Large amplitude nematicon propagation in a liquid crystal with local response Large amplitude nematicon propagation in a liquid crystal with local response Abstract AbstractThe evolution of polarized light in a nematic liquid crystal whose directors have a local response to reorienta-tion by the light is analyzed for arbitrary input light power. Approximate equations describing this evolution are derived based on a suitable trial function in a Lagrangian formulation of the basic equations governing the electric fields involved. It is shown that the nonlinearity of the material response is responsible for the forma-tion of solitons, so-called nematicons, by saturating the nonlinearity of the governing nonlinear Schrödinger equation. Therefore in the local material response limit, solitons are formed due to the nonlinear saturation behavior. It is finally shown that the solutions of the derived approximate equations for nematicon evolution are in excellent agreement with numerical solutions of the full nematicon equations in the local regime.

The use of microwaves for the rapid heating of materials has found widespread industrial use. However, a number of potential problems are inherent in this rapid heating, including the hotspot phenomenon. A hotspot is a type of thermal instability which arises because of the nonlinear dependence of the electromagnetic and thermal properties of the material on temperature. The evolution of a hotspot in a cylindrical material is studied. The propagation of the microwaves is treated in the Wentzel-Kramers-Brillouin (WKB) limit (geometric optics), and the thermal behaviour is studied in the limit of small thermal diffusivity. The resulting temperature distributions are in excellent agreement with full numerical solutions of the governing equations, even outside the strict range of the asymptotic validity of the WKB approximation.

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