This paper presents a theoretical analysis of sum-frequency generating optical parametric oscillators where a single nonlinear crystal is used for both parametric generation and sum-frequency generation. In these devices, the parametric and sum-frequency generation processes are both phase matched for the same direction of propagation inside the crystal. Different polarization geometries for which this simultaneous phase-matching condition can potentially be satisfied are identified and categorized, for both birefringent and quasi-phase-matching methods. Plane-wave coupled-mode equations are presented for each of these categories. Solutions of these coupled mode equations and calculation of the single-pass saturated signal gain are outlined. Intracavity signal photon flux density calculations based on these solutions lead to stable steady-state upconversion, multistability, and chaos. The dependence of the photon conversion efficiency on various design parameters are investigated.
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