The dispersion relations of two nonlinearly interacting LP01 modes are derived from a perturbation procedure. A step-index optical waveguide is considered here, but it should be emphasized that other index profiles can be introduced without any increase in conceptual difficulty. The cross-phase modulation couples waves with the same polarization and different frequencies. The nonlinear contributions to the linear wave numbers arising from the effects of both self-phase and cross-phase modulation are obtained. The method used for deriving the nonlinear dispersion coefficients is novel because it uses nonlinear changes in the wave-field distribution in the transverse direction. As a consequence, the results differ from those obtained by the usual method of determining the nonlinear wave number shift. A set of coupled nonlinear Schrodinger equations is considered and a new nonlinear effective area involved in the cross-phase modulation effect is defined.
Journal of Modern Optics
Sprott School of Business

Boardman, A.D. (A. D.), Shivarova, A. (A.), Tanev, S, & Zyapkov, D. (D.). (1995). Nonlinear coefficients and the effective area of cross-phase modulation coupling of LP01 optical fibre modes. Journal of Modern Optics, 42(11), 2361–2371. doi:10.1080/09500349514552061