Supporting Information: Nonlinear generation of vector beams from. AlGaAs nanoantennas

Transcription

1 Supporting Information: Nonlinear generation of vector beams from AlGaAs nanoantennas Rocio Camacho-Morales, Mohsen Rahmani, Sergey Kruk, Lei Wang, Lei Xu,, Daria A. Smirnova, Alexander S. Solntsev, Andrey Miroshnichenko, Hark Hoe Tan, Fouad Karouta, Shagufta Naureen, Kaushal Vora, Luca Carletti, Costantino De Angelis, Chennupati Jagadish, Yuri S. Kivshar, and Dragomir N. Neshev, Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra ACT 2601, Australia The MOE Key Laboratory of Weak Light Nonlinear Photonics, School of Physics and TEDA Applied Physics Institute, Nankai University, Tianjin , China Department of Electronic Materials Engineering, Research School of Physics and Engineering, The Australian National University, Canberra ACT 2601, Australia Department of Information Engineering, University of Brescia, Via Branze 38, Brescia, Italy 1

2 Contents I. Nanofabrication II. Linear Measurement of Arrays III. Experimental Setup for Nonlinear Measurements IV. Third Harmonic Generation V. Stokes Parameters Polarimetry VI. Multipolar Spectral Decomposition VII. Thickness Dependence VIII. Crystalline Axis Orientation Dependence IX. Near-Field Distributions 2

3 I. Nanofabrication a) AlGaAs AlAs SiO2 GaAs AlAs Layer b) Interface Surface treatment Interface Figure S1: Illustration of the first two steps of nanofabrication, accompanied by side view SEM images. Figure S1 is an extension to the Fig. 1 in the main text. This figure contains scanning electron micrograph (SEM) images for the first two steps of the fabrication process. The right panels of Fig. S1(a) show the side view of the initial pillars consisting of SiO x mask on the top followed by AlGaAs layer, AlAs layer and GaAs wafer at the bottom. The magnified images show the AlAs layer in the structure. The SEM images in Fig. S1(b) show the structure s side views after removing SiO x and AlAs layers. The interface between AlGaAs disks and GaAs wafer can be seen in the enlarged SEM image. 3

4 N a n o d i s k s D i a m e t e r s, n m b Experiment c Theory 6 a 5 ω ω Transmission Wavelength, nm Figure S2: (a) Schematic of transmission measurements of an array of nanodisk antennas. (b and c) Transmission spectra of the nanodisk arrays measured experimentally and calculated theoretically, respectively. Different colors correspond to different diameters of the nanodisks, as indicated above the plots. II. Linear Measurement of Arrays By employing aforementioned reproducible fabrication method, we managed to fabricate and transfer hundreds of nanodisks in arrays fashion in an area of 100 µm 100 µm. We measured the linear transmission spectra of the different arrays, as schematically depicted in Fig. S2(a). The measured and calculated zero-order forward scattering spectra are shown in Fig. S2(b and c), respectively. The experimentally measured spectra are in a good agreement with our numerical calculations. 4

5 III. Experimental Setup The schematic of the experimental setup for observation of the second harmonic generation (SHG) from a single AlGaAs nanodisk is shown in Fig. S3. Ray tracing for the Real Space Image CAMERA Ray tracing for the Fourier Space Image FS LASER 1556 nm λ/4 λ/2 dichroic mirror Filters IR X100 NA0.85 AlGaAs nanoantenna VIS X100 NA0.9 Filters Objective Back-Focal Plane (Directionality Image) Real-Space Image Directionality Image CAMERA Figure S3: Schematic of the experimental setup for SHG characterization. IV. Third Harmonic Generation The third-order nonlinear term of the AlGaAs nonlinear polarization is much weaker than second-order nonlinear term, however it is non-zero, and third harmonic generation (THG) signal from AlGaAs can be observed. The THG is expected to be similar to the THG from other well-studied materials like silicon and germanium. Therefore, in terms of the radiation pattern, the THG signals is non-zero in the direction normal to the disks axis. This characteristic is in contrast to the SHG radiation pattern, which is reflected in the doughnut shape of back-focal plane (BFP) images because of zero diagonal components of the second-order tensors. This difference is clear in Fig. S4, proving that our measured doughnut shapes of SHG are indeed characteristic to the SH emission. 5

