Selectable mode cross-transformation in orbital-angular-momentum- and wavelength-multiplexing channels

Data exchange across various orbital-angular-momentum (OAM) channels is a crucial interconnection process within mode-multiplexed optical communication networks. However, the versatile cross-connection of multidimensional hybrid channels, especially those involving modes and wavelengths, has been constrained in conventional monochromatic operations, impeding their advancement in multiwavelength systems. Herein, we introduce a selectable mode cross-transformation solution for OAM mode-wavelength hybrid cross-connections by constructing wavelength-dependent rotatable diffractive deep neural networks ($\mathrm{R}\text{\ensuremath{-}}{\mathrm{D}}^{2}$NNs). Incorporated with wavelength-sensitive free-space Fresnel diffraction, this framework achieves chromatic dispersion decoupling of three wavelength channels with an 8-nm interval. By deploying spatially engineered rotatable diffractive layers, the $\mathrm{R}\text{\ensuremath{-}}{\mathrm{D}}^{2}$NNs unlock switchable unitary transformations for paired OAM modes, allowing for parallel yet independent multimode interconversions across each wavelength dimension, with insertion losses under \ensuremath{-}5.82 dB and mode purities above 85.8%. As an application demonstration, dynamic data exchange of quadrature phase-shift keying signal streams is successfully implemented by selectively cross-connecting six mode-wavelength multiplexing channels, obtaining bit-error rates close to ${10}^{\ensuremath{-}5}$. The feasibility of the presented method for both partial and full channel cross-connections under seven static interconnection scenarios is validated and highlighted. Our solutions establish a scalable and miniaturized diffractive network architecture for comprehensive manipulation of both OAM modes and wavelengths, offering a foundational platform for multidimensional channel processing in optical communications and dynamic interconnections.