Analytical Solutions Describing New Features of Guided Wave Modes in a Circular Fiber Consisting of a Constant-Index Core and a Graded-Index Cladding with Saturation

Abstract

New features of the light beam localization in radial direction in an optical medium with a spatial saturation of the refractive index are described analytically. A new model of radial-dependent distribution of the dielectric function, which allows obtaining the exact analytical solutions to the wave equation, is formulated. Two types of waveguide modes characterized by different transverse electric field distributions are found. The first type of modes is characterized by minimum of the electric field at the core center maximum inside the core. These modes correspond to different values of the angular distribution number. The second type of modes is characterized by oscillations of the electric field inside the core. These modes correspond to different numbers of the dispersion equation solution with fixed values of the angular distribution number. The light intensity increases and the beam localization radius increases with the growth of the core radius. An increase of the value of change in the dielectric constant over the cladding leads to a slight increase of the light intensity but the beam localization radius stays almost the same. The propagation constant enlarges monotonically with the growth of the core radius and it decreases very little with the growth of the value of change in the dielectric constant over the cladding. The minimum core radius, starting from which it is possible to excite the waveguide mode, and the critical core radius for which the power flow is minimal, are found. It is derived analytically that the confinement factor monotonically increases with the growth of the core radius.