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The operation of a parametric oscillator phase matched in a GaAs thin-film waveguide is considered. Parametric equations of motion for interacting waveguide fields at three frequencies are developed. From these equations we derive expressions for parametric gain and oscillation threshold. A specific orientation of GaAs allows optically smooth cleaved surfaces to form the oscillator cavity. Conditions for which three waveguide modes at three different frequencies can be phase matched are presented for several specific waveguide-substrate structures. These conditions are in each case determined for a wide variety of mode orders, for a laser pump wavelength of 1.06 μ, and for a large range of signal wavelengths. The deviation in thin-film thickness that can be tolerated while maintaining phase matching over a given interaction length is calculated. We find that transverse coupling strength and oscillation threshold powers are widely variable for different phase matched mode order combinations. Oscillator frequency tuning is investigated by first deriving expressions for variations in waveguide parameters required to effect tuning over a specific range and then evaluating these expressions for some of the previously determined phase-matching situations.