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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∝ PL2*[deff *
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
|
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 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. |
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Walk-Off
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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. |
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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. |
