## 1 Introduction  
Tunable, ultrashort laser pulses in different spectral ranges are powerful tools with applications in scientific research including ultrafast time-resolved spectroscopy [1; 2; 3; 4; 5; 6; 7], nonlinear microscopy [8; 9; 10; 11; 12; 13; 14] and laser micro-machining [15; 16; 17; 18]. In the case of ultrafast time-resolved spectroscopy, which is widely used in the investigation of electronic and vibrational dynamics in molecules, the absorption peaks vary from sample to sample, and some of the molecular dynamics under investigation take place in less than 100 fs. As a result, sub-20 fs pulses with a time resolution high enough to observe real-time vibrational quantum beat and that are wavelength tunable in a wide range will play a key role. Nonlinear microscopy, such as two- or three-photon and second- or third-harmonic generation (SHG/THG) microscopy, are technologies widely used in biological research. Two-photon microscopy can be used in tissue imaging with a depth of several hundred \(\upmu\)m [8; 9], and three-photon microscopy can image to a depth of 1.4 mm [10]. SHG/THG microscopy can be used to image some biological tissues without the need for fluorescent proteins or staining with dyes, and can achieve imaging depths of several hundred \(\upmu\)m due to its use of long excitation wavelengths [11; 12; 13; 14]. The pump laser sources used in nonlinear microscopy have pulse widths of \(\sim\)100 fs or shorter, and a visible to middle-IR spectral range [8; 9; 10; 11; 12; 13; 14]. Some spectroscopy and microscopy experiments, such as the multicolor pump-probe experiment [19], two-dimensional spectroscopy [20], or multicolor nonlinear microscopy [21; 22; 23] require ultrashort pulses with several colors. Conventionally-used ultrashort laser sources have a spectral range of 650-950 nm (Ti:sapphire laser), 1000-1100 nm (Yb-/Nd-doped solid-state laser or fiber laser), or 1550 nm (Er-doped fiber laser). Great efforts have been made to extend the spectral range using nonlinear processes [24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40]. Optical parametric amplifier (OPA) and optical parametric oscillator (OPO) technologies are among the most successful methods for generating \(\upmu\)J-level pulses with spectral ranges from UV to mid-IR [32; 33; 34; 35]. Spectrally tunable few-cycle pulses can be generated using a noncollinear optical parametric amplifier (NOPA) [36; 37; 38; 39; 40]. Commercial NOPA setups are available from several companies, although the price is still too high for many research groups. Pulses with broadband spectra from visible to IR (known as super continuum white light) also can be generated through filamentation in gases, bulk media, or fibers [41; 42; 43; 44; 45], although there are problems with the stability of the supercontinuum laser pulses [46; 47; 48]. Recently, four-wave mixing (FWM) has been studied as new method for the generation of ultrashort pulses, including few-cycle pulses, with a spectral range from deep-UV (DUV) to mid-IR [49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66]. Among these results, the multicolored laser pulses that can be generated using cascaded four-wave mixing (CFWM) in transparent bulk materials are particularly attractive, due to their ultra-broadband spectral range, large wavelength tunable range and compact configurations [54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66]. Multicolored laser pulses generated by CFWM were first shown in semiconductor lasers in the 1980s [67]. Highly efficient multicolor (\(>\)4 color) signals were generated in a nearly degenerate intracavity FWM experiment in a GaAs/GaAlAs semiconductor laser with a dye laser as the pump source for both the semiconductor laser and the FWM process. This was used as a method for quantitative determination of the third-order nonlinear optical susceptibility of the semiconductor.