Direct-substitution method for studying second harmonic generation in arbitrary optical superlattices

In this paper, we present the direct-substitution (DS) method to study the second-harmonic generation (SHG) in arbitrary one-dimensional optical superlattices (OS). Applying this method to Fibonacci and generalized Fibonacci systems, we obtain the relative intensity of SHG and compare them with previous works. We confirmed the validity of the proposed DS method by comparing our results of SHG in quasiperiodic Fibonacci OS with previous works using analytical Fourier transform method. Furthermore, the three-dimension SHG spectra obtained by DS method present the properties of SHG in Fibonacci OS more distinctly. What’s more important, the DS method demands very few limits and can be used to compute directly and conveniently the intensity of SHG in arbitrary OS where the quasi-phase-matching (QPM) can be achieved. It shows that the DS method is powerful for the calculation of electric field and intensity of SHG and can help experimentalists conveniently to estimate the distributions of SHG in any designed polarized systems.