  We propose and demonstrate localized mode coupling as a viable dispersion
engineering technique for phase-matched resonant four-wave mixing (FWM). We
demonstrate a dual-cavity resonant structure that employs coupling-induced
frequency splitting at one of three resonances to compensate for cavity
dispersion, enabling phase-matching. Coupling strength is controlled by thermal
tuning of one cavity enabling active control of the resonant
frequency-matching. In a fabricated silicon microresonator, we show an 8 dB
enhancement of seeded FWM efficiency over the non-compensated state. The
measured four-wave mixing has a peak wavelength conversion efficiency of -37.9
dB across a free spectral range (FSR) of 3.334 THz ($\sim$27 nm). Enabled by
strong counteraction of dispersion, this FSR is, to our knowledge, the largest
in silicon to demonstrate FWM to date. This form of mode-coupling-based, active
dispersion compensation can be beneficial for many FWM-based devices including
wavelength converters, parametric amplifiers, and widely detuned correlated
photon-pair sources. Apart from compensating intrinsic dispersion, the proposed
mechanism can alternatively be utilized in an otherwise dispersionless
resonator to counteract the detuning effect of self- and cross-phase modulation
on the pump resonance during FWM, thereby addressing a fundamental issue in the
performance of light sources such as broadband optical frequency combs.
