal Ag flakes 3. Experimental and simulated reflectivity spectra of Ag grating 4. Optical characteristics of planar SPP nanolasers 5. Far-field polarization of pseudowedge SPP nanolasers with different off-angles 6. Models of pseudowedge SPP nanolaser constructed by a ZnO nanowire placed on the Al2O3/Ag notch with a 75 off-angle 7. Far-field polarization patterns of planar SPP waves coupled out at notch 8. Threshold comparison of SPP nanolasers fabricated by colloidal Ag and E-gun Ag 9. Temperature characteristics of planar SPP nanolasers 10. Estimation of the quenching rate and Purcell factor of ZnO nanowires on Ag flakes and gratings 11. Lasing emission wavelength of samples with different grating periods and notch width 12. Calculations of carrier dynamics in ZnO nanowire placed on Ag and grating 13. References 2

3 S1 Properties of SPP waves in different metal structures. a, Schematic diagram of semiconductor-insulator-metal (SIM) structure with a flat surface. The interface with lateral confinement allows the SPP wave to travel in the in-plane direction with finite propagation length. b, A triangular SIM strip with a chamfered edge can compress the SPP wave to trap it at the tip of the metal strip. c, A metal/dielectric core-shell nanosphere can only excite the resonant LSP wave. Because the resonant LSP wave is restricted at the interface of the metal and the insulator/semiconductor, it cannot propagate in any direction. 3

4 Calculated mode profiles of different ZnO/Al2O3/Ag SIM structures are shown for d, the planar SPP wave, e, the wedge SPP wave, and f, the LSP wave. g, Dispersion relation of the fundamental planar SPP mode and wedge SPP mode with a 90-degree chamfered edge for r = 5 nm, 10 nm, and 15 nm, respectively. h, DOSs for SPP waves with different structures. Lines and stars of various colors indicate the SPP propagation modes for flat metal and metal strips with distinct chamfers and localized LSP modes for metal nanospheres with different diameters. To emphasize the SPP structural effect, triple-layer plasmonic structures (ZnO/Al2O3/Ag) with different restrictions on their geometry structure were constructed as illustrated in Fig. S1d f. For a SPP waveguide with planar structure such as that shown in Fig. S1a and d, SPP only propagates in the x- and y-directions along the interface between the insulator and the metal, with a propagating length (Lp) from hundreds of nanometers to hundreds of microns depending on the waveguide parameters; fields restricted in the z- direction evanescently fall to 1/e with a dimension on the order of tens to hundreds of nanometers. The calculated field distribution illustrated in Fig. S1e demonstrates the nature of the wedge SPP mode. Because the electric potential on a continuous metal surface is in equilibrium, electrons tend to accumulate at the areas of the surface with large curvature. Thus, the fields will be more concentrated at the edges, resulting in a smaller mode volume than that of a planar SPP. 1 2 If we further reduce the metallic structure to zero dimension (LSP), as shown in Fig. S1f, the nonpropagating excitations that form on the surfaces of metallic particles with diameters close to or smaller than the optical wavelength are strongly confined to a subwavelength region in all directions; thus, only a quantized 4

5 discrete mode exists. To understand the dimensionality effect of the SPP mode, we solve a quasi-static Maxwell s equation in the frequency domain; Fig. S1g shows the calculated dispersions of fundamental SPP modes with different structures. The λ k relation is much more dispersive for the fundamental wedge SPP mode than for the planar SPP mode, because of the strong confinement of the optical field at the edge of the structure. When the radius of the edge is small enough and the wavelength is near the plasmonic resonance, very large propagation constant of the wedge SPP mode will be obtained. No formula exists to express the propagation properties of LSP. Therefore, to evaluate the interaction strength between light and matter, the density of states (DOSs), which is usually inversely proportional to the mode volume, can be a useful indication of the dimensional effects of SPP structures. Here, the DOSs of several SPP waveguides with different DOFs can be defined as follows 3 : 1 1 k ( ) Q( ) gplanar ( ), g ( ), g ( ) (1) L v A v V spp Wedge LSP eff 2 g ( ) eff g ( ) eff where is the reduced Planck constant and v ( ) is the group velocity calculated from the dispersion relation. k ( ) denotes the in-plane wave vector of the planar SPP mode spp and Q( ) is the quality factor of the LSP mode. L eff, A eff and V eff are the effective length, mode area, and mode volume of the planar, wedge, and localized SPPs, respectively. As shown in Fig. S1h, LSP modes for metal/dielectric core-shell nanospheres show large DOSs at discrete wavelength points, with a red-shift trend as the diameter increases. However, planar and wedge SPP modes exhibit continuously increasing DOSs as the wavelengths approach to the surface plasmonic resonance. Notably, the wedge SPP waveguide with a small-radius edge can have a comparable DOS to that of a LSP resonator. g 5

