Effect of Optical Inhomogeneities on Phase Matching in Nonlinear Crystals

Abstract

Experimentally, we have observed variations in the phase‐matching temperature (T_pm) for second harmonic generation (SHG) along the pull axis of lithium niobate (LiNbO₃) crystals. We have related these to variations in the extraordinary index of refraction caused by changes in crystal stoichiometry occurring in the growth process. We have established a technique, for filtering pathological crystals, based upon a point‐by‐point mapping of the birefringence variations along the direction of interest. This provides information about the details of the large and small‐scale spatial variations. Empirically we can get toleration limits on the birefringence variations for application to parametric oscillator design. We have studied several physical models (single step, multiple step, and linear ramp) for the manner in which monotonic changes in index, appropriate for LiNbO₃, are introduced as a function of position. We have found that the usual quality criterion based upon the width of the central peak in an SHG scan versus temperature is misleading because this width is rather sensitive to the manner in which a given total variation in birefringence is introduced. A criterion based upon the ratio of the first sideband peak to the height of the center maximum is found to be only somewhat model dependent, but this test becomes less meaningful when the distortion causes asymmetry in the SHG scan. Asymmetries which are typical in SHG scans can be accounted for by our step model. The most significant result of the theory is a quality test which is independent of the models which we have considered and which is based upon an effective width defined to be the area under the SHG scan divided by the height of the central peak. We have further demonstrated that this area criterion is quite generally model independent and will be useful in gauging index distortion of any nature in any nonlinear material. This technique would allow one to estimate the nonlinear susceptibility in any phase‐matchable ferroelectric crystal with multidomains. Such an evaluation of a scan of SHG power versus momentum mismatch can provide the only certain way to establish that a phase‐matchable ferroelectric crystal which can be multidomained is indeed single domain throughout its volume. We have examined theoretically, periodic and rapidly varying index distortions in barium sodium niobate, Ba₂NaNb₅O₁₅. We have considered a sinusoidal variation (first analyzed by Smith) and present birefringence mapping data which supports this representation of the growth striae and shows that this distortion may not significantly degrade SHG. In addition we have studied a step‐function periodic distortion which might apply to propagation in a uniformly twinned crystal. The effects of periodic distortion are quite different from the monotonic and slowly varying distortion in LiNbO₃, and the commonly employed evaluation criteria become useless. Finally we have considered two means by which one could either eliminate or get around the stoichiometric variations in LiNbO₃. The first involves crystal growth at the maximum melting composition in the phase equilibrium diagram while the second concerns the choice of a suitable geometry in an ordinarily grown c axis boule.