Many different properties of a nonlinear crystal can be important for an application e.g. in nonlinear frequency conversion:
The chromatic dispersion and birefringence properties determine the possibilities for phase matching and the phase-matching bandwidth, angular acceptance (for critical phase matching), etc.
The magnitude of the effective nonlinear coefficient deff, which depends on the nonlinear tensor components and on the phase-matching configuration, is important particularly if the achievable optical intensities are low.
Normally, the crystal material should have a high optical transparency for all wavelengths involved.
Additional properties can be relevant for a comparison:
the material’s potential to be periodically poled to achieve quasi-phase matching
linear absorption, which can cause heating at high optical power levels, so that the phase matching is disturbed, and thermal lensing may occur
the resistance against optical damage, gray tracking, photodarkening, green-induced infrared absorption, and the like
the resistance against photorefractive effects (which are often called photorefractive damage, even though this is usually reversible)
the availability of crystals with consistently good quality, large size and a reasonable price
the ease of fabricating high-quality anti-reflection coatings on the crystals
the chemical durability; e.g., some crystal materials are hygroscopic, others undergo chemical changes when heated in a vacuum chamber for application of a dielectric coating
The choice of the most suitable crystal material for a given application is often far from trivial; it should involve the consideration of many aspects. For example, a high nonlinearity for frequency conversion of ultrashort pulses does not help if the interaction length is strongly limited by a large group velocity mismatch and the low damage threshold limits the applicable optical intensities. Also, it can be highly desirable to use a crystal material which can be critically phase-matched at room temperature, because noncritical phase matching often involves the operation of the crystal in a temperature-stabilized crystal oven.