Page 362 - Tunable Lasers Handbook

322 Norman P. Barnes

and the size and optical quality has improved. With continued improvements,
optical parametric oscillators and amplifiers should find increasing use.
Selection of the best nonlinear crystal for a particular application depends
on several basic crystal parameters including the transparency. In approximate
order of consideration, the nonlinear crystal parameters that must be considered
in the selection process include range of transparency, phase matching, nonlin-
earity, birefringence, and temperature sensitivity. The rationale for nonlinear
crystal selection using these parameters is presented in some detail in the follow-
ing paragraphs. Germane parameters, where available, are listed for select non-
linear crystals in Table 1.
Transparency is an obvious requirement for the nonlinear crystal. However,
it has been shown that a nonlinear interaction can occur even if one of the inter-
acting waves is strongly absorbed [26]. Beyond the obvious, it is preferable to
avoid the absorption edges of the crystal from an average power point of view. In
addition, in cases where the crystal has limited birefringence, phase matching
cannot be effected near either the ultraviolet or the infrared absorption edges
since the absorption edges exhibit increased dispersion.
For efficient interactions. phase matching must be effected. Phase matching
allows the entire length of the nonlinear crystal to contribute positively to the
conversion efficiency. Nonlinear interactions can occur in situations where the
phase-matching conditions can only be approximated by using plates cut to the
coherence length. However. these situations require approximate phase matching
in order to have reasonable lengths for the nonlinear crystal [27]. If approximate
phase matching cannot be met. the coherence length and thus the nonlinear cry-
tal length become short. In the low-conversion-efficiency regime, the conversion
efficiency of a parametric interaction increases as the square of the length of the
nonlinear crystal. Thus, phase matching must be possible in order to obtain long
coherence lengths. and the concomitant long nonlinear crystal lengths, and
therefore reasonable efficiencies.
Efficiency of the optical parametric oscillator or amplifier also depends criti-
cally on the effective nonlinearity. Again in the low-conversion-efficiency
regime, the conversion efficiency depends on the effective nonlinearity squared.
Because the effective nonlinearity depends on the orientation of the nonlinear
crystal, the effective nonlinearity is dependent on the phase-matching conditions
and the interacting wavelengths. Inspection of the gain coefficient shows that the
effective nonlinearity is divided by the refractive indices. Consequently, a com-
monly used figure of merit for nonlinear crystal selection is de'/n,~~2n3. Often this
figure of merit is plotted as a constant over the range of transparency of the non-
linear crystal. That is, the variation of the effective nonlinearity with wavelength
is neglected. Because conversion efficiency is directly proportional to the figure
of merit in the low-conversion approximation. a high figure of merit is desirable.
Effective nonlinear coefficients depend on the direction of propagation,
polarization of the interacting wavelengths, and the point group. Given this