Weakly Guiding Fibers and LP Modes in Circular and Elliptical Waveguides

"New features of the light localization in a nonlinear and graded-index medium in the case of radial symmetry are described analytically. The model of nonlinear graded-index fiber assumes that the dielectric permittivity changes abruptly when the electric field amplitude reaches a certain level. The dielectric permittivity depends on the polar radius according to a parabolic law, in the regions where the electric field amplitude exceeds a certain level. Explicit exact solution to the wave equation is found, in terms of the Whittaker function and the modified Bessel function of the second kind, describing a new type of optical localized structure. The influence of the propagation constant and parameters of the nonlinear graded-index dielectric permittivity on the field profile over the fiber radius is analyzed. It is derived that the core radius and the dielectric permittivity of the core depend on the propagation constant. The dependence of the core radius on the propagation constant causes the appearance of local dispersion."

Modes of a Nonlinear Fiber Containing a Parabolic Graded-Index Core with Light Induced Variable Radius

SAVOTCHENKO

2023

Features of Self-Confinement of the Linearly Polarized Waves in a Nonlinear Fiber with a Light Induced Core

SAVOTCHENKO

2024

The fundamental modes of nonlinear optical weakly guiding fiber with circular cross section are studied analytically. The dielectric constant of the fiber core is assumed to be differing from the dielectric constant of the fiber cladding. The change between them occurs abruptly when the light intensity reaches a certain level. The core radius formed at a certain intensity level in dependence of the optical characteristics of the waveguide mode and fiber is specified. It is shown that the core radius can be reduced by increasing the frequency of the wave or the magnitude of the jump in the dielectric constant, and also by decreasing the propagation constant. The self-confinement core radius decreases with increasing frequency, but this increases the diameter of the light beam localization in the fiber cross section. Increasing the propagation constant has the opposite effect.

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

S.E.

2024

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.