# General framework for the analysis of imperfections in nonlinear systems

## TL;DR

This paper presents a general framework to analyze how imperfections affect the phasematching spectrum in nonlinear systems like waveguides and fibers, revealing a key product rule for system design and performance comparison.

## Contribution

It introduces a universal framework linking imperfections to phasematching properties, applicable across various nonlinear physical systems.

## Key findings

- Product of system length and imperfections determines phasematching
- Framework applicable to waveguides and fibers
- Simplifies comparison of nonlinear system performance

## Abstract

In this paper, we derive a framework to understand the effect of imperfections on the phasematching spectrum of a wide class of nonlinear systems. We show that this framework is applicable to many physical systems, such as waveguides or fibres. Furthermore, this treatment reveals that the product of the system length and the magnitude of the imperfections completely determines the phasematching 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.