Supporting information. GaN Metalens for Pixel-Level Full-Color Routing at Visible Light

Transcription

1 Supporting information GaN Metalens for Pixel-Level Full-Color Routing at Visible Light Bo Han Chen 1,, Pin Chieh Wu 2,, Vin-Cent Su 3,, Yi-Chieh Lai 1,4, Cheng Hung Chu 2, I Chen Lee 5, Jia-Wern Chen 1, Yu Han Chen 1, Yung-Chiang Lan 4, Chieh-Hsiung Kuan 5, and Din Ping Tsai 1,2,6* 1 Department of Physics, National Taiwan University, Taipei 10617, Taiwan 2 Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan 3 Department of Electrical Engineering, National United University, Miaoli 36063, Taiwan 4 Department of Photonics, National Cheng Kung University, Tainan 70101, Taiwan 5 Department of Electrical Engineering and Graduate Institute of Electronics Engineering, National Taiwan University, Taipei 10617, Taiwan 6 College of Engineering, Chang Gung University, Taoyuan, 33302, Taiwan *dptsai@phys.ntu.edu.tw These authors contributed equally to this work. 1

2 1. RCP-to-LCP conversion efficiency and phase shift of PR, PG, and PB nanopillars Figure S1. Simulated RCP-to-LCP conversion efficiency and phase shift of (a) P B, (b) P G and (c) P R GaN nanopillars with different oriented angles. Each data point is carried out from an array of GaN nanopillars with equal dimensions. 2

3 2. Phase profile for an out-of-plane metalens To converge the incident light onto a spot in a three-dimensional space, the phase profile on the metalens has to follow: Φ metalens (r p, φ p ) = 2π ( FO BF ) λ d where FO and BF denote the focal length f and the distance between the focal point F and an arbitrary position B on the metalens, respectively (see Figure S2). The point A shown in Figure S2 is the vertical projection point on x-y plane (metalens surface) from the focal point F. We consequently obtain the distance between points A and B: (E1) AB = r 2 p + f 2 sin 2 θ f 2r p fsinθ f cos (φ f φ p ) Then, the distance between focal point F and point B can be obtained: (E2) BF = f 2 + r 2 p 2r p fsinθ f cos (φ f φ p ) By combining eqs. (E1) with (E3), the required phase profile for an out-of-plane focusing metalens can be realized as: Φ metalens (r p, φ p ) = 2π λ d (f f 2 + r p 2 2r p fsinθ f cos (φ f φ p )) (E3) (E4) 3

4 Figure S2. Schematics used to describe the metalens which is able to converge the incident light into a spot positioned at an arbitrary location F in free space. O: the center of metalens; B: arbitrary position on the metalens surface; A: the vertical projection point from the focal point F onto the metalens surface. 4

5 3. Intensity profile of in-plane, on-axis and off-axis focal spots Figure S3. The cross-sectional cut of simulated intensity at corresponding focal spots from the (a-c) on-axis and (d-f) off-axis focusing metalenses carried out from Figure 2. The focal plane is at z = 110 μm and z = μm for the case of on-axis and off-axis focusing metalens, respectively. The center of metalens is O(0, 0, 0). 5

6 4. Simulated results of three out-of-plane focusing metalenses Figure S4. Simulated result of three single out-of-plane focusing metalenses with size of 6 μm 6 μm, focal length 2 μm, polar angle θ f = 45, and azimuthal angle φ f = 45. (a-c) Intensity distribution on the focal plane for three metalenses illuminated under the corresponding optimized wavelength. The dashed lines C1 and C2 indicate the cut lines for observing the intensity distribution on y-z plane (first row in (d-f)) and x-z plane (second row in (d-f)), respectively. (d-f) Two-dimensional intensity profile from the off-axis focusing metalenses. (g-i) The cross-sectional intensity cut along C2 line shown in (a-c). 6

7 5. Optical measurement setup Figure S5 shows the optical setup for experimentally examining the performance of fabricated metalenses. A Fianium supercontinuum laser combined with an acousto-optic tunable filter (AOTF) is utilized to select the required single wavelength in the visible spectrum. Since there is no small aperture in front of the metalens, a 20 /0.4 objective is used to focus incident light on the metalenses. To properly evaluate the working efficiency, the size of the incident focal spot has to be the same as the diameter of metalenses. A 50 /0.42 objective and a collection lens with a quarter-wave plate (λ/4) plus a linear polarizer (P) are used before the scmos for collecting the transmitted light with proper circular polarization. Figure S5. The measurement setup for optically evaluating the performance of fabricated metalenses. 7

