title: High fidelity simulations of optical waveguides for optical frequency conversion and frequency combs
Creators: name: Zhu, Yixuan
Publisher: name: University of Glasgow
Year: 2018
Subjects: subject: four-wave mixing, second-harmonic generation, AlGaAs waveguides, frequency conversion.

description: Conventional silicon-based electronics have developed dramatically in recent years; however, their optimum integration level is reaching its limits. To meet the requirements of dealing with this explosion of data, opto-electronic integrated circuits have provided a way out. Optical waveguides are crucial components which can be applied in opto-electronic integrated circuits to achieve specific functionalities, such as frequency conversion and frequency combs. Frequency conversion offers the possibility of converting the frequency components generated by lasers to a previously inaccessible frequency region in order to extend the application fields, such as gas sensing and optical communications. A frequency comb is a series of equally spaced frequency components, which could be utilized for frequency standards and optical clocks. 
This thesis has simulated frequency mixing processes, including second-harmonic generation and four-wave mixing in the optical waveguides based on second- and third-order nonlinearities in order to realize frequency conversion and generation of frequency combs. The focus of this thesis are silicon-based and AlGaAs waveguides because of their particular material characteristics. Silicon is the base of electronic devices so that silicon-based waveguides are complementary metal-oxide-semiconductor compatible and can be integrated with other electronic elements on a single chip. AlGaAs is a direct-band gap semi-conductor and has a small two-photon-absorption co-efficient. Both silicon and AlGaAs have a high refractive index and ensure the confinement of modes in waveguides. In addition, both have strong nonlinearity, leading to efficient nonlinear interactions and significant frequency mixing processes.
This method of simulation was based on the finite-difference time-domain algorithm, incorporating linear dispersion and nonlinearity. Material dispersion was described as Lorentz medium and incorporated through Sellmeier equations. Geometric dispersion was taken into account in mode solver, which was applied in order to produce the fundamental modes for excitation sources. Second- and third-order nonlinearities (including Kerr-nonlinearity and Raman scattering) were incorporated with a piecewise linear recursive convolution method, which was solved by the Newton-Raphson method. In addition, a perfectly matched layer absorbing boundary condition and circular boundary condition were designed in the simulations. Programs were written in Fortran 95 and parallel computation was applied to improve the efficiency. 
This thesis has simulated four-wave mixing of five optical waveguides: GaAs suspended waveguide, deep-etched multi-layer Al_0.25 Ga_0.75 As waveguide, Al_0.3 Ga_0.7 As-on-insulator waveguide, silicon-on-insulator waveguide and silicon nitride-on-insulator waveguide. Phase matching conditions and phase mismatch factors were discussed for these waveguides. The results of four-wave mixing were observed when the phase matching conditions were satisfied. In deep-etched multi-layer Al_0.25 Ga_0.75 As waveguide, Raman scattering was incorporated and the results of simulation showed a good match with experimental data. This thesis has also simulated second-harmonic generation of highly birefringent AlGaAs waveguide. Type-I phase matching condition was achieved so that efficient second-harmonic generation was obtained.