Third-order Riemann pulses in optical fibers

We introduce the concept of third-order Riemann pulses in nonlinear optical fibers. These pulses are generated when properly tailored input pulses propagate through optical fibers in the presence of higher-order dispersion and Kerr nonlinearity. The local propagation speed of these optical wave packets is governed by their local amplitude, according to a rule that remains unchanged during propagation. Analytical and numerical results exhibit a good agreement, showing controllable pulse steepening and subsequent shock wave formation. Specifically, we found that the pulse steepening dynamic is predominantly determined by the action of higher-order dispersion, while the contribution of group velocity dispersion is merely associated with a shift of the shock formation time relative to the comoving frame of the pulse evolution. Unlike standard Riemann waves, which exclusively exist within the strong self-defocusing regime of the nonlinear Schrödinger equation, such third-order Riemann pulses can be generated under both anomalous and normal dispersion conditions. In addition, we show that the third-order Riemann pulse dynamics can be judiciously controlled by a phase chirping parameter directly included in the initial chirp profile of the pulse.