Spatial multiplexing towards the communication capacity limit

To address future bandwidth issues, we demonstrate a set of information carriers with high divergence degeneracy and low error rate, capable of increasing the addressable spatial channels by two orders of magnitude than general orbital angular momentum (OAM) beams.

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Multiplexing of independent optical degrees of freedom (DoFs) such as polarization and wavelength have long been implemented to increase the capacity of optical communication systems. Mode-division-multiplexing scales the capacity by a factor equal to the number of spatial modes acting as independent information channel carriers. Among all spatial modes, the use of orbital angular momentum (OAM) beams, which can accommodate theoretically infinite orthogonal modes, has generated widespread and significant interest in the last decade. However, in practice, OAM modal basis set alone cannot reach the capacity limit of a communication channel, since the beam diverges rapidly as the OAM order enlarges, which gives rise to increased power loss for a limited-size receiver aperture. To guarantee sufficient received optical power for data recovery, the number of OAM modes that can be practically supported is severely limited mostly under 20.

To break the limit, we introduce a set of multi-vortex geometric beams (MVGBs), one type of ray-wave geometric beams, as high-dimensional information carriers for free-space optical communication, by virtue of three independent DoFs including central OAM, sub-beam OAM, and coherent-state phase (Fig. 1a). We verify the channel orthogonality of tri-DOF MVGBs for the first time (Fig. 1b). At the heart of our work is the exploitation of modes in ray-wave duality state, whereby crafted spatial modes appear to be both wave-like and ray-like, which allows us access to higher divergence degeneracy. We show the MVGB set is extremely densely packed in beam quality space and has a highly consistent propagation behavior that it can possess a divergence degeneracy as high as 20, and a divergence variation by merely 18% among 100 independent lowest order spatially multiplexed modes, in contrast to 900% for OAM counterpart (Fig. 1c). As a result, thousands of independently spatial channels in MVGB basis can be supported in a free space optical communication system, two orders of magnitude larger than that in OAM basis (Fig. 1d).

Figure 1. Divergence-degenerate high dimensional information carrier. a Diagram of multi-vortex geometric beam (MVGB) with three independent DoFs of coherent-state phase, central orbital angular momentum (OAM), and sub-beam OAM. b Orthogonality analysis of MVGBs in terms of three spatial indices. c Comparison on divergences of MVGBs, OAM modes and Laguerre–Gaussian (LG) modes, in respective 100 lowest orders, where the insets illustrate three-dimensional views of three types of modes, as well as the transverse intensity profiles of twenty MVGB modes in degenerated divergence. d Comparison on predicted numbers of independently addressable spatial channels in a free space spatial multiplexing system using three types of modes, versus the space–bandwidth product.

In addition to the novel concept, we validate the potentials of spatially multiplexed MVGB as high dimensional information carriers, by proof-of-concept experiments of the tri-DoF mode (de)multiplexing. Notably, we make the challenging demultiplexing task of tri-DoF modes possible, by proposing a novel approach based on conjugated modulation that can fully resolve the ray-wave duality state, removing the long-standing obstacle in the identification and sorting of ray-wave geometric beam that has prohibited its progress. Importantly, the demultiplexing results demonstrate another distinct advantage of MVGB modal basis, in terms of generating much lower bit error rates caused by center offset (Fig. 2 and Fig. 3a) and background noise (Fig. 3b), compared with OAM basis. Furthermore, we demonstrate the free-space data transmission by shift-keying method using the tri-DoF MVGBs. The data packet used is a 4-bit 16-level grayscale image composed of 64 × 64 pixels with an equalized gray-level histogram, as shown in Fig. 4. The novel carrier reliably transmits the image, outperforming the general OAM beams in terms of pixel error rate (ER).

Figure 2. Inherent advantage of MVGB modal basis in demultiplexing with lower bit error caused by the center offset. The centrosymmetric feature of single mode of MVGB is well maintained in the coherent superposition of four modes, in contrast to the case of OAM beam with distinct center offset.
Figure 3. Bit error rate (ER) performance of the demultiplexing process: tri-DoF MVGBs vs. OAM beams with different mode spacings. a The bit ER caused by center offset. b The bit ER caused by background noise.
Figure 4. Performance of image transmission. a 4-bit original image. b-d Retrieved image by the carriers of tri-DoF MVGBs. e 16-level grayscale histogram. f-h Retrieved image by the carriers of OAM beams with different mode spacings. The green pixels indicate the incorrect data received.

This work broadens the horizon of spatially multiplexing of structured light, and offers a promising basis for next generation of large-scale dense data communication. The MVGB multiplexing is compatible with and can combine with other techniques, such as wavelength and polarization division multiplexing, and may also work within fibers. Our technique could be extended to other types of ray-wave geometric beams, to explore even more spatial DoFs and higher divergence degeneracy. The concept of tri-DoF modal basis can also be applied to encoding in the quantum data channels.


Article Information

Divergence-degenerate spatial multiplexing towards future ultrahigh capacity, low error-rate optical communications, Light: Science & Applications, 11, 144 (2022)



Xing Fu

Associate Professor, Tsinghua University