Calculation of the propagation constants of inhomogeneous nonlinear double-layer circular cylindrical waveguide by means of the Cauchy problem method

Propagation of TE waves in a double-layer nonlinear inhomogeneous cylindrical waveguide

“…Here k 2 2 (ρ) = k 2 0 ε 2 (ρ)−γ 2 , the initial conditions are as follows: (9) where the values u(R 1 + 0) and u ′ (R 1 + 0) are determined from (7) and have the following form u(R 1 + 0) = C 1 I 1 (k 1 R 1 ),…”

“…Solution for the case of an inhomogeneous circular waveguide with the Kerr nonlinearity was obtained in the papers [9,10]. The method proposed in this paper can be applied to study different types of nonlinearities and heterogeneities.…”

Guided Electromagnetic Waves Propagating in a Two-Layer Cylindrical Dielectric Waveguide with Inhomogeneous Nonlinear Permittivity

“…Since the Kerr law is characterised by a small constant factor in front of the nonlinear term (coefficient of the nonlinearity), then this approach is justified. Numerical results are based on a numerical method that does not depend on the smallness of the parameter [7]. As is known the Kerr law is described by an unbounded function; in order to demonstrate difference between unbounded and bounded nonlinear permittivities we presented numerical results for both cases; we also gave a comparison between linear and nonlinear cases.…”

“…Currently there has been significant progress in studying of polarised electromagnetic TE and TM wave propagation in waveguide structures (for a planar waveguide, see [8][9][10][11]; for a circular cylindrical waveguide, see [1,8,[12][13][14][15]; for a circular two-layered cylindrical waveguide, see [7,16]) filled with nonlinear dielectric permittivities. In particular, theorems on existence and localization of eigenvalues in some of these problems have been proved.…”

“…Most of these papers are devoted to studying of polarized waves in waveguides filled with a homogeneous nonlinear medium. From aforementioned studies only [7,13,15,16] focus on inhomogeneous nonlinear permittivity.…”