6 Therefore, a wedge SPP mode with a large momentum and a high surface plasmon density could be utilized to strongly interact with the gain medium in an extremely small region, resulting in a strong Purcell effect. 6

7 S2 Properties of the colloidal Ag flakes. To minimize the surface scatter losses and the intrinsic ohmic damping losses, we chose the colloidal Ag as the metal layer 4. a, Optical image of the synthesis colloidal Ag on the glass substrate. b, SEM image of the colloidal Ag flake. The typical thickness of Ag flake is approximately 1 μm. The surface of the colloidal Ag is very smooth in a large area with a RMS value of about 0.5 nm over 1 1 mm 2 area. c, X-ray diffraction (XRD) measurement of the colloidal Ag with FWHM~0.05. d, The selected area diffraction (SAD) pattern of the Ag flake by TEM. The narrow FWHM of XRD and sharp SAD patterns clearly indicate excellent crystal quality of colloidal Ag flakes. 7

8 S3 Experimental and simulated reflectivity spectra of Ag grating. The fabricated metal grating covered with a 3 nm-thick Al2O3 contains a m 2 square notch array. The period is approximately 500 nm with 80 nm-wide notches. a, b, The OM images and schematics for simulation of Ag gratings under y-polarized and x-polarized excitation. In the y-polarized excitation, the grating areas show different color with respect to the flat Ag area. While in the x-polarized excitation, it s hard to identify the grating location. c, Measured y-polarized reflectivity spectrum and the calculated angle-averaged reflection spectra. Gray and blue lines shown in the figure are the results of experiment and simulation. In the calculation, the periodic condition is included and incident angle θ of plane wave is set to 0 ~5. The plasmonic modes are clearly observed as the dips in reflectance spectra, which match quite well to the measured ones. d, Measured x-polarized reflectivity 8

9 spectrum and the calculated angle-averaged reflection spectrum. There s no obvious dips in the reflectivity spectra. The slight difference between experiment and simulation is due to the fabrication imperfection and slight mis-alignment between polarizer and grating directions. The localized SPP modes below the 400 nm are difficult to observe because the reflectivity measurement system is built mainly for visible light. 9

10 S4 Optical characteristics of planar SPP nanolasers. The device composes a ZnO nanowire on a flat Ag flake coated with a 3 nm-thick Al2O3 layer. The measurement was done at 77K. a, Emission spectra of a planar SPP nanolaser at various pumping power. The multiple lasing peaks originates from the multiple longitudinal modes with the same transverse fundamental mode in the ZnO nanowire with a 1.5 μm cavity length 5. The estimated group index for this planar SPP waveguide is ng = 77 for a longitudinal mode spacing Δλ ~ 0.6 nm. The measured group index can match to the calculated value of 83 from Fig. 4a in the main text. b, The red spheres correspond to the L-L curve at the emission peak of nm, fitted with a black curve using modified rate equations. The spontaneous emission β factor is fitted to be 0.4. The linewidth of emission peak with increasing pumping power is indicated by blue spheres. 10

