How to select a NLO crystal for a frequency conversion process with a certain laser? The most important thing is to obtain high conversion efficiency. The conversion efficiency has the following relationship with effective nonlinear coefficient (d_{eff}), crystal length (L), input power density (P) and phase mismatching (Dk):
h∝ PL^{2}*[d_{eff} * sin(DkL)/DkL]^{2}

In general, higher power density, longer crystal length, larger nonlinear coefficients and smaller phase mismatching will result higher conversion efficiency. However, there is always some limitation coming from nonlinear crystals and lasers. For example, the d_{eff} is determined by the nonlinear crystal itself and the input power density has to be lower than the damage threshold of crystal. Therefore, it is important to select a right crystal for your applications. In the following Table we list the laser and crystal parameters for selecting right crystals:

Parameters For NLO Crystal Selection
Laser Parameters

Crystal Parameters

NLO Process
Power or Energy, Repetition Rate
Divergence
Bandwidth
Beam Size
Pulse Width
Environment

PhaseMatching Type and Angle, d_{eff}
Damage Threshold
Acceptance Angle
Spectral Acceptance
Crystal Size, WalkOff Angle
Group Velocity Mismatching
Temperature Acceptance, Moisture


Crystal Acceptance

If a laser light propagates in the direction with angleDq to phase matching direction, the conversion efficiency will reduce dramatically (see the right Figure). We define the acceptance angle (Dq) as full angle at half maximum (FAHM), where q = 0 is phasematching direction. For example, the acceptance angle of BBO for type I frequency doubling of Nd:YAG at 1064nm is about 1mradcm. Therefore, if a Nd:YAG laser has beam divergence of 3mrad for frequencydoubling, over half of the input power is useless. In this case, LBO may be better because of its larger acceptance angle, about 8mradcm. For NCPM, the acceptance angle is normally much bigger than that for CPM.
In addition, you have to consider the spectral acceptance (Dl) of crystal and the spectral bandwidth of your laser; crystal temperature acceptance (DT) and the temperature change of environment.


WalkOff

Due to the birefringence of NLO crystals, the extraordinary wave (n_{e}) will experience Poynting vector walkoff as shown in the right. If the beam size of input laser is small, the generated beam and input beam will be separated at a walkoff angle (r) in the crystal and it will cause low conversion efficiency. Therefore, for focused beam or intracavity doubling, the walkoff is a main limitation to high conversion efficiency.


Group Velocity Mismatching

For frequency conversion of ultrafast lasers such as Ti:Sapphire and Dye lasers with femtosecond (fs) pulse width, the main concern is fs pulse broadening induced by group velocity mismatching (GVM) or group velocity dispersion of NLO crystal. In order to keep efficiency frequency conversion without significant pulse broadening, the suggested thickness (LGVM) of crystals is less than Pulse Width divides GVM.

