Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients.

A broad class of exact self-similar solutions to the nonlinear Schrödinger equation (NLSE) with distributed dispersion, nonlinearity, and gain or loss has been found describing both periodic and solitary waves. Appropriate solitary wave solutions applying to propagation in optical fibers and optical fiber amplifiers with these distributed parameters have also been studied in detail. These solutions exist for physically realistic dispersion and nonlinearity profiles. They correspond either to compressing or spreading solitary pulses which maintain a linear chirp or to chirped oscillatory solutions. The stability of these solutions has been confirmed by numerical simulations of the NLSE with perturbed initial conditions. These self-similar propagation regimes are expected to find practical application in both optical fiber amplifier systems and in fiber compressors.

Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients.

A broad class of exact self-similar solutions to the nonlinear Schrödinger equation (NLSE) with distributed dispersion, nonlinearity, and gain or loss has been found. Appropriate solitary wave solutions applying to propagation in optical fibers and optical fiber amplifiers with these distributed parameters have also been studied. These solutions exist for physically realistic dispersion and nonlinearity profiles in a fiber with anomalous group velocity dispersion. They correspond either to compressing or spreading solitary pulses which maintain a linear chirp or to chirped oscillatory solutions. The stability of these solutions has been confirmed by numerical simulations of the NLSE.

Self-similar propagation and amplification of parabolic pulses in optical fibers.

Ultrashort pulse propagation in high gain optical fiber amplifiers with normal dispersion is studied by self-similarity analysis of the nonlinear Schrödinger equation with gain. An exact asymptotic solution is found, corresponding to a linearly chirped parabolic pulse which propagates self-similarly subject to simple scaling rules. The solution has been confirmed by numerical simulations and experiments studying propagation in a Yb-doped fiber amplifier. Additional experiments show that the pulses remain parabolic after propagation through standard single mode fiber with normal dispersion.

Self-similar propagation of high-power parabolic pulses in optical fiber amplifiers.

Self-similarity techniques are used to study pulse propagation in a normal-dispersion optical fiber amplifier with an arbitrary longitudinal gain profile. Analysis of the nonlinear Schrödinger equation that describes such an amplifier leads to an exact solution in the high-power limit that corresponds to a linearly chirped parabolic pulse. The self-similar scaling of the propagating pulse in the amplifier is found to be determined by the functional form of the gain profile, and the solution is confirmed by numerical simulations. The implications for achieving chirp-free pulses after compression of the amplifier output are discussed.