Page 70 - Tunable Lasers Handbook

3 Tunable Excimer Lasers 51

the medium or very little energy will remain to be extracted with good beam
divergence. Because the higher the magnification of the unstable resonator the
faster the convergence toward a diffraction-limited mode, high-gain, short-pulse
systems favor high-magnification unstable optics.
The second criterion deals with the suppression of threshold lasing by keep-
ing the system small-signal gain below a critical value so that the diffraction-
limited mode can develop first. Again, the higher the magnification, the harder it
is for threshold lasing to commence and the higher the permissible system gain.
In lasers where super fluorescence can develop in one pass or in systems where
the magnification is small and threshold lasing develops rapidly, it will be virtu-
ally impossible to generate diffraction-limited beams.
For a confocal positive-branch unstable resonator as shown in Fig. 15, the
time t necessary for the diffraction-limited mode to develop in a resonator sys-
tem of magnification M is given by

(9)

and the critical gain gcr, which the laser system must stay under to avoid thresh-
old lasing, is given by

where M, is a diffraction limit magnification parameter given by

M, = 2D/1.22hR2 . (1 I>

In Eqs. (9), (lo), and (ll), D is the large dimension of the discharge area, h is
the wavelength of the laser transition, L is the cavity separation, La is the gain
length, and A is the gain length product (usually between 20 to 30 for excimer
laser systems) for which superradiance becomes observable. The unstable res-
onator equations are

R, +R, =2L (12)

and

where R, and R, are the radii of curvature of the two mirrors with R, the less
curved of the two mirrors and R, having a negative value as indicated in Fig. 15.