Resonant wave interactions play a fundamental role in many fields of physics. Consequently, controlling resonant wave interactions is an important goal of both basic and applied physics research. We have studied a persistent nonlinear self-phase-locking (autoresonance) in several coupled wave systems.

In this talk I will focus on our most recent theory of autoresonant four-wave mixing in tapered optical fibers with application to Optical Parametric Amplification (OPA). In autoresonance the interacting waves (two pumps, a signal and an idler) stay phase-locked continuously despite variation of system parameters (spatial tapering). This spatially extended phase-locking allows complete pump depletion in the system and uniform amplification spectrum in a wide frequency band. We examined various aspects of autoresonant OPA, including the initial phase-locking, conditions for autoresonant transition, stability, and spatial range of the autoresonant interaction.