Optimum pre-emphasis in ultra-long-haul networks

We investigate experimentally and theoretically the shape of the optimum spectral pre-emphasis for ultra-long-haul networks and systems in the presence of optical nonlinearities. In a 40 x 10 Gbits/s x 2240 km system, we experimentally show the advantages of a pre-emphasis scheme that ensures minimum variations of path-averaged power among the wavelength-division-multiplexing channels between the cleanups performed by dynamic gain-flattening filters. This is achieved by enforcing a straight-line spectrum near the middle of the link between two consecutive gain-flattening nodes. We explain these results by a simple model, in which we derive the conditions for optimum pre-emphasis in the presence of either distortionlike ( e. g., self-phase modulation) or noiselike ( e. g., four-wave mixing) nonlinearities. We show that, for relatively small gain ripple, both of these optimum pre-emphasis techniques are equivalent to equalizing the optical signal-to-noise ratio for all channels and producing a flat power spectrum near the middle of the link. Hence, enforcing the straight-line spectrum in the middle of the link is the closest practical approximation to the optimum pre-emphasis. (C) 2006 Optical Society of America.