“…Fiber lasers with pure high-order-mode (HOM) output have been intensively studied in recent years owing to their unique polarization, amplitude and phase characteristics. Generally, there are several commonly used approaches to realize HOM operation, including adopting spatial light modulators [1], [2], employing long period gratings [3], [4], introducing adaptive control [5]- [7], using few-mode fiber Bragg gratings (FBGs) [8]- [10] and taking advantage of mode selective couplers [11], [12]. Currently, exploration on HOM fiber lasers has focused on power scaling [13], nonlinear conversion [4], [14], vector beam generation [15], etc.…”