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Weak material nonlinearity at optical frequencies poses a serious hurdle to realizing optical bistability at low optical powers, which is a critical component for digital optical computing. In this paper, we explore the cavity enhancement of the second-order optical nonlinearity in order to determine the feasibility of few photon optical bistability. Starting from a quantum optical formalism of a doubly resonant cavity (required to meet the condition of phase matching), we derive a dynamicdoi:10.1364/oe.23.016246 pmid:26193597 fatcat:ibhnqhcgnfbgxoyp5xmuqza3qq