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Hanbury Brown and Twiss interferometry with twisted light

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Science Advances  08 Apr 2016:
Vol. 2, no. 4, e1501143
DOI: 10.1126/sciadv.1501143
  • Fig. 1 Experimental setup for the study of the azimuthal HBT effect.

    (A) The 532-nm output of a solid laser is directed onto a DMD, where a random transverse phase structure is impressed onto the beam. A 4f optical systems consisting of two lenses with different focal lengths (figure not to scale) and a pinhole is used to isolate the first diffraction order from the DMD, which is a pseudothermal beam of light. This beam is then passed through a beam splitter (BS) to create two identical copies. Each copy is sent to a separate SLM onto which a computer-generated hologram is encoded. (B) For the HBT measurements, a pair of angular slits is encoded onto the SLMs. In addition, forked holograms corresponding to OAM values are encoded onto the same holograms to project out controllable OAM components. For our measurements of the OAM and angular position correlation functions, we do not use the double slit but simply project onto OAM values or angular wedges, respectively. (C) Intensity distribution of a generated pseudothermal beam of light.

  • Fig. 2 Interference transitions in the OAM-mode distribution of light.

    (A to D) First-order (Young’s) interference. (E to H) Second-order HBT interference. The first column (A and E) shows interference produced by coherent light, whereas the other panels show the measured interference for different strengths of the fluctuations of the pseudothermal light, as characterized by the Fried coherence length. In each case, the angular width of the slits α is π/12 and the angular separation of the slits φ0 is π/6. Bars represent data, whereas the line is the theoretical curve predicted by theory.

  • Fig. 3 Experimental demonstration of the azimuthal HBT effect of light.

    (A and B) Embedded Image plotted as a function of the OAM value of arm 2 for two different values of the OAM number of arm 1. The green bar shows the center of the interference pattern for singles counts shown in Fig. 2C, whereas the purple bar shows the center of the displayed interference pattern.

  • Fig. 4 Measurement of intensity correlations in the angular domain for random light.

    (A) Normalized second-order correlation function in the OAM domain. (B) Presence of strong correlations for the conjugate space described by the angular position variable.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/4/e1501143/DC1

    1. The HBT effect for symmetrically displaced modes (l and − l)

    2. The HBT effect for arbitrary mode indices l1 and l2

    3. Interference produced by a single slit displayed at different positions onto two SLMs

    4. Orbital angular momentum correlations and angular position correlations

    Fig. S1. Example of a frame sent to the DMD.

    Fig. S2. Examples of random beams of light.

  • Supplementary Materials

    This PDF file includes:

    • 1. The HBT effect for symmetrically displaced modes (l and −l)
    • 2. The HBT effect for arbitrary mode indices l1 and l2
    • 3. Interference produced by a single slit displayed at different positions onto two SLMs
    • 4. Orbital angular momentum correlations and angular position correlations
    • Fig. S1. Example of a frame sent to the DMD.
    • Fig. S2. Examples of random beams of light.

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