Asymptotically stable compensation of the soliton self-frequency shift

We report on the stable cancellation of the soliton self-frequency shift (SSFS) in nonlinear optical fibers. A soliton, which scatters a group velocity matched pump wave in a so-called optical event horizon regime, may experience a blueshift in frequency, which counteracts the SSFS induced by Raman scattering. The SSFS can easily be compensated by a suitably prepared pump wave, but usually the compensation is unstable and is destroyed after a certain propagation length. We study this kind of soliton-pump wave interaction by an adiabatic approach and quantify the parameter range in which the stable SSFS compensation is possible. The theory enjoys agreement with numerical simulations of soliton propagation.