Periodically poled lithium niobate (PPLN) predominantly has a random duty-cycle error (RDE), latent in them by virtue of poling mechanism. This error needs to be quantitatively predicted to abstain from parasitic harmonic generation. In this paper, we have calculated the influence of the RDEs degenerate noise in second-harmonic generation (SHG) consisting of PPLN. Here, we propose a method for calculating the random domain-wall distribution statistics by the SHG. We explored the equivalence between the statistics of random domain distribution by SHG and far-field diffraction pattern method.
Harnack inequality and gradient estimate for G-SDEs with degenerate noise