Optical solitons are spatially localized, pulse-like, nonlinear waves that almost retain their shapes while propagating in ideal lossless fibers. This steady propagation stems from an exact balance between nonlinear and dispersion terms in the conservative form of the nonlinear Schroedinger equation which describes ideal fibers. The fact that solitons are spatially localized and propagate with (little to) no deformation makes them the carriers of choice for modern optical communication, as they can be used to encode a bit in a small amount of space through the presence or absence of the pulse in a designated temporal window. However, the balance between nonlinearity and dispersion is not exact in real optical fibers, which may cause the pulse to broaden and “spill over” the designated window. This can result in transmission errors or, if the window size is increased to avoid spill-over, in a reduction of the transmission rate.
While error-correcting codes can be used at the receiving end to compensate for dispersion-induced errors, all-optical approaches are typically preferred because they do not affect the speed at which information is processed. A typical all-optical dispersion-management technique consists of periodically alternating lengths of fibers with positive and negative group-velocity dispersions, so as to compensate for pulse broadening on average. While traveling through the fiber, the pulse experiences broadening and recompression so that, at the end of each compensation element, the width and frequency chirp of the pulse are restored to the initial desired values. This method is effective if both fiber nonlinearity and residual dispersion only slightly affect the evolution of the pulse over one compensation period. If this is not the case, these dispersion maps may fail to work appropriately, especially if the characteristics of the fiber are uncertain.
From a control theory perspective, this (passive) dispersion technique can be seen as open-loop control, where the group-velocity dispersion is the input, pulse width is the output, and the goal is to regulate the output to its desired value at a fixed propagation length. With this analogy in mind, it seems tempting to try and use feedback control to improve dispersion management of optical solitons and, in particular, address the problem of soliton transmission along uncertain fibers, provided dispersion can be precisely tuned and pulse deformation can be precisely measured in real-time along the fiber. In this sense, several new technologies have been developed recently that allow for some degree of continuous dispersion tuning, from microfluidics-based tunable dispersion materials to fiber-based approaches ranging from fiber gratings to higher-order mode fibers, to name but a few.
While a number of challenges still need to be overcome to arrive at spatially continuous, fine resolution, sensing and actuation, the time seems ripe for the investigation of advanced control techniques for active dispersion management. Pioneering work on this area was done by Koehn and Langbort in 2010, where a nonlinear state-feedback control law was derived based on controlled Hopf bifurcation. However, similar to the existing passive techniques, this approach requires a priori precise knowledge of the characteristics of the fiber in order to achieve dispersion correction. To overcome this limitation, we are developing an L1 adaptive control scheme for the problem of active dispersion management for propagation of solitons along uncertain fibers.
Details about this project can be found in:
- Xargay, Langbort, and Hovakimyan, “L1 Adaptive Control for Optical Soliton Propagation,” in American Control Conference, San Francisco, CA, June-July 2011. [pdf]
- Xargay, Langbort, and Hovakimyan, “L1 Adaptive Control for Optical Soliton Propagation,” submitted to IEEE Transactions on Control Systems Technology, 2011.
|langbort (at) illinois (dot) edu
nhovakim (at) illinois (dot) edu
xargay (at) illinois (dot) edu