Mitigation of self-phase modulation by sinusoidally time varying phase

The propagation of intense ultra-short optical pulses in a Kerr medium such as an optical fibre remains a critical issue for many optical systems. This is because the self-phase modulation (SPM) of the propagating pulse usually causes a severe broadening of the pulse spectrum that is typically accompanied by an oscillatory structure. Several strategies have been proposed and successfully deployed to counteract the deleterious effects of SPM in fiber-optic systems, including spatial or temporal scaling to reduce the impact of nonlinearity. Other approaches rely on the exploitation of the peculiar properties of parabolic shaped pulses and self-similar evolution. However, none of these last techniques preserves the pulse temporal duration.
A simple technique to compensate the nonlinear phase due to SPM consists in using an electro-optic phase modulator to impart the opposite phase to the pulses. This method, which emulates the use of a material with a negative nonlinear index of refraction, has proved successful in fiber-optic and free-space optical telecommunication applications using phase-shift keying systems and in the generation of high-peak-power nanosecond pulses.
We have recently experimentally demonstrated that for Gaussian shaped input pulses, the use of a simple sinusoidal drive signal for the phase modulator with appropriate amplitude and frequency is sufficient to reduce the nonlinear spectrum broadening to a large degree, and to significantly enhance the spectral quality of the pulses while their temporal duration remains unaffected. In this paper, we present a comprehensive analysis of this SPM-mitigation approach. We derive an exact formula for the reduction of the SPM-induced rms spectrum broadening of an initially Gaussian pulse enabled by the sinusoidal compensation, and we assess the effects of the initial pulse shape and duration on the effectiveness of the technique by means of numerical simulation. The differences between pre- and post-propagation compensation schemes are also discussed.