Broadband hyperphase pure-high-even-order dispersion solitons from Mamyshev oscillators

Mamyshev oscillator (MO) represents a passively mode-locked fiber laser architecture that exhibits strong tolerance to nonlinear phase shifts through its dual-filter structure. The solitons that can accumulate extremely high nonlinear phase shifts in MO are defined here as hyperphase solitons. Meanwhile, pure-high-even-order dispersion (PHEOD) solitons challenge the traditional understanding of dispersion management beyond the second order through their unique energy-width scaling properties. Previous studies have only preliminarily investigated the basic characteristics of PHEOD solitons in saturable-absorber-based mode-locked fiber lasers. However, the generation mechanism, spectral behavior, and underlying physical nature of hyperphase PHEOD solitons in the MO remain unresolved. In this work, we experimentally achieved the stable generation of hyperphase PHEOD solitons in MO and focused on analyzing their spectral sidebands and broadening characteristics. A theoretical model was constructed to describe the formation and evolution of these spectral features, and its accuracy was verified through experiments and numerical simulations. The research results show that the proposed theoretical model can provide an effective tool for the precise analysis of the spectral characteristics of hyperphase PHEOD solitons, not only helping to deeply understand the physical mechanism of PHEOD solitons in MO, but providing important theoretical support for the performance optimization of ultrafast lasers.