Page 336 - Tunable Lasers Handbook

296 Norman P. Barnes

are available and the tuning is limited essentially by the range of transparency of
the nonlinear crystal.
Nonlinear optics devices in general and optical parametric oscillators in par-
ticular have received a significant amount of theoretical attention. Nonlinear
interactions between three waves have been investigated by several authors [ 2,3].
In the first, the interaction between planes waves was considered. A treatment that
allowed a variable phase between the interacting plane waves and also a depletion
of the various waves provided a description where complete conversion could be
achieved under ideal conditions. However. in reality, a plane wave is a mathemat-
ical fiction. Consequently, in the second of these treatments, the effects of a finite
beam size were considered under the approximation of negligible depletion of the
pump wave. In actual situations, the effects of both finite beam size and pump
depletion should be taken into account.
A comprehensive review of the progress to date on optical parametric oscil-
lators was given several years after the first introduction of the optical parametric
oscillator [4]. In this review, the effects of Gaussian beam radii on the interaction
were considered as well as the effects of singly resonant and doubly resonant
optical parametric oscillator resonators. In addition, a calculation of the thresh-
old pumping power was included and an estimate of the saturation and power
output was given, A figure of merit to characterize the utility of nonlinear crys-
tals was also introduced.
A later investigation of optical parametric oscillators focused on both the
threshold and the linewidth of the device. Dependence of the threshold on the res-
onator length, the nonlinear crystal length, and the pump beam radius was mea-
sured and compared with the model developed to describe the operation of the
device [5.6]. Linewidth was controlled by means of gratings, etalons, and the nat-
ural frequency-selective properties of the optical parametric interaction, including
the aperture effect imposed by the finite pump beam radius. Combining these
effects by using a square root of the sum of the squares technique, good agreement
was obtained between the measured linewidth and the combination of the calcu-
lated linewidths. It has also been shown that calculations of the linewidths require
an expansion of the phase mismatch retaining terms through second order [7].
Another treatment investigated the average power limit imposed on the opti-
cal parametric oscillator imposed by crystal heating that was caused by absorp-
tion of the interacting waves. Because absorption occurs throughout the volume
of the nonlinear crystal while cooling occurs at the surface, thermal gradients
within the nonlinear crystal are established. Because the refractive index
depends on the temperature, phase matching cannot be maintained over the
entire interaction volume. As the average power increases, the thermal gradients
also increase, thereby limiting the volume over which the nonlinear interaction is
effective. As the volume of the interaction decreases, the efficiency of the inter-
action also decreases. Average power limits have been estimated for the optical
parametric interaction for both Gaussian and circular beam profiles [SI.