## 1 Introduction  
In recent years, the sustained development of high power diode lasers and their application as pump devices in high peak and average power lasers have contributed to a growing research in different ytterbium-doped materials. In fact, the combination of these gain media and diode pumping has proved to be an extremely valuable option for development of dedicated systems for pumping high-energy, high repetition rate, ultrashort duration optical parametric amplifiers [1] and it is also a promising choice for the development of Yb-based chirped pulse amplification (CPA) systems on their own, aimed at reaching multi-Joule pulses in the sub-picosecond regime [2]. The interest in Yb-doped media is justified by their unique spectroscopic properties bringing more advantages for diode pumping than other traditional gain media [3]. They exhibit a broadband absorption cross-section and high fluorescence lifetime at millisecond time scales, low quantum defect and a simple electronic structure that avoids some parasitic effects. All these properties allow them to be pumped very efficiently at very high repetition rates by low-brightness semiconductor lasers with emission peaks in range 920 to 980 nm. Additionally, these media exhibit a large gain bandwidth in the spectral range between 1020 and 1070 nm capable of supporting ultrashort pulses lasting tens of femtoseconds, as was recently demonstrated by using Yb\({}^{3+}\):CaGdAlO\({}_{4}\) (Yb:CALGO) to generate 40 fs pulses [4]. A large number of Yb-doped hosts have been investigated, characterized by slight differences in their spectroscopic parameters depending on the host family. This great variety leads to a considerable sensitivity to the laser parameters, requiring a careful and reliable modeling in order to evaluate the performance of a given system in terms of e.g., wavelength tunability and bandwidth evolution over the course of regenerative or multipass amplification. In particular, in a regenerative amplifier the modeling is significantly more useful since the net gain of the amplification stage is usually 10\({}^{4}\) to 10\({}^{6}\) and the usually low single-pass-gain results in high number of round-trips [5]. For this reason, we have previously developed a simulation code that was benchmarked with real experimental data, in order to test and evaluate the laser performances of different Yb-doped gain media [6]. On the other hand, it is well known that flashlamp-pumped Nd:glass laser systems operating at 1053 nm are still a well-established technology for reaching pulsed energies above the kJ range with a lower cost per Joule. Petawatt level, Nd:glass-based CPA systems have been demonstrated, using high-performance front-ends based e.g., in regenerative amplification in Ti:sapphire or broadband parametric amplification. Fully ytterbium-based amplification systems are limited to 10 J [7] but they already represent a very competitive option up to Joule level [8,9], making them an interesting alternative for the pre-amplifier stages of a high energy/high power Nd:glass laser, provided they can perform efficiently at the required wavelength. Recent progress towards this hybrid amplification concept has consisted in the demonstration of a Q-switched cavity based in Yb:CaF\({}_{2}\) extending from 1028 to 1065 nm [10], and the development of high-efficiency Yb:YAG laser oscillators operating at 1048-1050 nm [11,12], although with pulse energies limited to a few tens of nanojoules. In this work, we evaluate numerically the energy and spectral performance for the gain media Yb:YAG and Yb:CaF\({}_{2}\) for different pump powers when used in a diode-pumped regenerative amplifier. The goal is to explore the tunability of these materials around 1053 nm and evaluate their application in the pre-amplifier stages of an Nd:glass-based power amplifier chain, up to the Joule level.