Page 326 - Tunable Lasers Handbook

286 Norman P. Barnes

where 9 is the angle of propagation, N is an integer, and ii is the refractive index
of the material between the mirrors [65]. Note that since n occurs in these rela-
tions rather than tio - ne, resonances are much closer together. Because the reso-
nances are closer together and the resolution is related to the wavelength interval
between the resonances. etalons tend to have much better spectral resolution
than birefringent filters.
Spectral resolution of the etalon is a function of the free spectral range
(FSR) and the finesse. FSR is defined as the spectral interval between the trans-
mission maxima. If h, corresponds to N half-wavelengths between the reflective
surfaces and h, corresponds to (N + 1) half-wavelengths, the difference between
the wavelengths is the FSR. It can be easily shown that

A,,, = h (39)
.
2d
Finesse F is related to the reflectivity of the mirror surfaces R by

Single-pass spectral resolution, Ah, is then AhF& To obtain good spectral res-
olution, either the FSR can be made small or the finesse can be made large.
Unfortunately, both of these options involve compromises. If the FSR is made
small. laser operation on two adjacent resonances of the etalon is more likely. To
avoid this, multiple etalons may have to be employed. If the finesse is made
large, the reflectivity of the mirrors must be made close to unity. As the reflectiv-
ity is increased, the power density internal to the etalon increases approximately
as (1 + R)/(l - R). Increased power density increases the probability of laser
induced damage. In general, laser induced damage is usually a concern for
etalons employed in pulsed lasers. In addition, as the reflectivity increases, the
losses associated with the etalon also increase.
Losses in etalons are related to the incident angle used with the etalon. In
practice. etalons are used internal to the laser resonator and are oriented some-
what away from normal incidence. Tuning is achieved by varying the orientation
of the etalon, although temperature tuning is sometimes utilized. When the
etalon is not oriented at normal incidence, the transmitted beam is distorted by
the multiple reflections occurring in the etalon. This beam distortion leads to
losses that increase as the angle of incidence is increased. Consequently, etalons
are usually operated near normal incidence. Typically, angles of incidence range
around a few times the beam divergence. However. as the orientation of the
etalon is varied to tune the laser. care must be taken to avoid normal or near nor-
mal incidence. Additional losses in etalons are associated with losses in the
reflective coatings and with nonparallel reflective surfaces.