Coupled electromagnetic transverse-electric–transverse magnetic wave propagation in a cylindrical waveguide with Kerr nonlinearity

Abstract

Nonlinear coupled electromagnetic TE-TM wave propagation in a cylindrical nonlinear dielectric waveguide with circular cross section is considered. Nonlinearity inside the waveguide is described by Kerr law. Physical problem is reduced to a nonlinear two-parameter eigenvalue problem for a system of (nonlinear) ordinary differential equations. It is proved that TE and TM waves that form (nonlinear) coupled TE-TM wave can propagate at different frequencies ωE and ωM, respectively. It is shown that nonlinear coupled TE-TM wave propagates at different frequencies ωE, ωM and with different propagation constants γE, γM in the waveguide. Frequencies ωE, ωM can be chosen independently. Existence of coupled surface TE-TM waves is proved. Intervals of localization of coupled eigenvalues (γE, γM) are found.

Nonlinear multi-frequency electromagnetic wave propagation phenomena

“…Particular cases for n=2 have been found recently: (coupled) TE-TM and TE-TE GWs in a layer with Kerr nonlinearity have been introduced and studied in [58] and [59], respectively; (coupled) TE-TM GWs in a cylindrical waveguide with Kerr nonlinearity are introduced and studied in [60,61]. The case of coupled TE-TM GWs in a layer with Kerr nonlinearity propagating at one frequency, however, was introduced theoretically long ago in [54,55].…”

“…Unfortunately, the theory of polarised GWs in waveguides with a circular cross-section is not developed as thoroughly as for the plane waveguides. Even the simplest cases of monochromatic wave propagation in such cylinders filled with Kerr media are studied only on the basis of perturbation methods [18,20,22,23,69]; the cases of coupled non-linear wave propagation are more complicated [60,61,70]. However, numerically novel guided regimes were predicted in [22,23].…”

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

“…This problem will be treated in a separate paper. For different types of phenomena of coupled wave propagation see [20][21][22].…”

“…Expressing 2 through 1 and substituting it into (37) one obtains an oper-atorÑ and a vectorh instead of N and h, respectively, wherẽ N andh are bounded. An example of how this can be done is seen, for example, in [21].…”