Page 211 - High Power Laser Handbook

180 So l i d - S t at e La s e r s Intr oduction to h igh-Power Solid-State Lasers 181

7.5 Wavefront Correction

Even with advantageous pumping, cooling, and beam extraction
geometries, the magnitude of typical thermal excursions of the gain
material during operation makes it very difficult to generate near-
diffraction-limited beam quality directly from a large-aperture, HAP
SSL device. Even if thermal gradients were reduced to a small frac-
tion of the overall thermal change in optical path length, this would
typically still be enough wavefront distortion to substantially degrade
the beam quality. As a rule of thumb, a laser application whose effi-
cacy is driven by the peak focused intensity can typically tolerate
root-mean-square (RMS). OPD on the order of ∆φ = 1/10 wave. Using
25
the Marechal approximation, this OPD reduces the far-field peak
2
intensity (or Strehl ratio) by ~1 – exp[–(2π∆φ) ] = 33 percent compared
with a planar wavefront beam.
In principle, OPD can be entirely eliminated by a combination of
uniform pumping, purely one-dimensional heat removal, and an
extraction path through the gain medium that has a vector component
along the primary thermal gradient. Yet, in practice, it is nearly impos-
sible to completely eliminate OPD. Edge effects that break the sym-
metry of one-dimensional heat removal will impose some OPD. Any
nonuniformity in pumping or cooling along dimensions transverse to
beam propagation will not be averaged out. Given that typical multi-
kilowatt gain modules exhibit multiple tens of waves’ increase in opti-
cal path due to temperature rises during operation, achieving residual
OPD less than ~λ/10 requires heat generation and removal to be uni-
form to within less than ~1% across the clear aperture. Due to uncon-
trolled variations in pump-diode emission, nonuniform aging, optical
surface tolerances, surface wetting, and thermal contact, these toler-
ances are difficult, if not impossible, to achieve.
In the worst case, the difficulty of obtaining near-planar wave-
fronts increases linearly with the number of gain modules or gain
passes in the beam path when assuming highly correlated aberra-
tions (e.g., with multiple passes through the same gain module vol-
ume). In the best case, with uncorrelated aberrations, the difficulty
increases as the square root of the number of gain module passes.
Many high-BQ and high-power CW SSLs incorporate some addi-
tional means of wavefront correction in their system design to accom-
modate higher values of OPD arising from uncontrolled components
or alignment processes.

7.5.1 Spatial Phase Plates
The simplest means for correcting residual wavefront aberration is
simply to insert a spatial phase plate (SPP) optic that imposes the
conjugate wavefront profile, so that downstream of this optic, the net
laser wavefront is near-planar. In the simplest case, the SPP is simply