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Pure-Quartic Solitons in the Presence of Quadratic Dispersion

Solitons in guided-wave structures usually arise from the balance of the (positive) nonlinear optical Kerr effect and negative (anomalous) quadratic dispersion. However, some of us recently demonstrated experimentally that solitons also form by balancing the nonlinear effect by negative quartic dispersion, which may have applications in ultrafast lasers [1]. That such solitons exist is perhaps not surprising since both types of dispersion describe the group velocity increasing with frequency. With quadratic dispersion the soliton has the well-known sech shape, whereas have pure-quartic solitons are approximately Gaussian with oscillating tails. Here we consider solutions in the presence of both quadratic and quartic dispersion, and show that these solutions continuously deform when the parameters change, and thus form a single family. We explore this family here for the first time.