General framework for the analysis of imperfections in nonlinear systems

In this Letter, we derive a framework to understand the effect of imperfections on the phase-matching spectrum of a wide class of nonlinear systems. We show that this framework is applicable to many physical systems, such as waveguides or fibers. Furthermore, this treatment reveals that the product of the system length and magnitude of the imperfections completely determines the phase-matching properties of these systems, thus offering a general rule for system design. Additionally, our framework provides a simple method to compare the performance of a wide range of nonlinear systems.