Optical orbital angular momentum (OAM) carried by vortex beams is an important fundamental property of the light field. The theoretically unlimited values of  provide an infinite number of orthogonal OAM eigenstates, which can infinitely elevate the capacity of communication system. Therefore, the optical orbital angular momentum (OAM) is regarded as a new dimension for the next-generation communication system for its potential to break the Shannon limit of communication capacity. However, since OAM modes cannot be stably transmitted in conventional fibers, all the OAM communication schemes proposed so far primarily utilize specialty fibers or multi-mode fiber (MMF) with weak mode coupling to transmit OAM modes, which hinders the widespread application of OAM communication. Here, we demonstrate the OAM communication in commercial MMF with strong mode coupling by utilizing the transmission matrix (TM) method.

Figure 1(a) Highly structured speckle patterns without TM method. (b) Focused OAM array generated by TM. (c) Demultiplexing of superimposed OAM modes.

In this study, the TM method is used to control the transmission of vortex modes through fibers. Figure 1 illustrate the schematic of OAM demultiplexing in MMF via TM method. The initial beam is Gaussian beam. As shown in Figure 1a, the intensity distribution on the output plane after transmission over MMF is chaotic and irregular without modulation by TM method. After measuring the TM, the optical phase conjugation (OPC) method can be adopted to realize the focusing of Gaussian beam or vortex modes on arbitrary positions. Figure 1b shows the creation of an OAM array composed of different OAM modes with arbitrary positions and topological charges. If the initial beam is multiplexed vortex beams, similar to the traditional anti-topological charge matching method, the focused OAM spots matching the incident OAM mode will be transformed into Gaussian-like foci, thereby achieving the OAM mode demultiplexing in MMF, as shown in Figure 1c.

Figure 2 (a) Demultiplexing of superimposed OAM modes consisting of 2 OAM modes. (b) Corresponding separation accuracy. (c) Separation accuracies of 3, 4, and 5 overlay OAM modes.

With the proposed TM method, the demultiplexing of superimposed OAM modes in MMF can be performed experimentally. The corresponding results are shown in Figure 2. Figure 2a shows the demultiplexing of 2 superimposed OAM modes after transmission over MMF. The function of the loaded phase pattern is simultaneously generating a focused OAM spot with l=-1 at position A and a focused OAM spot with l=1 at position B. Consequently, when the input mode is single OAM mode with l=1, a Gaussian focus is formed at position A, and at position B a focused vortex spot with l=2 is also formed. And when the input mode is the superposition of these two OAM modes, they are respectively converted to Gaussian focus at position A and position B, thereby realizing the demultiplexing. Figure 2b shows the corresponding separation accuracy, which is more than 97%. Moreover, we investigate its ability to separate overlap OAM modes composed of more modes. Figure 2c illustrates the demultiplexing results of 3, 4, and 5 overlap OAM modes, with the corresponding separation accuracy reaching over 95%, 90%, and 87%, respectively. The above results are repeatable, which confirms the validity and stability of our TM method to realize the OAM demultiplexing in MMF with strong mode coupling.

Figure 3 (a) Coding rule of OAM-SK. (b) Encoded data to be transmitted and the variation of photon counts in the two channels.

Further, we perform the experiment of both OAM-SK communication and OAM-DM communication in MMF via TM method to more comprehensively demonstrate the application potential of our method. Figure 3 illustrates the result of OAM-SK communication in MMF. The detailed binary coding rule is shown in Figure 3a. A 6-bit binary byte “001011” is encoded by using OAM modes. Each bit value is assigned to be 1 or 0 on the basis of whether the OAM mode exists or not. OAM mode is continuously varying in the time domain to form the whole byte. As the proof of principle, we present a dual-channel OAM-SK communication experiment here. We transmit 10-bit binary byte "1001001100" in Channel 1 and "0110100110" in Channel 2. The experimental result is shown in Figure 3b, in which the blue columns represent Channel 1 and the red columns represent Channel 2. By setting a threshold of 2000 photons, we can decode the collected data and achieve very low error rates of about 5% in dual-channel OAM-SK communication.

Figure 4 (a1) Demultiplexing results. (a2) Numerical results of the normalized intensity. (b) Loaded square wave signal. (c)-(d), Sampled carrier signal. (e)-(g), Encoded signal and decoded signals after setting an intensity threshold. (h)-(j), Sampled carrier signals at different internal modulation frequencies.

The corresponding experimental result of OAM-DM communication in MMF is illustrated in Figure 4. Figure 4a1 shows the result of demultiplexing. The numerical results of the normalized intensity at positions A and B under different input conditions are illustrated in Figure 4a2. The loaded modulation square wave signal at 10 kHz is shown in Figure 4b. The sampled carrier signal of the filtered beam before and after loading the demultiplexing phase pattern is shown in Figure 4c, d. Figure 4e is the encoded signal and Figures 4f, g are the decoded signal before and after loading the demultiplexing phase pattern after setting an intensity threshold. The results verify the success of OAM-DM communication in MMF via TM method. For a better demonstration of the performance of OAM-DM communication in MMF via TM method, we conduct OAM-DM communication experiments at different internal modulation frequencies of laser. The results are shown in Figures 4h-j, in which the modulation frequencies are 50,100,200 kHz, respectively.

This work is published in “Fengchao Ni, Zhengyang Mao, Haigang Liu, Xianfeng Chen, Orbital Angular Momentum Communications in Commercial Multimode Fiber with Strong Mode Coupling, ACS Photonics 12, 8, 4423–4431 (2025).”

Link: https://pubs.acs.org/doi/full/10.1021/acsphotonics.5c00816