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In this thesis a quite realistic complex model for describing light behavior in paraxial linear and nonlinear regimes in nematic liquid crystal planar cells is studied. Both one and two dimensional models for the optical eld are shown in these micrometric structures. Thus the in uence of nonlocal nonlinearity and the e ects of anisotropy are presented. Particularly it has been considered the case for XZ anisotropy for the one dimensional case (which means anisotropy in the plane of light propagation) and also the XY anisotropy which yields vectorial modes in the transverse plane. Besides, new regime due to non symmetric boundary conditions for the one dimensional orientation of the molecules is discovered. This new con guration exhibits a strong focusing linear regime since a deep graded index guide is induced by the molecular orientation at the boundary. Moreover the number of graded index guides inside the nematics can be tuned by the asymmetric boundary condition. Finally the behavior of light under linear and nonlinear regimes for this asymmetric setup is studied. From the numerical point of view,a nite di erence method is employed to solve all the partial di erential equations involved. This numerical method yields systems of nonlinear equations which are solved with standard iterative techniques such as Newton-Raphson method. Advanced numerical techniques such as alternating direction implicit schemes or MultiGrid techniques are employed to improve the computational performance of our codes. Besides, we introduce a novel transparent boundary condition which is used successfully to solve the two dimensional electric eld equation and the twist angle distribution of the nematic over the cell. This improves a bit more the computational cost needed to solve the complex optical devices we deal with. Finally, with respect to applications, we use the codes developed in this thesis to simulate the energy transfer between the channels of an optical directional coupler. We also design a new electro-optic device which pro ts the versatile properties of nematic liquid crystal cells to guide light in the linear regime. The electric voltage applied to the cell is used as a degree of freedom that allows us to control the trajectory of light.

Simulación de dispositivos ópticos de cristal líquido. Análisis de la propagación lateral en el régimen lineal y en el no lineal