# High Power All-Fiber Supercontinuum System Based on Graded-Index Multimode Fibers
## 1 Introduction  
The supercontinuum has gained tremendous progress in the last few decades. Supercontinuum sources are widely used in optical coherence tomography (OCT) [1] and biomedicine [2]. The rapid development of photonic crystal fibers (PCF) has attracted more research on supercontinuum [3, 4]. The dynamic of nonlinearity effects based on the generation of supercontinuum by picosecond and femtosecond lasers have been well explained [5]. The average power of PCF-based generation of supercontinuum has been reported to be higher than 200 W [6], however, the small core diameters of PCFs make it difficult to further increase its average power [7]. The splicing of photonic crystal fibers with other fibers is also a challenge, which usually requires a mode field adaptor to match the different cores [8]. The conversion efficiency of the supercontinuum is also challenging to exceed 50% [9]. Meanwhile water cooling at the splicing point of the PCF is required. Due to these issues, the core diameter of the gain fiber in the amplifier does not exceed 20 \(\upmu\)m before the photonic crystal to ensure efficiency, limiting the peak power of amplification.  
In recent years, the unique nonlinear dynamics in the grade-index (GRIN) multimode fibers has gained scientists' attention. Research on the generation of supercontinuum based on GRIN fiber geometric parametric instability has been reported [10]. In addition, the quasi-phase matched intermodal four-wave mixing (FWM) [11] and Kerr self-cleaning (KSC) [12] observed in GRIN fibers are also interesting. Compared to single-mode or few-mode fibers, GRIN multimode fibers offer greater advantages in high-power applications. [PERSON] et al. demonstrated ultra-broad supercontinuum generation (450-2400 nm) using a GRIN multimode optical fiber pumped in the normal dispersion regime at 1064 nm with an amplified Q-switched micro-chip laser [10]. [PERSON] et. al. reported that a supercontinuum with an output power of 3.96 W was achieved in a GRIN MMF with 62.5 \(\upmu\)m core diameter using picosecond pulses at MHz repetition rate [13].  
There are also some reports on the generation of supercontinuum in GRIN fibers [14; 15]. However, current studies on the generation of supercontinuum spectra based on GRIN fibers were all performed at lower average powers (below 5 \(W\)).  
In this paper, we report an all-fiber supercontinuum source with an average power of 25 W and a repetition frequency of 8.27 MHz. The spectrum width of the supercontinuum covered 480 nm to 2440 nm. The all-fiber structure was achieved by directly splicing the GRIN fiber with the pigtail of the picosecond laser. The variation of the supercontinuum spectrum was studied by varying the input powers and the length of the GRIN fiber. Self-cleaning of the beam in the GRIN fiber was observed. The GRIN fiber can be pumped at high peak powers and does not require water cooling. The conversion efficiency from the injected laser pulse to the supercontinuum is about 82% higher than the other schemes generating supercontinuum based on GRIN fibers. To the best of our knowledge, this is the highest average power reported to date for supercontinuum generation based on a GRIN fiber.