Ultra-Low-Loss Fiber Bragg Grating Mode Scrambler Design Exploiting Propagation Constant Engineering

Periodic insertion of mode scramblers can reduce the accumulation of group-delay spread and mode-dependent loss in mode-division-multiplexed links. Past effective mode scramblers, however, exhibit too much loss, owing to coupling from guided to unguided modes, specifically cutoff modes. We present a mode scrambler design based on long-period fiber Bragg gratings for links employing graded-index transmission fibers with $D=12$ guided spatial and polarization modes. In typical graded-index fibers, the guided and lowest-order cutoff modes have nearly equally spaced propagation constants. Hence, a grating will induce coupling not only between all the guided modes but also to the lowest-order cutoff modes, causing high losses. To remedy this problem, we design the mode scrambler transverse refractive index profile to yield equal spacing between the propagation constants of the guided mode groups and a different and larger propagation constant spacing between the highest-order guided modes and the lowest-order cutoff modes. We also ensure that the highest-order guided modes cannot be phase-matched to any other unguided modes by a grating. This enables a uniform grating, obtained by a grid search optimization of the grating parameters, to couple all the guided mode groups with minimal loss. We obtain a design with mode-averaged and mode-dependent loss standard deviations less than 0.027 dB and 0.011 dB, respectively, over the C-band. We perform numerical simulations to study the effect of fabrication errors and show that the choice of grating modulation depth involves a tradeoff between mode scrambler loss and sensitivity of link group-delay spread to fabrication errors.