Page 209 - High Power Laser Handbook

178 So l i d - S t at e La s e r s Intr oduction to High-Power Solid-State Lasers 179

Primary mirror
λL
Secondary
mirror
Fresnel
core

Figure 7.8 Unstable resonator cavity.

at the edges. This latter configuration is widely used in present-day
unstable resonators to eliminate diffraction from the hard-edged
aperture. For nonspatially varying reflectivities, the outcoupling
2
fraction is approximately 1 – 1/M .
Whereas unstable resonators provide large mode volumes, they
also impose some challenges when used to extract high-power SSL
gain materials. To maintain good wavefront control and single-mode
output, any OPD imposed by the gain material must be small enough
that it is overwhelmed by the mirror curvatures. Otherwise, OPD
from the gain module can effectively form a lens over a small aper-
ture that can drive the resonator over the stability boundary, hence
forming a locally stable resonator. This, in turn, causes “filamenta-
tion” of the unstable resonator mode, in which multiple independent
output beams with uncorrelated wavefronts colase over different
subapertures of the gain medium.
To avoid such an event and to provide some robustness against
thermal OPD, unstable resonators for SSLs are typically designed
with high-curvature mirrors, leading to short resonator lengths and
large magnifications. However, high M leads to large outcoupling
fractions and, thus, to a requirement for correspondingly high laser
gain to make up for the loss on each round trip to maintain laser oscil-
lation. Hence, unstable resonators tend to achieve the most success
with high gain materials, such as Nd, or with geometries that provide
a long gain path for the extracting beam (e.g., zigzag slabs). To further
increase laser gain, the modules are often operated in a pulsed or
quasi-CW format, even when the goal is high average, rather than
peak, power. 22
This is not to say that unstable resonators cannot be made to work
with low gain materials and module architectures such as Yb:YAG
thin disks. Even with a low-gain SSL medium, unstable resonator
extraction has been demonstrated successfully by combining multiple
gain modules, or gain module passes, per resonator round trip, often
with the use of image-relay optics to accommodate long physical