Fig. 1. Concept of intelligent tailoring of OAM comb. The on-demand customization of OAM comb settings includes mode range, interval, and distribution, forming a target OAM comb. The corresponding complex-amplitude patterns serve as input data for the neural network training. The overall workflow of the proposed intelligent tailoring scheme consists of a feature extraction structure and a feature fusion structure, enabling the generation of a phase-only hologram thus tailoring the target OAM comb. The difference between output and target OAM spectrum is used as a constraint for loss backward in network training. This proposal can also be employed to conduct optical convolution calculation. For any arbitrary OAM combs F(l) and G(l), their convolution result can be easily obtained by solely detecting the OAM spectrum of their phase-only holograms’ superposed diffraction field.

Fig. 2. Structure of MSUNet. (a) The feature extraction workflow. (b) The U-shaped neural network structure, which serves as the feature extractor for feature extraction process. (c) Details of the feature fusion process for generating phase-only hologram that incorporates angular spectrum transmission and a pre-trained DRN model to analyze the OAM spectrum for loss backward propagation. (d) The multi-scale scheme, which plays a crucial role in feature fusion for generating the phase-only hologram.

Fig. 3. Experimental OAM comb intelligent tailoring. (a) The experimental setup. DFB, a 1617 nm distributed feedback laser diode; SMF, single-mode fiber; Col., collimator; HWP, half-wave plate; PBS, polarized beam splitter; SLM, liquid-crystal spatial light modulator; L, plano-convex lens with focal length 200 mm; CCD, infrared CCD camera. (b), (c) Phase-only holograms of broadband OAM combs with a minimum mode interval 1, and mode range of −75 to +75, respectively, along with visualizations of the simulated and experimental intensity distributions of the optical fields modulated by the phase-only hologram. (d), (f) OAM spectrum measurement results corresponding to the OAM comb in (b) and (c), with the target and experimental intensity distributions represented by blue and red bars, respectively. (e), (g) Density matrix difference between the target OAM comb and the experimental OAM comb from (b) and (c). The values close to zero indicate the high fidelities of the experimentally generated OAM combs.

Fig. 4. Highly efficient optical convolution employing OAM combs. (a) Overview of the OAM-comb-based optical convolution. (b) OAM comb F(l). (c) OAM comb G(l). (d) Results of the convolution calculation of the two OAM combs, F(l)*G(l).

Fig. 5. Experimentally captured back-converted patterns for the generated OAM combs. The orders of the back-converting spiral phases are labeled at the top left corner of each inset. The orange dashed circle represents the sampling area, where intensities inside it are regarded as the back-converted OAM channel.

Fig. 6. Results of the spectrum measurement before and after calibration. The target OAM comb, and the experimental OAM spectrum before and after refining by the calibration curve, are represented by blue, red, and green bars, respectively. The calibration curve, measured using a standard spiral phase pair, is shown in yellow.

Fig. 7. Extended experimental results of various OAM mode numbers. (a) 5 modes (RMSE = 0.0041, fidelity = 91.33%), (b) 10 modes (RMSE = 0.0033, fidelity = 93.44%), (c) 15 modes (RMSE = 0.0034, fidelity = 84.80%), (d) 20 modes (RMSE = 0.0025, fidelity = 84.43%), (e) 25 modes (RMSE = 0.0030, fidelity = 81.79%), (f) 30 modes (RMSE = 0.0038, fidelity = 81.60%), (g) 35 modes (RMSE = 0.0058, fidelity = 81.19%), and (h) 40 modes (RMSE = 0.0037, fidelity = 81.53%).

Fig. 8. Variation of RMSE and fidelity with increasing number of modes in an OAM comb. The blue line represents the variation of RMSE with the increasing number of OAM modes, where a lower RMSE indicates better performance. The orange line illustrates the variation of fidelity with the increasing number of OAM modes, where higher fidelity reflects better accuracy.