Conversion Efficiency

How does one select an 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 (deff), crystal length (L), input power density (P) and phase mismatching (Δk): η∝ PL(2)[d(eff) * sin(ΔkL)/ΔkL](2)

In general, higher power density, longer crystal length, larger nonlinear coefficients and smaller phase mismatching will result in higher conversion efficiency. However, there is always some limitation coming from nonlinear crystals and lasers. For example, the deff is determined by the nonlinear crystal itself and the input power density has to be lower than the damage threshold of the crystal. Therefore, it is important to select the right crystal for your applications. The proceeding table lists the laser and crystal parameters for selecting right crystals:

Parameters For NLO Crystal Selection

Crystal Acceptanc

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

Walk-Off

Due to the birefringence of NLO crystals, the extraordinary wave (ne) will experience Poynting vector walk-off as shown in the right hand Figure. If the beam size of the input laser is small, the generated beam and the input beam will be separated at a walk-off angle (ρ) in the crystal and it will cause low conversion efficiency. Therefore, for a focused beam or intracavity doubling, the walk-off 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 the fs pulse broadening induced by group velocity mismatching (GVM) or group velocity dispersion of an NLO crystal. In order to keep the efficiency frequency conversion without significant pulse broadening, it is suggested that the thickness (LGVM) of the crystals is less than the Pulse Width divided by the GVM.