Features of dispersion properties of a waveguide with a modified Kerr weak nonlocal nonlinearity coated with a metal thin film.

New features of light propagation in nonmagnetic lossless medium with weak nonlocal nonlinear response are described. The function of nonlinear response in a weak nonlocal approximation included in the dielectric permittivity is proposed. Stationary self-consistent wave equation in the term of the average of the field intensity is formulated. The procedure allowing to find the spectrum of stationary states of such an equation in relation to the metal-film covered waveguide is indicated. Dispersion equation determining the propagation constant as a function of the waveguide system parameters in general form of the waveguide region is obtained. The proposed theory is applied to calculate the eigenmode spectrum of metal-film covered circular fiber. Exact solution to the self-consistent wave equation describing the radial symmetric distribution of the electric field in a fiber cross section is found. Explicit equation determining the discrete spectrum of the propagation constant is obtained. It is shown that each mode corresponds to a set of the propagation constant values, which are generated by the zeros of the Bessel functions. Discrete spectrum of the propagation constant is linearly shifted by a value proportional to the coefficient of nonlinearity. Varying the value of the nonlinearity coefficient is effectively used to adjust the fiber diameter, which optimizes the characteristics of the waveguide. [ABSTRACT FROM AUTHOR]