Noncritical Phase-Matching

If the refractive indices can be adjusted so that Θ_m = 90^◦, by variation of a parameter such as the temperature or chemical composition of the crystal, the dependence of Δk on beam divergence or angular misalignment δθ is due to a much smaller quadratic term, instead of a linear relationship as is the case in critical phase-matching.
For example, second-harmonic generation in LiNbO₃ occurs at 90◦ for 1.064 μm radiation provided the crystal is at a temperature of ≈ 107^◦ C (for a crystal doped with 5% MgO). The allowable departure from the phase-matched direction is greater than 26mrad if the coherence length is to be 1 cm. For these reasons, 90^◦ phase-matching is often called noncritical phase-matching. Provided that n^o₁ and n^e₂ are nearly equal and d(n^o₁− n^e₂)/dT ≠ 0, noncritical phase-matching can be achieved by temperature tuning the crystal.
In addition, at Θ_m = 90^◦ there are no walk-off effects due to double refraction.

TABLE 1. Properties of important nonlinear materials (data are for 1064 to 532 nm conversion).