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We develop a theoretical model of triply-resonant optical parametricoscillators (OPOs) based on degenerate four-wave mixing (FWM) that includesphysics and degrees of freedom relevant to microphotonic (on-chip) deviceimplementations, including nonlinear loss, a general resonant mode fieldstructure, and mode-selective coupling to external ports. The coupled modetheory model addresses the effect of two-photon absorption and free-carrierabsorption on parametric gain and oscillation thresholds, and ultimately on theoptimum design for an OPO. The model goes beyond a typical free-space cavityconfiguration by incorporating a full modal analysis that admits distributedmodes with non-uniform field distribution, relevant to photonic microcavitysystems on chip. This leads to a generalization of the concept of nonlinearfigure of merit (NFOM) to a vector of coefficients. In addition, by consideringunconstrained signal, pump and idler resonance coupling strengths to excitationports, not usually available in simple cavity geometry, we show that theefficiency-maximizing design will have unequal external Q for the threeresonances. We arrive at generalized formulas for OPO oscillation thresholdthat include nonlinear absorption and free carrier lifetime, and provide anormalized solution to the design problem in the presence of nonlinear loss interms of optimum choice of coupling. Based on the results, we suggest a familyof coupled-cavity systems to implement optimum FWM, where control of resonantwavelengths can be separated from optimizing nonlinear conversion efficiency,and where furthermore pump, signal, and idler coupling to bus waveguides can becontrolled independently, using interferometric cavity supermode coupling as anexample. Using the generalized NFOM, we address the efficiency of single andmulti-cavity geometry, as well as standing and traveling wave excitation.

Triply-resonant micro-optical parametric oscillators based on Kerr  nonlinearity: nonlinear loss, unequal resonance-port couplings, and  coupled-cavity implementations