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Catenary optics for achromatic generation of perfect optical angular momentum

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Science Advances  02 Oct 2015:
Vol. 1, no. 9, e1500396
DOI: 10.1126/sciadv.1500396
  • Fig. 1 Schematic representation of the geometric phase in optical catenaries.

    (A) Sketch map of a catenary aperture illuminated at normal incidence by CPL. Light is assumed to propagate along the +z direction throughout this paper. The inclination angle with respect to the x axis is denoted as ξ(x). (B) Phase distributions of the catenary (red), parabola (orange), crescent (blue), and discrete antennas (black dot) for LCP illumination (σ = 1). (C) Three typical kinds of phase profiles for the generation of pure OAM (left), HOBB (middle), and focused beam (right). (D and E) Arrangement diagrams of the catenary arrays for ordinary OAM (D) and HOBB or focused beam (E).

  • Fig. 2 OAM generators based on catenary arrays.

    (A to C) The topological charges for (A) to (C) are −3, −6, and 12 (σ = 1), respectively. The first column represents the scanning electron microscopy (SEM) images of the fabricated samples. Scale bar, 2 μm. The second column shows the spiral phase profiles. The last two columns depict the measured (the third column) and calculated (the last column) results of Ix, Iy, and Itotal for λ = 532 nm (top row), 632.8 nm (middle row), and 780 nm (bottom row). The distances between the recording planes and the sample are indicated in each row.

  • Fig. 3 Measured conversion efficiencies of the OAM generators.

    Mean values of repeated measurements are given for the samples with l = −3, −6, and 12 (σ = 1) at wavelengths of λ = 532, 632.8, and 780 nm. The error bars give the maximum range of errors.

  • Fig. 4 Catenary arrays for the generation of HOBB and focused OAM beam.

    (A and B) SEM images of the catenary arrays for HOBB (A) and focused OAM (B). (C) Scaled view of the rectangular region shown in (B). (D and E) Measured cross-polarized intensity distributions of the HOBB (D) and focused OAM (E) at a wavelength of λ = 632.8 nm for RCP illumination (σ = −1). The intensities at the xy plane (x, y ∈ [−20, 20] μm, z = 40 μm) are plotted in the insets.

  • Fig. 5 Comparison of the conversion efficiencies and electromagnetic modes of the catenary apertures and discrete nano-antennas.

    (A and B) Schematics of the unit cells in catenary apertures (A, s = p) and discrete antennas (B, s < p). The two cells differ from each other in the length of the metallic bar with respect to the period. (C) Numerically calculated polarization conversion efficiency η for the catenary apertures and nano-antennas. The small discrepancy between the theoretical expectations and the experimental results (Fig. 3) is mainly due to fabrication imperfections. (D and E) Schematic of the orthogonal modes in the u-v coordinates for the catenary (D) and discrete antennas (E). The surface impedances as a function of frequency are depicted by the nanocircuit model. The resistances stemming from the ohmic loss are neglected.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/9/e1500396/DC1

    Text

    Fig. S1. Schematic of the integration procedures to design the catenaries.

    Fig. S2. Transmission coefficients of the subwavelength grating.

    Fig. S3. Design, fabrication, and characterization of the sample with l = ±1.

  • Supplementary Materials

    This PDF file includes:

    • Text
    • Fig. S1. Schematic of the integration procedures to design the catenaries.
    • Fig. S2. Transmission coefficients of the subwavelength grating.
    • Fig. S3. Design, fabrication, and characterization of the sample with l = ±1.

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