## 1 Introduction  
Supercontinuum generation via frequency conversion provides a way to extend the frequency coverage of a fiber laser, which is usually required in scientific and industrial applications, such as coherent anti-Stokes Raman scattering spectroscopy, stimulated emission depletion microscopy, fluorescence polymersomes, biological sensing, and ophthalmc treatments [1; 2; 3; 4]. As we know, FWM in large mode area (LMA) fibers is desirable to generate supercontinuum spanning several octaves [5; 6].  
Up till now, various approaches have been extensively exploited to manage effective parametric wave generation by FWM processes. One way is to monitor the geometrical parameters in a photonic crystal fiber (PCF) in order to retain the phase matching for frequency conversion. By this scheme, watt-level supercontinuum was generated from either CW pumped or pulsed-systems [7]. Another way is to introduce birefringence-assisted FWM by propagating a fundamental wave along one of the polarization axes, while Stokes and anti-Stokes waves are propagated along the orthogonal polarization axis. For instance, in 2015, [PERSON] et al. demonstrated that the parametric gain can be tuned on and off by switching the polarization direction of the pump field between the fast and slow axes of a hybrid PCF [1; 8]. Besides, by manipulating the multimode dispersion in high-order modes to compensate the material dispersion, nonlinear parametric amplification was also realized during the amplification of the fundamental wave in LMA fibers [9; 10]. Nevertheless, supercontinuum-generation-resolved applications usually prefer a multi-wavelength, ultrashort, pulsed laser with high peak intensity. For instance, in case of vibrational spectroscopic imaging in biology and medicine, pulses with durations larger than hundreds of picoseconds might induce inevitable heating effects, which might damage the biological samples [11]. Intense parametric wave generation usually gives rise to gain saturation, which limits the gain bandwidth and broadens the pulse duration. Besides, some of the approaches take hybrid PCF to implement parametric gain, which requires more instruments and brings about more losses in the system.  
In this work, we present nonlinear parametric amplification in the red and near-infrared region via cascaded-Raman-assisted FWM processes by pre-compressing the input pulse of the main amplifier [12; 13; 14]. In this all-fiber scheme, a compact, self-made fiber laser oscillator provided the fundamental pulse at 1030 nm with 4.3 ps pulse-duration. After 3-stage pre-amplification, a pair of gratings was employed as the pre-compressor for optimizing the parametric gain in the main amplifier [7; 9]. Pre-compression increased the peak power of the fundamental pulse before entering the main amplifier by shortening the pulse duration, which enhanced self-phase modulation in the main amplifier. It broadened the frequency coverage and led to shorter pulse duration. The gain of the main amplifier was obtained in a 1-m-long LMA Yb-doped PCF with a core diameter of 40 \(\upmu\)m, which enabled the fundamental and parametric waves to propagate with different modes. This finally promoted the cascaded nonlinear frequency mixing in the main amplifier [4; 15; 16]. Therefore, up to five sidebands, such as 751, 864, 1134, 1203, and 1273 nm, were generated. Here, we concentrated on the anti-Stokes lines in red (751 nm) and near infrared (864 nm), since they exhibited high gain. The strong intensity of both the fundamental and parametric waves also guaranteed the compression, along with the amplification of the parametric components at 864 and 751 nm, which overcame the gain saturation and shortened the pulse duration during amplification [17].