Principles of Nonlinear Optical Crystals - Conversion Efficiency

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How to select a Nonlinear Optical Crystal(NLO) 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 (Dk):

hPL2(deffsin(DkL)/DkL)

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 deff 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:

 

Parameter For NLO Crystal Selection  
Laser Parameters
Crystal Parameters
NLO Process
 Phase-Matching Type and Angle, deff
Power or Energy, Repetition Rate
 Damage Threshold
Divergence
Acceptance Angle
Bandwidth
Spectral Acceptance
Beam Size
Crystal Size, Walk-Off Angle
Pulse Width
Group Velocity Mismatching
Environment
Temperature Acceptance, Moisture
 

Crystal Acceptance

If a laser light propagates in the direction with angle Dq 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 phase-matching direction. For example, the acceptance angle of BBO for type I frequency doubling of Nd:YAG at 1064 nm is about 1 mrad-cm. Therefore, if a Nd:YAG laser has beam divergence of 3 mrad for frequency-doubling, over half of the input power is useless. In this case, LBO may be better because of its larger acceptance angle, about 8 mrad-cm. For NCPM, the acceptance angle is normally much bigger than that for CPM, for example, 52 mrad-cm1/2 for Type I NCPM LBO.

Acceptance Angle (FAHM)

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

Walk-Off

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

Walk-Off Angle (r)

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. For frequency doubling a Ti:Sapphire laser at 800 nm, for example, the inverse group velocities (1/VG) of BBO are respectively 1/VG = 56.09 ps/cm at 800 nm and 1/VG = 58.01 ps/cm at 400 nm and GVM = 1.92 ps/cm. That means an 1 mm long BBO crystal will make 192 fs separation between the pulses at two wavelengths. Therefore, for an 100 fs Ti:Sapphire laser, we normally recommend a 0.5 mm long BBO crystal (with 96 fs separation) in order to obtain high efficiency without dramatic pulse broadening. Red Optornics is able to manufacture as thin as 0.02mm BBO crystals for as short as 5fs laser application.

 

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