Investigation of the dependence of the field energy in a low conductive fiber optic with a gradient profile of the refractive index

A circular, cross-sectionally low conductive fiber optic with a power-law profile of the refractive index is considered. A general solution for the field inside the fiber is obtained for the single-mode operation. In the first approximation, the analytical expression for the field and energy inside the fiber for any power-law profile is obtained. The dependences of energy on the waveguide parameter for the second-and third-degree profiles of the refractive index expression are plotted. It is shown that in this approximation, the energy grows as the waveguide parameter increases up to a particular value of the parameter, after which the growth for the second and third powers changes places.