Page 354 - Tunable Lasers Handbook

31 4 Norman P. Barnes

Expansion is usually limited to first order because the variation of the refractive
index with temperature is usually known only to first order. Expanding the first-
order term yields

(44)

For ordinary waves in uniaxial crystals. values for the variation of the refractive
index with temperature can be used directly. For extraordinary waves, in general,
the variation of the refractive index with temperature depends on the variation of
the refractive index with temperature of both the ordinary and extraordinary
waves. In uniaxial crystals this becomes

Substituting these expressions into the allowable phase mismatch yields the
allowable temperature variation. Allowable temperature variation also enters into
the calculation of the average power limit for a nonlinear interaction as well as
the temperature tuning rate.

5. BIREFRINGENCE EFFECTS
Even though birefringence is necessary to produce an efficient interaction
by compensating for dispersion. birefringence will eventually limit the efficiency
of the interaction. Efficiency limitations can arise since the direction of energy
propagation of ordinary beams and extraordinary beams is not. in general,
collinear in a birefringent crystal. Even when both the ordinary and extraordi-
nary beams are normally incident on the birefringent crystal. a difference in the
direction of the energy propagation exists. The direction of energy propagation
of a normally incident ordinary beam does not suffer any deviation when enter-
ing the crystal. On the other hand. the direction of energy propagation of a nor-
mally incident extraordinary beam occurs at an angle to the normal, denoted by
p. For non-normal angles of incidence, both the ordinary and extraordinary
beams are deviated by refraction. in accordance with Snell's law. However. in
addition, the extraordinary beam still experiences the effects of the birefrin-
gence. again characterized by the birefringence angle p. To satisfy the phase-
matching condition. at least one of the interacting beams is an ordinary beam
and at least one is an extraordinary beam. Thus, eventually the interacting beams
separate, causing a decrease in the efficiency of the nonlinear interaction.