Analysis of a first-order reflection grating with second-harmonic generation

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Abstract
The operation of a first-order reflection grating, superposed on a dielectric waveguide with a second-order nonlinearity, is analyzed. Such a grating termination to a second-harmonic generating waveguide is shown to operate as an efficient wavelength-selective reflector(ω)/radiator(2ω) for the two respective harmonic input guided waves, in particular in a second-harmonic (SH) resonator. It is shown that radiation efficiency for the input SH wave depends on the phase difference between the two input waves and on the ratio between the input SH power and the SH power generated inside the grating. In certain cases the input SH wave experiences gain as it is radiated, with the fundamental input wave acting as a pump.

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