Pure Quartic Solitons and their generalizations: theory and experiments

Solitons are wave packets that can propagate without changing shape by balancing nonlinear effects with the effects of dispersion. In photonics they have underpinned numerous applications, ranging from telecommunications and spectroscopy to ultrashort pulse generation. Though traditionally the dominant dispersion type has been quadratic dispersion, experimental and theoretical research in recent years has shown that high-order, even dispersion enriches the phenomenon and may lead to novel applications. In this Tutorial, which is aimed both at soliton novices and at experienced researchers, we review the exciting developments in this burgeoning area, which includes pure-quartic solitons and their generalizations. We include theory, numerics and experimental results, covering both fundamental aspects and applications. The theory covers the relevant equations and the intuition to make sense of the results. We discuss experiments in silicon photonic crystal waveguides and in a fiber laser, and assess the promise in additional platforms. We hope that this tutorial will encourage our colleagues to join in the investigation of this exciting and promising field.