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7 July 1998 Accurate modeling of second harmonic generation in optical waveguides
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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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B. M. Azizur Rahman, Ferdinand Apietu Katsriku, and Kenneth T. V. Grattan "Accurate modeling of second harmonic generation in optical waveguides", Proc. SPIE 3283, Physics and Simulation of Optoelectronic Devices VI, (7 July 1998);

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