###### Abstract  
Ultrafast mid-infrared (mid-IR) lasers with a high pulse repetition rate are in great demand in various fields, including attosecond science and strong-field physics. Due to the lack of suitable mid-IR laser gain medium, optical parametric amplifiers (OPAs) are used to generate an ultrafast mid-IR laser. However, the efficiency of OPA is sensitive to phase mismatches induced by wavelength and temperature deviations from the preset points, which thus limits the pulse duration and the average power of the mid-IR laser. Here, we exploited a noncollinear phase-matching configuration to achieve simultaneously wavelength- and temperature-insensitive mid-IR OPA with a LiGaS\({}_{2}\) crystal. The noncollinearity can cancel the first-order dependence of phase matching on both wavelength and temperature. Benefitting from the thermal property of the LiGaS\({}_{2}\) crystal, some collinear phase-matching solutions derived from the first-order and even third-order wavelength insensitivity have comparatively large temperature bandwidths and can be regarded as approximate solutions with simultaneous wavelength and temperature insensitivity. These simultaneously wavelength- and temperature-insensitive phase-matching designs are verified through numerical simulations in order to generate few-cycle, high-power mid-IR pulses. mid-infrared lasers; ultrafast lasers; optical parametric amplification; LiGaS\({}_{2}\) crystal +
Footnote †:  
However, non-oxide crystals usually exhibit a stronger absorption than matured oxide crystals (e.g., at 2 \(\upmu\)m: \(\beta\)-BBO, \(-\)0.07 cm\({}^{-1}\)[7]; LiGaS\({}_{2}\), \(-\)0.47 cm\({}^{-1}\)[8]; ZnGeP\({}_{2}\), \(-\)0.15 cm\({}^{-1}\)[7]). As near-IR OPAs with \(\beta\)-BBO crystals have suffered from a thermal effect under an average power of several tens of watts [9; 10], the mid-IR OPA with non-oxide crystals will also face thermal issues in future high average power operations, although current low-power experiments have not encountered this problem [11; 12; 13; 14; 15; 16; 17]. In this study, we focus on the semiconductor LiGaS\({}_{2}\) crystal, which has been popular in recent years because it has a high transparency from 0.32 to 11.6 \(\upmu\)m (at the 5 cm\({}^{-1}\) absorption level), covering both the near-IR pump source around 1 \(\upmu\)m and the mid-IR output beyond 10 \(\upmu\)m [8]. Compared with other promising non-oxides (e.g., BaGaS\({}_{7}\)), LiGaS\({}_{2}\) has a relatively large absorption across its transparent range. For example, the absorption coefficient at 1 \(\upmu\)m is 0.51 cm\({}^{-1}\) for LiGaS\({}_{2}\)[8], but \(<\)0.1 cm\({}^{-1}\) for BaGaS\({}_{7}\)[18]. In addition, the effective nonlinear coefficient of LiGaS\({}_{2}\) is moderate (\(-\)5 pm\(\cdot\)V\({}^{-1}\)[19]), much lower than that of AgGaS\({}_{2}\) (\(\sim\)12 pm\(\cdot\)V\({}^{-1}\)[20]), BaGa\({}_{4}\)Se\({}_{7}\) (\(-\)20 pm\(\cdot\)V\({}^{-1}\)[20]), and ZnGeP\({}_{2}\) (\(-\)70 pm\(\cdot\)V\({}^{-1}\)[7]). This means that a longer LiGaS\({}_{2}\) crystal may be needed to achieve efficient amplification, which not only sacrifices gain bandwidth, but also aggravates heat load. Therefore, it is necessary to develop PM with simultaneous wavelength and temperature insensitivity for future LiGaS\({}_{2}\)-based high-power OPA processes. Unfortunately, there have been few studies on the thermal properties of PM in LiGaS\({}_{2}\) crystal, with very little consideration of simultaneous wavelength- and temperature-insensitive PM. This article aims to reveal the possible PM solutions with simultaneous wavelength and temperature insensitivity for mid-IR OPA with LiGaS\({}_{2}\) crystals in both noncollinear and collinear PM configurations. By tuning the PM parameters such as signal wavelength and crystal temperature, the noncollinear angles corresponding to the wavelength-insensitive PM (WIPM) and temperature-insensitive PM (TIPM) can overlap, creating a simultaneous wavelength- and temperature-insensitive PM (WTIPM).