Integrated microring resonators have a broad range of applications in diverse fields with the potential to design compact, robust, energy-efficient devices crucial for quantum applications. Degenerate optical parametric oscillations (DOPOs) realized in dual-pumped microring resonator with third-order optical nonlinearity are of special interest. They demonstrate both bistability of the phase of the excited signal mode and generation of nonclassical light, which can be used for coherent photonic computing. Using coupled mode equations, we perform a comprehensive numerical analysis of DOPO conditions with normal group velocity dispersion and with bichromatic pumping. Through analytical and numerical approaches, we identify optimal setup parameter values that minimize the threshold power, highlighting the importance of considering the full spectrum of mode interactions. Additionally, we show that dispersion engineering, achievable in photonic molecules or photonic crystal microresonators, may provide a targeted frequency shift of specific microresonator modes resulting in pump power threshold reduction.

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• Nonlinear optics
• Optical microcavities
• Optical parametric oscillators & amplifiers
• Third order nonlinear optical processes