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Free-space propagation of high-dimensional structured optical fields in an urban environment

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Science Advances  25 Oct 2017:
Vol. 3, no. 10, e1700552
DOI: 10.1126/sciadv.1700552

Figures

  • Fig. 1 Experimental setup.

    (A) Our 1.6-km free-space link is over the city of Erlangen in Germany. The optical beam is transmitted over both buildings, roads, and wooded areas as pictured. Image is courtesy of Google Map data 2016. (B) A fiber-coupled optical linearly polarized source with a wavelength of 809 nm is collimated and illuminates a spatial light modulator (SLM). An ℓ-forked hologram is displayed on the surface of the SLM. This diffractive hologram imparts the desired azimuthally varying phase pattern onto the wavefront of the incident optical beam. The beam is then magnified by a telescope (consisting of two lenses, L1 and L2) to give a maximum diameter of approximately 40 mm. After propagation over the 1.6-km free-space optical link, the light is collected by a receiver lens with a diameter of 150 mm and a focal length of 800 mm (L3). L4 is used to demagnify the beam to approximately 10 mm in diameter, allowing the analysis of the received light. A beam splitter is used to simultaneously image the received beams on a camera, C1, and pass the light through an OAM mode sorter (MS) to measure the modal content of the received light (C2).

  • Fig. 2 Images of the optical field at transmitter and receiver.

    (A to D) Image of the generated modes at the transmitter telescope. (E to H) Images of the received beam with Embedded Image, and 4 captured by a camera, C1, in Fig. 1B, respectively. As the ℓ of the transmitted mode increases, the beam diameter of the optical mode also increases. As the receiver lens has a fixed diameter, this increase in beam waist results in power loss that increases with ℓ. The measured power loss is the difference between the transmitted power, 0.75 mW, and the respective received power at the receiver measured by C1. The power loss (and that expected from the theoretical divergence of the beam) was measured to be 5.64 dB (0.043 dB), 10.29 dB (1.14 dB), 22.23 dB (6.70 dB), and 37.3 dB (17.11 dB), respectively.

  • Fig. 3 Tip-tilt and thin-phase turbulence model comparison.

    (A) CofM variation from an on-axis position resulting from tip-tilt atmospheric turbulence measured over 20 s. (B) To analyze the contribution of tip-tilt atmospheric turbulence, the CofM tracking data were used to simulate the expected channel cross-talk arising solely from this tip-tilt variation, which is overplotted with the experimental measured OAM spectrum. It can be seen that these two data sets do not match, indicating that turbulence beyond solely tip-tilt is affecting the optical beam as it propagates over the link. (C and D) Averaged broadened OAM spectrum measured for an Embedded Image and Embedded Image mode transmitted over the 1.6-km link, overplotted with the expected spectrum arising from thin-phase turbulence. Dashed lines represent the error in the measurement of D/r0.

  • Fig. 4 Observation of change in average OAM value.

    (A to D) Mean OAM value for the measured OAM spectrum for each recorded frame over 70 s, with a frame rate of 120 frames/s. It is observed that the average value of OAM measured, marked as a black dashed line, at the receiver does not match the transmitted mode. (E and F) Simulation of the measured average value of OAM as a function of vortex-splitting ratio for the cases where the transmitter is restricting the collection of the optical field and for the case where the beam is completely collected by a 1-m receiver aperture.

  • Fig. 5 Superpositions of OAM.

    Superpositions have previously been shown to propagate over long turbulent optical paths, without drastic degradation of their intensity profile. (A to D) To assess this situation in our 1.6-km link, superpositions of Embedded Image, and ±4 were generated and propagated over the optical link. The superposition states were projected on a large white screen, and the scattered light was imaged by a camera. (E to H) The same modes were collected by the 150-mm receiver aperture; however, the structure is truncated due to the restricted aperture size, as indicated by the dashed circles overlaid on each image.

  • Fig. 6 Change in vortex-splitting ratio.

    Modal purity is an important consideration for the long-distance transmission of spatial modes for use in communications. To enhance our determination of a change in purity, an = 0 component, with a 30% weighting, was added to an = 2 mode. This yields a vortex-splitting ratio of V = 0.4. By saturating the CCD, we can locate the intensity nulls that indicate the position of the vortices in the beam. (A to D) Four samples are shown, where each recorded incidence is respectively separated in time by 0.08 s. Overlaid is a fixed-size bar, indicating the expected vortex separation from a system simulation. It can be seen from frame to frame that there is a small but noticeable change in the separation and relative position of the vortex locations. This change in relative position and separation indicates that dynamic variations in the free-space channel are causing a variation in the vortex splitting observed.

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