Pure-high-even-order dispersion bound solitons complexes in ultra-fast fiber lasers.

Temporal solitons have been the focus of much research due to their fascinating physical properties. These solitons can form bound states, which are fundamentally crucial modes in fiber laser and present striking analogies with their matter molecules counterparts, which means they have potential applications in large-capacity transmission and all-optical information storage. Although traditionally, second-order dispersion has been the dominant dispersion for conventional solitons, recent experimental and theoretical research has shown that pure-high-even-order dispersion (PHEOD) solitons with energy-width scaling can arise from the interaction of arbitrary negative-even-order dispersion and Kerr nonlinearity. Despite these advancements, research on the bound states of PHEOD solitons is currently non-existent. In this study, we obtained PHEOD bound solitons in a fiber laser using an intra-cavity spectral pulse shaper for high-order dispersion management. Specifically, we experimentally demonstrate the existence of PHEOD solitons and PHEOD bound solitons with pure-quartic, -sextic, -octic, and -decic dispersion. Numerical simulations corroborate these experimental observations. Furthermore, vibrating phase PHEOD bound soliton pairs, sliding phase PHEOD bound soliton pairs, and hybrid phase PHEOD bound tri-soliton are discovered and characterized. These results broaden the fundamental understanding of solitons and show the universality of multi-soliton patterns.