# Ultrafast Mid-IR Laser Pulses Generation via Chirp Manipulated Optical Parametric Amplification
## 1 Introduction
As the signal frequency changes with \(\Delta\omega\), the phase-mismatch becomes \(\Delta k=\Delta k_{1}+\Delta k_{2}+\ldots\), where \(\Delta k_{1}=-\partial k_{s}/\partial\omega_{s}\times\Delta\omega+\partial k_{ i}/\partial\omega_{s}\times\Delta\omega=\Delta\omega\times\left(1/v_{gi}-1/v_{gs}\right)\). Based on the equation, a straightforward way of obtaining ultrabroadband gain in OPA is to exploit the phase-matching bandwidth at degeneracy. Using signal and idler pulses centered at the same wavelength, phase-matching is realized to the first order and the pulses are amplified with an ultrabroad bandwidth. Degenerate OPA systems have been investigated in a number of previous works, and the possibility of producing degenerate few-cycle pulses has been confirmed theoretically and experimentally [47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57]. Despite the ultrabroad gain bandwidth, the concept of degenerate OPA can only be applied to certain center wavelengths with poor tunability due to the limit on the types of available ultrafast lasers [46]. At non-degenerate spectral regions, as the center wavelengths of signal and idler move away from degeneracy, the first-order phase-mismatch increases, which reduces the gain bandwidth severely. As discussed above, the first-order phase-mismatch \(\Delta k_{1}\) is proportional to the group velocity mismatch (GVM) between the signal and idler pulses \(\delta_{si}=1/v_{gs}-1/v_{gi}\). The idea of removing GVM to realize first-order phase-matching leads to the development of noncollinear OPA (NOPA) schemes [58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74]. In NOPA, the pump and seed beams enter the nonlinear crystal with a noncollinear angle \(\alpha\) in between. As a result, the interacting pulses propagate toward different directions during the amplification, and group velocity matching between the signal and idler pulses can be met when \(v_{gs}\) is equal to \(v_{gi}\times cos\Omega\), \(\Omega\) being the noncollinear angle between the two beams. Furthermore, the pulse-front tilting method has been proposed to improve the spatial overlap and the conversion efficiency in NOPA systems [75]. Note that the idler pulse in NOPA is obtained with an angular dispersion, which makes it impossible to be directly used in the following stages. Compared to the signal pulse, the idler has advantages such as a longer center wavelength and a passively stabilized carrier-envelope phase (CEP) [76]. As proposed and experimentally investigated in [76], the white-light continuum pulse from the self-phase-modulation (SPM) effect retains the same CEP as that of the input pulse. When the pump and seed are produced from the same laser source, the CEP of the idler pulse is defined by \(\psi_{i}=-\pi/2+\psi_{p}-\psi_{s}=-\pi\), which is stabilized passively. The CEP stability determines the shape of the electric field in ultrafast laser pulses, especially when the pulse has a few-cycle duration. Therefore, the CEP-stable idler pulses have attracted abundant attention in OPA research. In order to obtain applicable idler pulses in NOPA, the angular dispersion of the beam has to be compensated, which requires energy-consuming procedures and complicates the system drastically [77; 78]. Other than NOPA, several collinear OPA schemes have been proposed for non-degenerate pulse generation. Quasi-phase-matching (QPM) has been widely implemented in conditions where normal broadband phase-matching cannot be achieved. Using a periodically poled nonlinear crystal where the orientation of the crystalline axis inverts periodically as a function of the crystal thickness, the non-zero phase-mismatch is compensated during amplification. Few-cycle pulses, ranging from near-infrared (NIR) to Mid-IR, have been successfully generated from QPM-OPA schemes using crystals such as PPLN, PPSLT, and PPKTP, etc. [79; 80; 81; 82].