The nonlinear carrier wave dispersion relation at weak nonlinearity is derived for the linearly polarized (LP) modes of a step-index optical fibre that has both a nonlinear core and a nonlinear cladding. The calculation begins with the exact equations for the nonlinear fibre and the nonlinear shift (coefficient), from its linear value, of the propagation wave-number is given in closed analytical form. The nonlinear coefficient is completely general and accounts both for the nonlinearity and the structure of the guided mode. Some numerical results for the LP01 mode are presented which show that significant deviations occur from the conventionally accepted (averaged) nonlinear coefficient.
Journal of Modern Optics
Sprott School of Business

Boardman, A.D. (A. D.), Popov, T. (T.), Shivarova, A. (A.), Tanev, S, & Zyapkov, D. (D.). (1992). Nonlinear dispersion coefficients of a cylindrical optical waveguide. Journal of Modern Optics, 39(5), 1083–1096. doi:10.1080/09500349214551091