Orbital angular momentum (OAM) has demonstrated great success in the optical communication field, which theoretically allows an infinite increase of the transmitted capacity. The recognizable ability of the receiver is crucial for both OAM shift keying (OAM-SK) and OAM division multiplexing (OAM-DM) in terms of OAM-based optical communication. Some techniques utilize traditional optics theories that transform the azimuthal position into transverse position based on interferometers and vortex diffractive gratings. One currently efficient sorting method is to implement coordinate transformation that separates states with different topological charges by a distinct focal spot on the detect plane. And a computational method to measure the transmission matrix (TM) provides an anti-interference approach to retrieve the propagation of vortex beams. In addition, the OAM-to-polarization coupling effect is also proposed to sort different OAM states of light. All those methods pave the way for effective OAM-based optical communication. However, owing to the limitation of the resolution, only eigenmodes where topological charges are integers are considered in all methods mentioned above. With the increase of an integer topological charge value, the growing phase singularity and the diffraction effect enormously affects the intensity distributions of vortex beams, which extremely adds the difficulties of being focused in free space and being coupled in fibers. This problem limits the development of the OAM-based optical communication. Consequently, it is of fundamental importance to expand communication capacity adequately with more OAM states but smaller phase singularity.

Our goal here is to develop a superhigh-resolution technique to precisely separate modes into subdivisible space between adjacent eigenmodes. That is, the minimum interval among recognized modes is a fractional value and can be as small as possible. Figure 1 shows four pairs of the gray scale phase hologram and the corresponding intensity distributions of the OAM mode with 0.01 state interval. The annotation demonstrates good agreement between actual topological charges and predictions, indicating that the invisible difference between adjacent modes is seized easily by the trained OAM-recognition neuron network (ORNN).

Fig. 1 The recognized OAM modes with fractional topological charge of 0.01 state interval.
First row: Phase pictures uploaded on the SLM. Second row: The intensity distributions of vortex modes recorded by the CMOS camera.

Fig. 2 (a) An 8-bit OAM superstate multiplexed demonstration encoded by fractional modes. (b) Detailed process of transmitting an Einstein portrait utilizing the superhigh-resolution OAM multiplexing system.

To further demonstrate the availability of our method in exploiting fractional OAM modes, we experimentally implement a superhigh-resolution OAM multiplexing system. We encode an 8-bit binary byte using 8 different OAM modes, the topological charge of which is chosen from 1.93 to 2.00. Each bit value is assigned to be 1 or 0 on the basis of whether the corresponding mode exists or not. After training, perfectly quantified 100% test accuracy is achieved without any manual intervention. As Fig. 2(a) shows, an 8-bit code only occupies a small region of the superstate, which indicates that large capacity can continuously be used to encode. Then, we transfer an image using above a completed free-space system to further verify its performance, as shown in Fig. 2(b).

The method proposed here shows its powerful ability to distinguish ultrafine OAM modes that traditional approaches cannot realize. The capacity of communication in our encoded method can be further increased by combining wavelength-division multiplexing (WDM) and polarization multiplexing (PM). And the transmitting rate can also be further improved by the higher frame rate of the device. In addition, due to the high performance of recognizing fractional modes, the ORNN possesses the enormous potential for multiplexing as many modes with 0.01 intervals as possible, which unlimitedly expands the communication capacity in theory. More importantly, challenges that existed in previous integer-topological-charge OAM-based optical communication, such as beam divergence, aperture size, and misalignment of transmitter and receiver, can be solved by using the fractional topological charge ORNN proposed here. The <0.02% bit error ratio (BER) shows this intelligent recognition concept offers new opportunities for next generation DL-based ultrafine OAM optical communication. In principle, such a method as proposed here might even be applied to microwave, millimeter wave, and terahertz OAM communication fields.

Link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.183902