Study of Dependence of the Energy of the Field in Weakly Conductive Fiberlight-Guide with Gradient Refractive Index Profile Without Regard to Polarization

Abstract

A round-in-cross-section weakly guiding fiber optic light guide is considered. The system of Maxwellian equations for electrically conductive transparent media without due regard to polarization with an index of refraction in the case under consideration is reduced to the homogeneous Helmholtz equation, a particular solution of which is found using the Green's function. For a unimodalmode a common decision was obtained for the field and energy inside the fiber in the general case of a gradient refractive index profile depending on the radial coordinate. The concept of normalized energy is introduced as the ratio of the energy inside a fiber with gradient refractive index profile to the energy inside a fiber with a step-index profile. Since in a single-mode regime the zero-order Bessel function, which describes the field inside a step-index profile fiber, can be replaced by a Gaussoid, then, when extending this replacement to the case of a single-mode gradient fiber, as a first approximation we shall obtain a finite expression for the normalized energy for a general gradient profile. The dependences of the normalized energy on the waveguide number were obtained for each of the degrees from the first to the fourth inclusive. It is shown that in the considered approximation, the energy increases up to a certain parameter values (for the first degree – a triangle profile) or slowly decreases (other profiles), after this value the energy increases for all profiles. The results obtained will help to select a suitable single-mode fiber for practical application.