Differential-Frequency Generation (DFG):
ω1 - ω2 = ω3 (or 1/λ1 - 1/λ2 = 1/λ3 in wavelength) It mixes one high energy photon and one low energy photon into another low energy photon. For example:
532 nm - 810 nm -> 1550 nm
Differential Frequency Generation
Optical Parametric Generation (OPG):
ωp = ωs + ωi (or 1/λp = 1/λs + 1/λi in wavelength) It splits one high-energy photon into two low-energy photons.
355 nm -> 532 nm + 1064 nm
Optical Parametric Generation (OPG) is an inverse process of Sum Frequency Generation. It splits one high-frequency photon (pumping wavelength, lp) into two low-frequency photons (signal, ls, and idler wavelength, li). If two mirrors are added to form a cavity as shown in following Figure, an Optical Parametric Oscillator (OPO) is established. For a fixed pump wavelength, tilting a crystal can generate an infinite number of signal and idler wavelengths. Therefore, OPO is an excellent source for generating wide tunable range coherent radiation. BBO, KTP, LBO and LiNbO3 are good crystals for OPO and Optical Parametric Amplifier (OPA) applications.
In order to obtain high conversion efficiency, the phase vectors of input beams and generated beams have to be matched:
Δk = k3 - k2 - k1 = 2π3/λ3 - 2πn2/λ2 - 2πn1/λ1 = 0 (for sum frequency generation)
Where: k is phase mismatching, ki is phase vector at λi and ni is refractive index at λi.
Conversion Efficiency Vs Δk
The phase-matching can be obtained by angle tilting, temperature tuning or other methods. The angle tilting is mostly used to obtain phasematching as shown in the left figure. If the angle between optical axis and beam ropagation (θ) isn't equal to 90o or 0o, we call it critical phase-matching (CPM).Otherwise, 90o non-critical phasematching (NCPM) is for θ = 90o and 0o NCPM is for θ = 0o.
Type I Phase Matching
Type II Phase Matching
Parameters For NLO Crystal Selection
|NLO Process||Phase-Matching Type and Angle, deff|
|Power or Energy, Repetition Rate||Damage Threshold|
|Bandwidth Spectral||Spectral Acceptance|
|Beam Size||Crystal Size, Walk-Off Angle|
|Pulse Width||Group Velocity Mismatching|
If a laser light propagates in the direction with angle △θto phase matching direction, the conversion efficiency will reduce dramatically (see the right Figure). We define the acceptance angle (△θ) as full angle at half maximum (FAHM), where θ = 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.
In addition, you have to consider the spectral acceptance (△λ) of crystal and the spectral bandwidth of your laser; crystal temperature acceptance (△T) and the temperature change of environment
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 (ρ) 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.
Group Velocity Mismatching