Page 349 - Tunable Lasers Handbook

7 Optical Parametric OsciIIators 309

FIGURE 6 Definition of orthogonal acceptance angles for a uniaxial crystal.

index varies as the angle in the optic plane varies but is independent. to first
order. of a variation of the angle orthogonal to the optic plane. In the optic plane,
the derivative of the refractive index with angle is

Having evaluated the derivative of the refractive index with angle, the variation
of the wave vector for extraordinary waves is

(33)

FOP ordinary waves, this derivative is, of course, zero. In most cases, the first-
order derivative will dominate. As such, the acceptance angle will be determined
using the first-order approximation. However. orthogonal to the optic plane, the
first-order teim vanishes. Here, the acceptance angle is determined by the second-
order term. Usually, the first-order term will restrict the acceptance angle an order
of magnitude more than the second-order term. First-order acceptance angles are
often an the order of a few milliradians, comparable to the beam divergence of
the laser in many cases. Because the second-order term is so much less restric-
tive, the acceptance angle orthogonal to the optic plane is often ignored. In biax-
ial crystals, fhe acceptance angles in orthogonal directions assume much more
importance. In these cqvstals, the refractive index will, in general. depend criti-
cally on variations in the direction of propagation in both directions.
Measured acceptance angles agree well with the acceptance angles pre-
dicted using Ihe preceding analysis. Although many examples are available, only