Page 369 - Tunable Lasers Handbook

7 Optical Parametric Oscillators 329

In this expression, C represents the ultraviolet resonance wavelength squared
and E represents the infrared resonance wavelength squared. In the same con-
text. B and D represent the strengths of the ultraviolet and infrared absorption
resonances, respectively.
If the ultraviolet or infrared resonances are not approached too closely, this
form can represent the refractive index quite accurately. As the resonances are
approached, effects such as the finite width of the resonance and the possibility
of multiple resonances can detract from the accuracy. Typically, by adding a sec-
ond ultraviolet resonance, the fit may be improved; especially as the ultraviolet
resonance is approached. For example. the refractive index of AI,O, has been
accurately expressed using two ultraviolet resonances and an unit; value for A
[33]. However. away from the resonance, a nonunity value for A can be used to
satisfactorily describe the refractive index without the added complexity of a
double ultraviolet resonance.
Although the Sellmeier equation [given in Eq. [59)] has many desirable fea-
tures. it is not universally utilized. However, to compute the refractive indices as
well as the first and second derivatives of the refractive index with respect to
wavelength. it is convenient to have a standard form for the expression relating
the refractive index with the wavelength. Toward this end. original measure-
ments of the refractive index as a function of wavelength were found and fitted
to the standard form L34-441. Results of the curve-fitting procedure are found in
Table 5 for visible and mid-infrared crystals. In addition, the root mean square
deviation between the calculated experimental values appears in Table 5. Typi-
cally, the experimental values are presented with four significant figures beyond
the decimal point. Except for LBO, the root mean square deviation is in the
fourth place after the decimal point. In cases where five significant figures were
quoted in the cited literature (specifically ADP. KDP, and BBO). the fit is much
better. The accuracy of this approach in describing the phase-matching angle has
been demonstrated [17].
It is useful to have the temperature dependence of the refractive index built
into the Sellmeier equation. With this feature, temperature tuning of the nonlin-
ear Interaction can be computed in a straightforward manner. In one case, this is
possible since the refi-active indices were measured accurately at two tempera-
tures [36]. It is very convenient to have this information for LiNbO, because this
nonlinear crystal is often operated at elevated temperatures when short ware-
lengths are among the interacting wavelengths. Operation of this nonlinear crys-
tal at elevated temperatures helps control the optically induced refractive index
inhomogeneities associated with the short wavelengths. If the material can be
grown with close attention to the impurities, the optically induced refractive
index inhomogeneities are annealed at about 105°C. Consequently, when a short-
wavelength pump is used with this material, such as a 0.532ym frequency-
doubled Nd:YAG laser, the refractive indices associated with an elevated temper-
ature should be used. Appropriate Sellnieier coefficients can be determined from
the following relations.