Page 357 - Tunable Lasers Handbook

7 Optical Parametric OsciIIators 3 17

can be effected. it is often referred to as noncritical phase matching. If noncriti-
cal phase matching is achieved. the birefringence angles become zero leading to
an infinite effective length for the nonlinear crystal. In addition, the acceptance
angle for the nonlinear interaction becomes much larger since the first-order term
in the expansion of the phase mismatch vanishes. Since the ordinary and extraor-
dinary indices of refraction have different dependencies on the temperature, non-
critical phase matching may be possible by varying the temperature. However, if
this is not possible, it is advantageous to select a nonlinear crystal that minimizes
the deleterious effects of birefringence. Minimization can be accomplished by
minimizing the difference in the ordinary and extraordinary index of refraction,
that is, the birefringence. without compromising phase matching. Thus, it is of
interest to determine how much birefringence is required.
A4n estimate of the required birefringence is dependent on the dispersion of
the nonlinear crystal. Dispersion of the nonlinear crystal is characterized by the
first derivative of the index of refraction with respect to the wavelength4nldh.
If the interacting wavelengths are far from the absorption edges of the nonlinear
crystal, the dispersion can be approximated as being nearly independent of wave-
length. As a natural extension of this, birefringence also tends to be independent
of wavelength. Within these constraints, the required birefringence An can be
estimated for the various types of interactions. For Type I interactions. the
required birefringence can be approximated as

For Type I1 interactions, a similar expression exists with the signal or idler wave-
length replacing the pump wavelength. depending on which of these wave-
lengths has a different polarization compared to the pump wavelength. Birefrin-
gence in excess of this tends to limit the acceptance angle. In addition, more
birefringence than required for phase matching exacerbates birefringence angle
effects and thus the interaction length.

6. AVERAGE POWER LIMITATIONS
Thermally induced changes in the phase matching will limit the average
power available from a nonlinear interaction. For all practical nonlinear crystals.
significant absorption of the interacting wavelengths occurs even if the interact-
ing waves are nominally in a transmitting region of the crystal. Absorption of the
interacting wavelengths deposits heat throughout the volume of the nonlinear
crystal. However, to dissipate the deposited heat, it must be conducted to the sur-
face of the nonlinear crystal. Volumetric heating and surface cooling establish
thermal gradients in the nonlinear crystal. Because the ordinary and extraordi-
nary indices of refraction. in general, behave differently with temperature, the
phase-matching condition cannot be maintained throughout the volume of the