11 S5 Far-field polarization of pseudowedge SPP nanolasers with different off-angles. The off-angle between nanowires and the notch are a, Δθ=15, b, Δθ=45 and c, Δθ=80, respectively. When the polarizer locates at the top of samples, all of the polarization directions of the laser emission are perpendicular to the notch, which is independent to the orientation of the wire. The results indicate the emission from the fabricated sample were related to the pseudowedge SPP mode rather than the planar SPP mode or photonic waveguide mode. 11

12 S6 Models of pseudowedge SPP nanolaser constructed by a ZnO nanowire placed on the Al2O3/Ag notch with a 75 off-angle. a, Near-field cross-section image of Fabry-Pérotlike surface plasmonic mode existing in the pseudowedge SPP nanolaser for ZnO nanowire using three-dimensional mode solver. The ZnO nanowire is placed with an off-angle of 75 to the notch. b, Radiation profile of pseudowedge SPP nanolaser out-coupling to the air. The color map displays the y-z plane cross-section image of radiating electric field emitting from the pseudowedge SPP nanolasers. c, Calculated polarization curve of pseudowedge SPP nanolaser right on top. Black line demonstrates the electric field intensity variation with polarization angle. The green and gray stripes represent the ZnO nanowire and Ag notch, respectively. The polarization direction of the laser emission is clearly perpendicular to the notch. 12

13 S7 Far-field polarization patterns of planar SPP waves coupled out at notch. Here we d like to investigate the far field polarization patterns for a pure planar SPP wave coupled to the top direction at the far field. a, Schematic top-view of ZnO nanowire rotated with an θ off-angle to the Al2O3/Ag notch. Green and gray stripes are ZnO nanowire and metal notch, respectively. Purple arrow shows the planar SPP wave excited at the lateral cross section of ZnO/Al2O3/Ag. b, Schematic of a three-dimensional FEM simulation model for ZnO nanowires placed on an Al2O3/Ag notch. Bright spot shows that the planar SPP wave was confined at the bottom of ZnO nanowire and will propagate along the nanowire waveguide and further strike the edge of notch to generate the scattering field. We then observe the electric field intensity at the top plane with varied polarization angles. c, The black solid curves are the calculated polarization patterns of ZnO nanowires rotated 50, 75 and 90, respectively to the notch. The polarization directions change as the off- 13

14 angles between nanowire and notch change. It indicates that if the planar SPP modes are dominated in the ZnO nanowire, the far-field polarization angle will be influenced by the nanowire direction. On the contrary, pseudowedge SPP mode will only support far-field radiation with polarization angle perpendicular to the notch. 14

15 S8 Threshold comparison of SPP nanolasers fabricated by colloidal Ag and E-gun Ag. Quarter box chart of threshold power showing that the average threshold values of a, 16 ZnO nanowires are 170 MW/cm 2 and 13 MW/cm 2 for the Al2O3/E-gun Ag and Al2O3/ colloidal Ag flat templates, and b, 8 nanowires are 600 MW/cm 2 and 92 MW/cm 2 for the Al2O3/E-gun Ag and Al2O3/ colloidal Ag grating templates. The scattering effect caused by the surface roughness and intrinsic ohmic losses caused by grain boundaries inside the metal increases the threshold of sample fabricated by E-gun. 6 On the other hand, samples fabricated by colloidal Ag shows lower and uniform threshold values, which can be attributed to the high crystal quality with ultra smooth surface and less grain boundary inside the metal. 15

16 S9 Temperature characteristics of planar SPP nanolasers. a, The lasing spectra of planar SPP nanolasers with the increasing temperature from 77K to 300K. b, The threshold pumping power versus the temperature for planar SPP nanolasers. The corresponding characteristic temperatures (T0) can be extracted to be 180K for planar SPP nanolasers. Such a low threshold behavior is mainly due to the excellent crystal quality of Ag flakes. 5 16

