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Nonlinear waveguides
Author(s) -
Sjöberg Daniel
Publication year - 2003
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/2001rs002579
Subject(s) - nonlinear system , partial differential equation , mathematical analysis , physics , waveguide , hyperbolic partial differential equation , coupling (piping) , electromagnetic field , mode (computer interface) , wave propagation , differential equation , mathematics , optics , computer science , quantum mechanics , materials science , metallurgy , operating system
We investigate the propagation of electromagnetic waves in a cylindrical waveguide with an arbitrary cross section filled with a nonlinear material. The electromagnetic field is expanded in the usual eigenmodes of the waveguide, and the coupling between the modes is quantified. We derive the wave equations governing each mode with special emphasis on the situation with a dominant TE mode. The result is a strictly hyperbolic system of nonlinear partial differential equations for the dominating mode, whereas the minor modes satisfy hyperbolic systems of linear, nonstationary, and partial differential equations. A growth estimate is given for the minor modes.