Exploring Nonlinear Propagation with Higher Order Dispersion: Exact Soliton Solutions and the Structure of Their Poles

Solitons are a unique phenomenon which appear throughout nature, characterised by pulses which are unchanged in shape as they propagate. Optical solitons in particular balance nonlinear effects with dispersion; studies of these pulses have largely focused on quadratic dispersion, for which the inverse group velocity is proportional to frequency. Generally speaking, quadratic dispersion dominates higher order dispersion effects, however studies have shown that higher order dispersion solitons exist [1], [2] and can be generated experimentally using a fibre laser with a pulse shaper [3]. These new experimental capabilities allow for the generation of soliton involving up to 16
^th
order dispersion [4], and have prompted increased numerical and analytical studies of soliton solutions involving combinations of different orders [1], [2], [5]. We analyzed combinations of even dispersion up to 6
^th
order, which in turn provides the necessary insight to make predictions concerning the form and nature of solutions for arbitrary orders [6].