17 S10 Estimation of the quenching rate and Purcell factor of ZnO nanowires on Ag flakes and gratings. a, Estimated quenching rate from TRPL measurement through 5 samples. Quenching effects such as surface roughness scattering, poly crystalline scattering and intrinsic ohmic loss will result in a smaller Purcell factor compared to the theoretical prediction. We neglect the non-radiative recombination at 10K and define the measured carrier life time as r, and the non-radiative life time at higher temperature can be observed by the TRPL measurement with ZnO nanowire placed on the sapphire substrate. Although the quenching lifetime is hard to verify, there should be a reasonable lower and upper limit for the quenching lifetime. The detailed analysis is reported elsewhere. 7 b, the corresponding Purcell factor calculate from a. 17

18 Wavelength (nm) period / notch width 160nm / 80nm 400nm / 50nm 500nm / 80nm S11 Lasing emission wavelength of samples with different grating periods and notch width. The sub-wavelength grating with different periods and notch width will not affect on the emission wavelength of pseudowedge SPP nanolasers. Since the length of fabricated nanowire can only across 1 to several notches, the effect of distributed feedback is negligible in our case. In addition, since the field is strongly localized at the edges of notch, changing the notch width from 80 nm to 50 nm will also not affect the lasing wavelength, which is another feature of this pseudowedge SPP nanolaser. 18

19 S12 Calculations of carrier dynamics in ZnO nanowire placed on Ag and grating. To calculate the effective Purcell factor inside the ZnO nanowire, the carrier rate equation was implemented, 2 n( r, t) t D n( r, t) F( r) n( r, t) 0. Due to the strong interaction between light and matter, the local Purcell factor enhanced radiative recombination rate can be written as F() r. Here, F() r is the local Purcell factor of SPP mode calculated by the EM eigenmode solver shown in Fig. 5d of the main text and 300 ps is the exciton lifetime. The carrier diffusion behavior is also considered in the calculation and the exciton diffusion coefficient of ZnO used for simulation is set to D 13cm 2 s. 8 As a result, the calculated carrier lifetimes are plotted. The decay times are listed in the figure and the estimated effective Purcell factors for ZnO placed on Ag and Ag grating are 17.4 and 22.2, respectively which means the pseudowedge SPP mode induced by an Ag grating gives rise to a relatively stronger Purcell effect compared with the planar SPP mode formed by Ag flake. It s interesting to note that although the local Purcell factor is very large for the 19

20 pseudowedge SPP mode as shown in Fig. 5d of the main text, the effective Purcell factor is not substantially increased. This is because the strong electric field intensity is only localized in a small volume in comparison to the whole gain volume for the pseudowedge SPP. When carrier rate equations include the diffusion and spatial dependent Purcell factor, the effective Purcell factor is not significantly increased. References 1. Gramotnev, D. K.; Bozhevolnyi, S. I. Nat. Photonics 2010, 4 (2), Barthes, J.; Bouhelier, A.; Dereux, A.; Francs, G. C. des. Sci. Rep. 2013, 3 (1), Genov, D. A.; Oulton, R. F.; Bartal, G.; Zhang, X. Phys. Rev. B 2011, 83 (245312), Wang, C.-Y.; Chen, H.-Y.; Sun, L.; Chen, W.-L.; Chang, Y.-M.; Ahn, H.; Li, X.; Gwo, S. Nat. Commun. 2015, 6, Chou, Y.; Chou, B.; Chiang, C.; Lai, Y.; Yang, C.; Li, H.; Lin, T. ACS Nano 2015, 9 (4), Chou, B.; Chou, Y.; Chiang, C.; Wu, Y.; Lin, T.; Lin, S.; Lu, T. IEEE JSTQE 2015, 21, Chou, Y.; Wu, Y.; Hong, K.; Chou, B.; Shih, J.; Chung, Y.; Chen, P.; Lin, T.; Lin, C.; Lin, S.; Lu, T. Nano Lett. 2016, 16 (5), Fu, X.; Jacopin, G.; Shahmohammadi, M.; Liu, R.; Benameur, M.; Ganiere, J.-D.; Feng, J.; Guo, W.; Liao, Z.-M.; Deveaud, B.; et al. ACS Nano 2014, 8,