## 1 Introduction  
Ultrashort, high-peak-power lasers such as femtosecond and attosecond lasers have become indispensable in many applications spanning the fields of physics, chemistry, biology, medicine, and engineering [1, 2]. Ultrashort lasers operate fundamentally in the infrared region, but there is much demand in the ultraviolet (UV) wavelength region for numerous applications, including time-resolved spectroscopy [3], micromachining for the fabrication of micro-lens arrays, photonic crystals, optical waveguides, gratings, micro-sized optical sensors [4, 5], high-efficiency laser processing of materials [6], and high-resolution ultrafast imaging [7]. Traditionally, high-order harmonic generation using nonlinear crystals has been utilized to convert ultrashort laser pulses from the fundamental infrared to UV wavelengths. The conversion efficiency of such a scheme has reached levels sufficient for the aforementioned applications [8]. However, power scaling is limited, the experimental setup is complex, and conversion efficiency is low. On the other hand, direct generation of pulsed tunable UV laser wavelengths has been achieved using trivalent cerium ion (Ce\({}^{3+}\))-doped fluorine-based host materials. Solid-state tunable lasers have been developed using the following host materials doped with Ce\({}^{3+}\) ions: yttrium lithium fluoride (YLiF\({}_{4}\) or YLF) [9], lanthanum fluoride (LaF\({}_{3}\) of LaF) [10], lithium lutetium fluoride (LiLuF\({}_{4}\) or LLF) [11], lithium calcium aluminum fluoride (LiCaAlF\({}_{6}\) or LiCAF) [12], and lithium strontium aluminum fluoride (LiSrAlF\({}_{6}\) or LiSAF) [13]. Based on the dipole-allowed interconfigurational 5d-4f transitions in the Ce\({}^{3+}\) activator ions, these new class of solid-state tunable UV lasers are efficient, compact, and are especially attractive for ultrashort pulse generation and amplification in the UV wavelength region. Several works have used these Ce\({}^{3+}\)-doped laser materials to develop tunable narrow linewidth UV lasers [14] and high-peak-power UV lasers using various amplifier configurations, including multipass amplification [15], direct amplification of femtosecond pulses [16; 17], and chirped pulse amplification [18]. Recently, 100 fs UV pulses were directly generated using a synchronously-pumped mode-locked Ce\({}^{3+}\)-doped LiCAF laser [19]. Despite the considerable success of these Ce\({}^{3+}\)-doped fluoride laser materials, their full potential has not yet been fully realized. For example, it has been proposed that terawatt UV pulses can be generated directly using Ce\({}^{3+}\)-doped LiCAF [20], but that is yet to be realized. An ultrashort pulse with high peak intensity propagating in a medium can experience nonlinear optical effects, for example self-focusing, such that the medium acts as a Kerr lens [21]. Self-focusing arises from the dependence of a material's refractive index on the intensity of the laser beam propagating through that material. It has been leveraged to generate ultrashort pulses through Kerr lens mode-locking [22]. However, self-focusing can also have damaging effects, as the laser fluence at the focus could exceed the damage threshold of the laser material as well as the peripheral optical elements. To avoid the damaging effects of self-focusing, parameters such as the length of the laser material and pump beam radius could be adjusted. However, information about the nonlinear refractive index of fluoride materials in the UV region is lacking. Determination of the nonlinear refractive index in the UV region is important for optimizing the parameters of UV lasers and amplifiers to minimize self-focusing. While doping with rare-earth activator ions, for example Ce\({}^{3+}\) activator ion, dictates the spectrum of laser emission, the performance of the laser and amplifier itself is largely influenced by the optical properties of the host crystal.