We study the use of nonlinear self-phase modulation (SPM) in coupled optical microresonators for ultrasensitive refractive index sensing. SPM leads to a positive feedback enhancement of the resonance frequency shift caused by a perturbation of the index of refraction in a resonator. Moreover, the use of two resonators coupled through input and output waveguides leads to a further improvement in the sensitivity owing to constructive interference and feedback via the waveguides. For parameters based on Si microresonators, the sensitivity is more than 10~2 larger than a single resonator without SPM leading to a minimum detectable index change of 10~(-11) RIU with resonator Q-factors of ～10~4. We show that the nonlinearly enhanced system is robust with respect to laser noise when operated at input powers below the onset of bistability.
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