Low-Loss All-Fiber Mode Permuter Design Exploiting Propagation Constant Engineering and Cascaded Bragg Gratings

Managing group-delay (GD) spread is vital for reducing the complexity of digital signal processing (DSP) in long-haul systems using multi-mode fibers. GD compensation through mode permutation, which involves periodically exchanging power between modes with lower and higher GDs, can reduce GD spread. GD spread is maximally reduced when the modal GDs of the transmission fiber satisfy a specific relation and the mode permuter exchanges power between specific modes. Mode permuters with fiber Bragg gratings have been developed for links accommodating $D=6$ guided spatial and polarization modes; however, to the best of our knowledge, there have been no designs for links supporting a greater number of modes. We present two mode permuter designs based on fiber Bragg gratings for links employing graded-index transmission fibers with $D=12$ guided spatial and polarization modes. One design utilizes a step-index (SI) transverse profile, and the other features a free-form-optimized transverse profile achieving improved performance. For the SI design, we achieve mode-dependent loss standard deviation (MDL STD) and mode-averaged loss (MAL) of less than $0.14$ dB and $0.27$ dB, respectively, over the C-band. For the design with a free-form-optimized transverse profile, we achieve MDL STD and MAL of less than $0.11$ dB and $0.07$ dB, respectively, over the C-band. We numerically evaluate the designs through link simulations and quantify the reduction in GD spread for different levels of random inter-group coupling in the fiber. Our results show that in a link with periodic mode permutation and mode scrambling, the GD STD is reduced by a factor over $3.13$ compared to a link relying solely on periodic mode scrambling.