6 d = 490nm SHG BFP THG BFP 1 y x Normalized intensity 0 Figure S4: Experimentally measured SHG and THG backward back focal planes for AlGaAs disk with 490 nm diameter. V. Stokes Parameters Polarimetry Figure S5: Schematic of the polarization ellipse with the Stokes coefficients of ellipticity angle χ and polarization-inclination angle ψ. E a and E b are the main polarization axes (solid blue lines) of the polarization ellipse. The Stokes coefficients provide a complete description of the light polarization state in terms of its total intensity I tot, (fractional) degree of polarization ρ, polarization inclination angle ψ, and the ellipticity angle χ. The ellipticity tan(χ) is defined as the ratio of the two axes of the polarization ellipse (see Fig. S5), and the polarization inclination is described by the angle between the main polarization axis and the x-axis of the laboratory coordinate system. Experimentally, we find the Stokes parameters by measuring light transmission through a set of six different polarizers: linear horizontal, vertical, two diagonal and two circular 6

7 Figure S6: Back-focal plane images of second harmonic signal in backward direction transmitted through six different polarizers: linear horizontal, vertical, two diagonal and two circular. polarizers realized by different orientations of the quarter-wave plate and a linear polarizer. The set of measurements for the backward directionality of SH emission from a disk with diameter of 490 nm are shown in Fig. S6. We next retrieve the Stokes vector I Q M =, U V where I = H + V = D a + D b = L + R Q = H V U = D a D b V = L R Here, H is the transmission through horizontal polarizer, while V, D a, D b, L, R are the transmissions through vertical, two diagonal, left- and right-circular polarizers, respectively. A set of four back-focal plane images forming the Stokes vector are shown in Fig. S7. 7

8 I Q U V Figure S7: Four components of the Stokes vector for backward directionality of the second harmonic signal. We next calculate the coefficients as follows: Q2 + U ρ = 2 + V 2 I ψ = 1 arg(q + iu) 2 ( ) χ = 1 2 arctan V U 2 + Q 2 The coefficients are shown in Fig. S8. Polarization Degree Inclination Ellipticity Figure S8: Retrieved spatially-resolved degree of polarization, inclination and ellipticity. 8

9 VI. Multipolar Spectral Decomposition In Fig. 2 of the main text we observe both theoretically and experimentally multiple resonances in spectra of the nanodisks. Here we attribute the observed spectral resonances in linear regime to excitation of Mie multipoles by performing multipolar decomposition of spectrum. We use polarization currents for this task, and choose the best-performing disk with the diameter of 490 nm. The results are shown in Fig. S9. Figure S9: Calculated scattering efficiency and multipole decomposition (up to fourth order) for AlGaAs nanodisk with a diameter of 490 nm. The pump is set to be a plane wave polarized along x axis. Next, we perform multipolar decomposition in nonlinear regime of the SH fields for three disk sizes: 340 nm, 490 nm and 640 nm. For the three cases we plot pie charts visualizing the relative contributions of different multipoles into the SH. The results are shown in Fig. S10. 9

10 N a n o d i s k D i a m e t e r s, n m 340 nm 490 nm 640 nm Figure S10: Chart diagrams of the SH multipolar contributions calculated for three different disk diameters: 340 nm (left), 490 nm (centre), and 640 nm (right). VII. Thickness Dependence We study the dependence of SH directionality on nanodisk height. Below in Fig. S11 we provide directionality diagrams of SH for nanodisks of 490 nm diameter and three different thicknesses of 100 nm, 300 nm and 500 nm. N a n o d i s k H e i g h t, n m 100 nm 300 nm 500 nm Figure S11: SH directionality versus nanodisk height for disk diameter of 490 nm. VIII. Crystalline Axis Orientation Dependence We study dependence of SH efficiency on relative orientation of in-plane crystalline axis to the orientation of pump polarization. We find strong dependence for the efficiency as shown in Fig. S12. 10

11 Figure S12: Efficiency of the second harmonic generation versus polarization orientation with respect to the crystalline axis. IX. Near-Field Distributions Below in Fig. S13 we provide distributions of the near-fields at both pump wavelength and second harmonic wavelength. 11

12 Figure S13: First row: spatial profiles of the fundamental field (left), induced nonlinear current (center), and second-harmonic field (right) inside the nanodisk of 490 nm diameter; near-field distributions of the fundamental (second row) and SH (third row) fields shown in three different cross-sections. 12