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):
hPL^{2}(d_{eff}sin(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

PhaseMatching Type and Angle,
d_{eff}

Power or Energy, Repetition Rate

Damage Threshold

Divergence

Acceptance Angle

Bandwidth

Spectral Acceptance

Beam Size

Crystal Size, WalkOff 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 phasematching direction. For example, the acceptance
angle of BBO for type I frequency doubling of Nd:YAG at 1064 nm is
about 1 mradcm. Therefore, if a Nd:YAG laser has beam divergence of 3
mrad for frequencydoubling, over half of the input power is useless.
In this case, LBO may be better because of its larger acceptance
angle, about 8 mradcm. For NCPM, the acceptance angle is normally
much bigger than that for CPM, for example, 52
mradcm^{1/2} 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
WalkOff
Due to the birefringence of NLO crystals, the
extraordinary wave (n_{e}) will experience Poynting vector
walkoff. 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.


WalkOff 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/V_{G})
of BBO are respectively 1/V_{G}
= 56.09 ps/cm at 800 nm and 1/V_{G}
= 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.
