## 4 Review and Status of Cryogenic Laser Technology
### Cryogenic Ultrafast (Picosecond and Femtosecond) Lasers
We list, in order from left to right, the year, the crystal type, the pulse energy \(Ep\), repetition rate \(\
u_{r}\), average power \(P\)av, the gain bandwith \(\Delta\lambda_{C}\) (from Table 6), laser operating wavelength \(\lambda_{L}\), the Gaussian transform-limited pulsewidth \(\delta t_{TL}\), the seed bandwidth \(\Delta\lambda_{S}\), the seed pulsewidth \(\delta t_{TLS}\), the amplifier bandwidth \(\Delta\lambda_{A}\), the amplifier expected pulsewidth \(\delta t_{TLA}\), the measured output pulsewidth \(\delta t_{MEAS}\), the peak power \(P_{P}\), and the corresponding reference [132; 155; 158; 159; 160; 161; 162; 163; 164; 165; 166; 167; 168; 169]. Other acronyms found in the Table are BC (before-recompression), AC (after-recompression), R (cryogenic regenerative amplifier), SHG (second-harmonic-generation), UC for (not re-compressed), and E for estimated. We also use \(\sigma\) to denote use of the \(\sigma\) transition in Yb:YLF. The majority of demonstrations listed in Table 10 involve the use of multi-pass cryogenic Yb:YAG or Yb:YLF amplifiers to boost the peak and average powers of picosecond laser systems, with most systems targeted for use as pumps in OPCPA femtosecond lasers. Another application of interest is the generation of table-top X-ray lasers. We also show in Table 10 the frequency-doubled results, where applicable. Most of the reported cryogenic systems in Table 10 use the CPA technique to stretch seed pulses so as to obtain a higher damage threshold; in a few cases, direct amplification was used to avoid the losses and added complexity of CPA systems. The Gaussian transform-limited pulsewidth \(\delta t_{TL}\) is calculated for cryogenic temperatures near 80 K, and uses the bandwidths taken from Table 6 as well as the operating wavelength of the specific laser system. The bandwidth of the seed laser, \(\Delta\lambda_{S}\), is taken from the referenced paper where provided, and used to calculated the transform-limited output pulsewidth \(\delta t_{S}\) value supported by that bandwidth. For the cryogenic multi-pass or regenerative amplifier, the amplifier bandwidth \(\Delta\lambda_{A}\) measurement reported in the publication is stated, and again the transform-limited pulse duration \(\delta t_{A}\) supported by that value is calculated. We then show the reported pulsewidth measurement \(\delta t_{MEAS}\), allowing one to ascertain, in the reported stretcher-compressor CPA systems, how closely the obtained pulsewidth after compression is to the transform-limited value. The transform-limited pulsewidth for Yb:YAG at 80 K is about 1.04 ps (bandwidth of about 1.5 nm at 80 K), a value that has not yet been closely approached. This is a consequence of gain-narrowing that takes place in multi-pass amplifiers, and particularly in regenerative amplifiers where many passes of the gain medium occur. Regenerative amplifiers can have bandwidths \(<\)0.2 nm, so the obtained output pulsewidths tend to be \(>\) about 8 ps. Imperfect compression stretches the pulses even further. A number of techniques have been used to reduce the effects of gain-narrowing and to provide a seed laser for the demonstrations listed in Table 10 with broadband pulses entering the regenerative amplifier. In order to obtain pulsewidths in the femtosecond regime, researchers have sought laser materials with a broader bandwidth at 80 K. One such material is Yb:YLF, which has a gain bandwidth of about 27 nm and is capable of producing \(\sim\)100 fs pulses. Table 10 shows that sub-ps pulses have been produced by two groups [155; 167]. Other materials such as Yb:GSAG [30] have been developed as well to drive obtained pulsewidths from Yb based lasers into the femtosecond regime. Yb:CaF\({}_{2}\) has also been recently developed as a promising fs laser materials, due to a broad bandwidth that remains broad even at 80 K. At room temperature, a Yb:CaF\({}_{2}\) laser is reported with a pulsewidth of 99 fs [111]. A cryogenic laser using the closely related material Yb:CaNaF\({}_{2}\) laser has produced 173 fs pulses [170].