We recover the shape and orientation of an object by analyzing the spatial phase and amplitude of a transmitted optical beam using a single pixel. We experimentally demonstrate using the complex spatial spectrum of multiple sequential measurements of a varying probe beam. Specifically, we transmit a structured beam that is tailored to have one mode of the Laguerre-Gaussian (LG) modal basis set, and the beam is varied to sequentially have a unique azimuthal (l) and radial (p) value. When each uniquely structured beam probes an object, there will be coupling of power from the pure mode to other LG modes. The complex phase and amplitude coefficients of this modal power coupling will provide a “signature” of the probed object’s 2D structure, and this signature can be detected using a single pixel. We identify a “fan-shaped” object with an opening angle of 120˚ and different angular orientations by analyzing the corresponding complex spatial spectrum of multiple sequential measurements, such that each subsequent tailored mode has l and p indices in the range -15 - +15 and 0-30, respectively. Results show that the amplitude spectrum is insensitive to the object’s angular orientation, whereas the phase spectrum predictably shifts with orientation. Additionally, we demonstrate that an irregular image with a ‘SC’ logo can be reconstructed using the complex modal spectrum. The structural similarity (SSIM) of the reconstructed image increases as the number of modes increases. Specifically, the SSIM increases by 83.5% when the number of modes increases from 36 (6 by 6) to 961 (31 by 31).
Proc. SPIE. 9739, Free-Space Laser Communication and Atmospheric Propagation XXVIII
KEYWORDS: Digital signal processing, Switches, Gaussian beams, Receivers, Multiplexing, Computer programming, Free space optics, Data communications, Atmospheric propagation, Free space optical communications
Free-space optical communications can play a significant role in line-of-sight links. In general, data can be encoded on the amplitude, phase, or temporal position of the optical wave. Importantly, there are environments for which ever-more information is desired for a given amount of optical energy. This can be accomplished if there are more degrees-of-freedom that the wave can occupy to provide higher energy efficiency for a given capacity (i.e., bits/photon). Traditionally, free-space optical links have used only a single beam, such that there was little opportunity for a wave to occupy more than one spatial location, thereby not allowing the spatial domain to be used for data encoding. Recently, space- and mode-multiplexing has been demonstrated to simultaneously transmit multiple data-carrying free-space beams. Each spatially overlapping mode was orthogonal to other modes and carried a unique amount of orbital-angular-momentum (OAM). In this paper, we consider that OAM modes could be a data-encoding domain, such that a beam could uniquely occupy one of many modes, i.e., 4 modes would provide 4 possible states and double the bits of information for the same amount of energy. In the past, such OAM-based encoding was shown at kHz data rates. We will present the architecture and experimental results for OAM-based data encoding for a free-space 1.55-μm data link under different system parameters. Key features of the results include: (a) encoding on several modes is accomplished using a fast switch, and (b) low bit-error-rates are achieved at >Gbit/s, which is orders-of-magnitude faster than previous results.