## 2 Review of Cryogenic-Cooling Benefits
### Spectroscopic, Lasing, Linear and Nonlinear Optical Parameters
#### 2.7.3 Optically-Induced Laser Damage  
Perhaps the most important parameter in the design of any laser system is the laser-induced damage threshold (LIDT), the value of fluence, intensity, or average power that if exceeded, will result in irreversible damage to at least one (usually critical) optical or lasing element in the laser system. If the weakest component in a laser system has an LIDT that is a fraction of the laser saturation fluence, one cannot obtain a high overall system efficiency because for high extraction efficiency the input laser fluence must be at least equal to the saturation fluence, and in the case of Gaussian beams, many times the saturation fluence [28]. A small saturation fluence is obtained for laser materials with a large stimulated-emission cross-section (see Equation (76)). Because the LIDT has a laser pulsewidth dependence that results in picosecond pulses having a smaller damage threshold than nanosecond pulses, and femtosecond less than picosecond [93], it was a challenge in early ultrafast lasers to be able to scale laser output due to the limiting value of LIDT's in the picosecond and particularly in the femtosecond regime. It was because of those damage limitations, as well as to avoid the type of nonlinear effects discussed in the aforementioned, that the technique of CPA was invented [66]. Using CPA, a short femtosecond pulse for example is stretched using diffraction gratings or other means, to the picosecond regime where damage thresholds are substantially larger, After stretching, the initial pulse is amplified in a following beam line of amplifiers where the larger pulsewidth allows nonlinear effects to be avoided or minimized, and where more efficient extraction can be obtained due to the larger damage threshold. After amplification, the stretched pulse is compressed, in many cases using a diffraction grating compressor, to restore the pulsewidth close to its' initial value. Managing the accumulated dispersion, and compensating for it using certain types of compressor configurations determines how close to the initial pulse width the final compressed pulse comes. The literature of LIDT's is vast. Interested readers that have a need to thoroughly explore the field may consult the book by Wood [94], as well as the many publications of the Annual Boulder Damage Symposium (Boulder, CO, USA), a conference that celebrated its 45 th year in 2013. The LIDT of laser and optical materials is a consequence of the many physical mechanisms connected with the high fields achievable with laser. When intense beams are transmitted through crystals or glasses, many nonlinear effects such as harmonic generation, self-focusing and self-phase modulation, nonlinear absorption, excited-state absorption, stimulated Brillouin or Raman scattering, and others may occur, and contribute to irreversible damage. In addition electron avalanches may occur in the laser in response to a strong E field, and plasmas may form on a surface or internally. High average power effects, that are now becoming more and more important, can be caused by absorption and melting of dielectric crystals or dielectric coatings, and can lead to distortion depolarization, and ultimately fracture of crystals or other optics. It is a general observation, supported by measurements, that the LIDT of surfaces are substantially smaller than bulk LIDT's. LIDT's are a strong function of the laser wavelength, with visible and UV LIDT's much less than those obtained around 1000 nm [93; 94]. The pulsewidth dependence of LIDT's is rather simple in the nanosecond regime, varying as the pulsewidth to the 1/2 power [93; 94], however for picosecond and femtosecond pulses the dependence is more complicated [95].