Vector Theory of Optical Nonlinearities in Birefringent Fibers

Understanding the effects of optical nonlinearities on wave propagation is crucial for applications such as fiber optic communication, optical signal processing, frequency generation, signal amplification, optical sensing, and quantum optics. While optical nonlinearities such as self-phase modulation, cross-phase modulation, four-wave mixing, Brillouin scattering, and Raman scattering are extensively studied in optical fibers, a comprehensive model considering all of these nonlinearities in the most general case of a birefringent fiber has not been reported. In this paper, we present a vectorial model that considers the effects of these nonlinearities on co-propagating and counter-propagating fields for the most general case of birefringent fibers, i.e., elliptically birefringent fibers. Additionally, unlike previous studies, we represent the vector interaction using the frequency-dependent polarization eigenmodes of the fiber. We then use this model and show how elliptically birefringent fibers enable frequency-dependent control over the nonlinear interaction between counter-propagating fields.