## 3 Experimental Results and Analyses  
An autocorrelator (PulseCheck50 NIR, APE) and an optical spectrum analyzer (OSA, AQ6370, Yokogawa) were used to characterize the properties of the laser output. The spectral resolution for the OSA is 0.05 nm. The autocorrelator had a detection range from 700 to 1100 nm. For measurements, the laser output was incident on a dichroic mirror with \(\approx\)95% reflection rate from 1000 to 1240 nm and \(\approx\)90% transmission rate from 700 to 950 nm. The fundamental wave was selected by taking the reflection, while the transmission was used for further investigations of the red (751 nm) and near-infrared (864 nm) components. Bandpass filters centered at 1030, 750, and 850 nm with a 40 nm transmission band were also applied to separate the fundamental, red, and near-infrared components, respectively. The oscillator emitted up to 4.5 mW average power at a repetition rate of 25 MHz and a central wavelength of 1030 nm, corresponding to 0.18 nJ for the pulse energy. The spectrum of the compressed pulses is depicted in Figure 2a. The spectrum covered a full width at half-maximum (FWHM) bandwidth of 12.5 nm, as compared with that of 1.3 nm for the laser oscillator. The autocorrelation trace in Figure 2b exhibited a FWHM of 653 fs, corresponding to a pulse duration of 371 fs by taking hyperbolic secant fitting. Figure 1: Schematic diagram of the laser system. FBG, fiber bragg grating; ISO, isolator; LD, laser diode; WDM, wavelength division multiplexer; YDF, Yb-doped fiber; DCF, double-clad fiber; PCF, photonic crystal fibers; MMLD, multi-mode laser diode; DM, dichroic mirror; HWP, half wave plate; AOM, acousto-optic modulator. As the pump power exceeded 10.85 W, the parametric waves increased drastically, giving rise to a visualized red laser. In this case, the supercontinuum generated from the Yb-doped main amplifier covers from 751 to 1273 nm, which is shown in Figure 3. The Stokes series at 1134, 1203, and 1273 nm with 13 THz between adjacent lines was originated from cascaded Raman processes, which were attained at high peak powers [5; 18]. Here, Raman components would also generate anti-Stokes through FWM processes with the fundamental pulse. Dramatically, FWM processes were promoted when the parametric waves coupled and overlapped with Raman spectrum [9; 10; 19]. As depicted in Figure 3, the first-order FWM process involved the fundamental wave at 1030 nm, signal wave at 864 nm, and idler wave at 1273 nm, while the second-order FWM process involved the second fundamental wave at 864 nm, signal wave at 751 nm, and idler wave at 1030 nm. The Stokes lines at 1134, 1203, and 1273 nm also satisfied the parametric relation. The cascaded FWM processes can be expressed as,  
\[2\times\omega\left(1030\right)=\omega\left(864\right)+\omega\left(1273\right), \tag{1}\]  
\[2\times\omega\left(864\right)=\omega\left(751\right)+\omega\left(1030\right), \tag{2}\]  
Figure 3: The spectrum measured by optical spectrum analyzer (blue curve) from 850 to 1350 nm and by HR4000 (red curve) from 700 to 1000 nm on a logarithmic scale. The spectral resolution for the HR4000 is 0.27 nm. Five parametric sidebands were generated, such as 751, 864, 1134, 1203, and 1273 nm, with the fundamental wave at 1030 nm. The peak at the wavelength of 976 nm indicates the residual pump laser. Figure 2: The measured (**a**) spectral intensity and (**b**) autocorrelation of the compressed pulse from the three-stage pre-amplifiers, which were measured after the grating-based compressor. The inset in (**a**) shows the spectral profile of the oscillator. \[2\times\omega\left(1203\right)=\omega\left(1134\right)+\omega\left(1273\right). \tag{3}\]  
In Equation (1), both signal \(\omega\) (864) and idler wave \(\omega\) (1273) generated in the first FWM process participated in the higher-order FWM process. This was realized by the high intensity of the fundamental and parametric waves during the amplification in the LMA PCF fiber.