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Analysis of optical propagation in isotropic nonlinear devices by the finite element method

Csaszar, Eduardo Gonzalez; (1995) Analysis of optical propagation in isotropic nonlinear devices by the finite element method. Doctoral thesis (Ph.D.), University College London (United Kingdom). Green open access

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Abstract

This work deals with the formulation and implementation of the Finite Element Method (FEM) to the scalar analysis of optical propagation in isotropic nonlinear devices. The resulting computer programmes are used to study structures of practical interest and can be applied to optimize device design. Starting from Maxwell's equations, approximations are used to derive specific formulations to treat different classes of problems which include a two-transverse dimension lion paraxial approach for the steady state case, leading to the Helmholtz equation; and the time domain analysis of slab structures (one dimensional transverse structure). The numerical treatment is mainly based on the combination of first order finite elements (for the transverse coordinates) and the Crank-Nicolson's approximation (FEM/CN). A variant of this method, the split operator method (SOM), is also used and a criterion for optimizing the modelling of the nonlinearity is developed. Practical applications studied for the steady state case include switching, couplers and multi-state devices. Results are tested against previously reported research or analytical results. Numerical stability and convergence are studied for the FEM/CN. Examples are also used to verify the range validity of the SOM and FEM/CN, by investigating stability and convergence of the numerical solution and speed of the algorithms. The formulation for the time domain analysis, which has been developed for the study of forward proopagation of short pulses, includes the modelling of second order dispersion and the Debye equation for modelling the delayed response of the nonlinearity. That approach has been validated with the analysis of practical examples. An extension of this formulation has also been developed to analyze pump-controlled devices.

Type: Thesis (Doctoral)
Qualification: Ph.D.
Title: Analysis of optical propagation in isotropic nonlinear devices by the finite element method
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Thesis digitised by ProQuest.
Keywords: (UMI)AAI10017216; Applied sciences
URI: https://discovery.ucl.ac.uk/id/eprint/10099793
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