Equations for second-harmonic generation under quasi-phase-matched interaction conditions in nonlinear crystals with a regular domain structure

Equations describing second-harmonic generation under quasi-phase-matched interaction conditions in crystals with a regular domain structure are derived. It is shown that appropriate substitution of variables makes these equations exactly identical with those describing second-harmonic generation in the usual homogeneous crystals. This analogy is used to obtained an expression for the second-harmonic amplitude in the case of inexact quasi-phase-matched interaction.