The rigorous and efficient FEM based beam propagation method is used to model SHG in semiconductor waveguides. The effect of material loss on the overall efficiency of SHG is also analyzed. It is shown that under certain conditions, GaAlAs based devices with a lower non-linear susceptibility tensor could be more efficient than GaAs with a higher non-linear susceptibility tensor due to their low material loss. Numerical results are also presented, of the effect of domain fabrication error, in the case of quasi phase matched devices on the efficiency of SHG. The finite element method is also extended to the study of cascaded second harmonic generation in optical waveguides. The accuracy of the method is demonstrated by comparison with previously published results. The effect of the second harmonic on the fundamental in the presence of an intense input beam is discussed, through application to a practical waveguide structure.
A wide range of photonic guided-wave devices may be modelled by using rigorous numerical approaches based on the finite element method (FEM). In this work, representative modal solutions for linear, nonlinear, anisotropic, passive and active waveguides are discussed. Photonic devices incorporating several butt-coupled uniform waveguide sections, such as optical modulators, switches, filters, polarizers, and duplexers, are shown by incorporating the least squares boundary residual (LSBR) method and the FEM. The FEM-based beam propagation method (BPM) is used to characterize photonic devices incorporating arbitrarily nonuniform guided wave sections or optical devices with second and third order material nonlinearity.
An accurate numerical approach has been developed and is presented, based on the use of finite element method (FEM) to study the nonlinear effect of Second Harmonic Generation (SHG) in optical waveguides. The evolution of the fundamental and second harmonic fields is followed by the implementation of a beam-propagation-type program using a split-step Crank Nicholson procedure based on the FEM. For the purpose of comparison, second harmonic generation using the Cherenkov radiation scheme in a planar waveguide is first considered and the results obtained in this research show very close agreement with those of earlier published work. Also presented are results obtained on frequency doubling for guided modes in planar waveguides using the quasi-phase matching scheme. Whilst planar waveguides allow for a comparatively easy analysis and modeling, practical waveguides are 2D devices with arbitrary diffusion profiles, and in this paper the work is extended to SHG in channel waveguides, with confinement in two transverse dimensions. Results are presented for both Cherenkov and quasi-phase matched devices. This method could prove to be very useful in the design and optimization of optical guided-wave devices and the present approach can be extended to the study of cascaded effects in nonlinear devices.
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