Second harmonic generation in periodically poled crystals in the fixed-intensity approximation

The SHG efficiency is calculated in periodically poled crystals in the fixed-intensity approximation. It is shown that, as in homogeneous crystals, the solution obtained in this approximation coincides, with an accuracy of the factor (l/L)⁶, with the exact solution for a nonlinear regime even when the quasi-phase-matching condition is exactly fulfilled. The relative accuracy of this approximation increases with increasing mismatch (l is the crystal length and L is the nonlinear length). The fixed-intensity approximation can be used for such crystals up to l ≈ L even in the case of exact quasi-phase matching, while the fixed-field approximation is valid only for l < 0.3 L.