Slowly varying amplitude approximation appraised by transfer-matrix approach

The slowly varying amplitude approximation that is widely adopted in nonlinear optics is appraised by the transfer-matrix method. Rigorous solution for second harmonic generation in nonlinear optical superlattices shows that this approximation is invalid when the reflection of the second harmonic (SH) wave from the crystal interface cannot be neglected. When the modulation period of the superlattice is comparable to the wavelength of the SH wave, the approximation is far from accurate even if no reflection from the crystal interface occurs. The transfer-matrix method may provide a novel approach to investigate various nonlinear optical processes in superlattices in a precise way.