8 6. List for the working efficiency of previous reported visible metalenses Table S1. Working efficiency of previous reported visible metalenses Category Materials Scheme Working wavelength Efficiency Reference Dielectric TiO 2 Transmission VIS (532 nm) 50% 1 Dielectric TiO 2/SiO 2/Al Reflection VIS ( nm) 20% 2 Dielectric TiO 2 Transmission VIS (405, 532, 660 nm) 86, 73, 66% 3 Dielectric Si 3N 4 Transmission VIS (633 nm) 40% 4 Dielectric Si Transmission VIS (532 nm) 58% 5 Dielectric SiO 2 Transmission VIS (632.8 nm) 59.60% 6 Dielectric Si Transmission VIS ( nm) 25-70% 7 Metal Al/Ag/Au Transmission VIS (450, 550, 660 nm) 40% 8 Metal Au Transmission VIS (676 nm) 50.12% 9 Dielectric GaN Transmission VIS (430, 532,633 nm) 87%, 91.6%, 50.6% this work 8

9 7. Simulated results of miniaturized mutiplex color router Figure S6. Simulated results of a RGBG multiplex router with size of μm μm, focal length 4 μm, polar angle θ f = 45, and azimuthal angle φ f,r = 45, φ f,g1 = 135, φ f,b = 225 and φ f,g2 = 315. (a-c) The intensity distribution on the focal plane with three individually incident wavelengths. The corresponding intensity distribution on y-z plane and x-z plane are shown in (d-f). (g-i) The cross-sectional intensity cut and FWHM of each focal spot. 9

10 8. Dispersion of RGB multiplex color router To further understand the origins of crosstalk, which is mainly from the dispersion effect of GaN nanopillars, we subsequently discuss the diffracted angle by varying incident wavelengths. The relation between refracted angle and incident wavelength can be deduced by generalized Snell law 10 : 2π sin θ λ t = dϕ in dx (E5) where ϕ is the phase discontinuities from two adjacent nanopillars, θ t is the angle of refraction, λ in is the incident wavelength. When we consider the periodic unit cell of nanopillar as a set of grating, it introduces an additional momentum to the incident wave: 2π λ in sin θ t = G (E6) where G is the reciprocal vector. By combining the (E5) with (E6), we can simply obtain the relation between incident wavelength and structure period Λ: sin θ t = λ in Λ (E7) According to eq. (E7), one can find that the refracted angle is larger when the incident wavelength is longer if the period is fixed. Take the out-of-plane focusing metalens, which composed of PG nanopillar as an example, the refracted light from the red color is located on the left side of the green focal spot while the one from the blue color is located on the 10

11 opposite side (see yellow solid line square in Figure S7(c)). It results in the crosstalk at each desired position, as shown in Figure S7(c). Figure S7. A demonstration of complex RGB color router for the discussion of color crosstalk. (a) Schematic of complex unit cell and (b) SEM image for the RGB color router. (c) Measured intensity distribution at the focal plane. The white-dashed line depicts the boundary of metalens with size 50 μm 50 μm. (d) Schematic for the crosstalk effect deduced from generalized Snell s law of refraction. Take P G nanopillar as an example, the incident red, green, blue light will be refracted into the direction with angle θ t,r > θ t,g > θ t,b. Λ G denotes the period of P G nanopillars. 11

12 Reference 1. Chen, W. T.; Zhu, A. Y.; Khorasaninejad, M.; Shi, Z.; Sanjeev, V.; Capasso, F. Nano Lett. 2017, 17, Khorasaninejad, M.; Shi, Z.; Zhu, A. Y.; Chen, W. T.; Sanjeev, V.; Zaidi, A.; Capasso, F. Nano Lett. 2017, 17, Khorasaninejad, M.; Chen, W. T.; Devlin, R. C.; Oh, J.; Zhu, A. Y.; Capasso, F. Science 2016, 352, Zhan, A.; Colburn, S.; Trivedi, R.; Fryett, T. K.; Dodson, C. M.; Majumdar, A. ACS Photonics 2016, 3, Cheng, J.; Jafar-Zanjani, S.; Mosallaei, H. Sci. Rep. 2016, 6, Ke, Y. G.; Liu, Y. C.; Zhou, J. X.; Liu, Y. Y.; Luo, H. L.; Wen, S. C. Appl. Phys. Lett. 2016, 108, Lin, D. M.; Fan, P. Y.; Hasman, E.; Brongersma, M. L. Science 2014, 345, Avayu, O.; Almeida, E.; Prior, Y.; Ellenbogen, T. Nat. Commun. 2017, 8, Ni, X. J.; Ishii, S.; Kildishev, A. V.; Shalaev, V. M. Light-Science & Applications 2013, 2, e Yu, N.; Genevet, P.; Kats, M. A.; Aieta, F.; Tetienne, J.-P.; Capasso, F.; Gaburro, Z. Science 2011, 334,