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Finite Element Study of the Second Order (X²) Nonlinear Process of Second Harmonic Generation in Optical Waveguides

Katrisku, Ferdinand Apietu (2000). Finite Element Study of the Second Order (X²) Nonlinear Process of Second Harmonic Generation in Optical Waveguides. (Unpublished Doctoral thesis, City, University of London)

Abstract

At the heart of future communication systems will be integrated, all optical devices. The role of the second order nonlinear process in the realisation of such devices is well known and has been documented. Research activity in the field of second order nonlinear processes has focused primarily on the generation of new frequencies, which have an important role to play in multimedia systems. The second order process also has great potential for use in all-optical switches, all-optical transistor and intensity-dependent phase modulation. For the theoretical study of such devices, efficient mathematical models are required. The finite element method has established itself as an accurate, efficient and versatile method in the modal analysis of both linear and nonlinear systems but its application to the evolutionary analysis has been minimal.

The application of the finite element method to the theoretical study of such devices is the subject of this thesis. A formulation of the finite element method that takes into consideration material anisotropy and different diffusion profiles is developed, as is a finite element based beam propagation model. Such a model combines the strengths of the finite element method with the well-established beam propagation method for the evolutionary analysis of the fundamental wave and the generated second harmonic wave. The model is applied to the study of second harmonic generation in various material systems and waveguide structures.

The propagation model developed has been applied to the study of second harmonic generation in both LiNb03 and semiconductor waveguides. Second harmonic generation in waveguides with one-dimensional confinement is first studied and provides a basis for comparative analysis with previously published results. The method is then extended to more realistic guides with two-dimensional confinement. Second harmonic generation by the Cerenkov radiation scheme is illustrated. Quasi-phase matching schemes for enhancing the output power are also discussed. Semiconductor material systems provide the basis for the monolithic integration of optical waveguides and hence are of great technological importance. The method developed is thus applied to the study of SHG in GaAs and AIGaAs devices. Methods of QPM and fabrication tolerances on output power as well as waveguide loss are treated. Finally the phenomenon of cascaded second harmonic generation is considered.

As a first task, it was necessary to determine the modes or characteristic solutions of the waveguide structure through the solution of the stationary wave equation. The finite element vector H formulation was thus extended to the study of 3-D waveguides with material anisotropy and diffused index profiles, both the transverse directions. Some new and interesting observations were made. The solution obtained from the above is then used at the second stage, an input for the BPM. A step by step solution of the paraxial wave equation in the propagation direction then produces a second harmonic output. Various types of waveguides are analysed and the results fully discussed.

Publication Type: Thesis (Doctoral)
Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering
Departments: Doctoral Theses
Doctoral Theses > School of Mathematics, Computer Science and Engineering Doctoral Theses
School of Mathematics, Computer Science & Engineering
School of Mathematics, Computer Science & Engineering > Engineering
School of Mathematics, Computer Science & Engineering > Engineering > Electrical & Electronic Engineering
URI: http://openaccess.city.ac.uk/id/eprint/20273
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