Stabilizing optical solitons by frequency-dependent linear gain–loss and the collisional Raman frequency shift

Abstract

We study transmission stabilization against radiation emission for solitons of the nonlinear Schrödinger (NLS) equation (optical solitons) by frequency-dependent linear gain–loss and the collisional Raman frequency shift. For this purpose, we consider soliton propagation in nonlinear optical waveguides in the presence of weak linear gain–loss, cubic loss, and the collisional Raman frequency shift perturbation. We first show how the collisional Raman perturbation arises in three different nonlinear physical setups. We then show by numerical simulations with a perturbed NLS equation that transmission in waveguides with weak frequency-independent linear gain is unstable. The radiative instability is stronger than the radiative instabilities that were observed in all earlier studies of soliton propagation in the presence of weak linear gain, cubic loss, and various frequency-shifting physical mechanisms. Moreover, we demonstrate by numerical simulations with another perturbed NLS equation that transmission in waveguides with weak frequency-dependent linear gain–loss, cubic loss, and the collisional Raman frequency shift is stable, despite the stronger radiative instability in the corresponding waveguide setup with weak linear gain. Additionally, we find that stabilization occurs via the following process: the collisional Raman frequency shift of the soliton leads to partial separation of the soliton’s and the radiation’s Fourier spectra, while the frequency-dependent linear gain–loss leads to efficient suppression of radiation emission. Thus, our study significantly extends the range of applicability of the soliton stabilization method, by showing that the method works even when the radiative instability is strong.