Controllable optical rogue waves: Recurrence, annihilation and sustainment

► We investigate optical rogue waves in nonlinear optical fiber with distribute coefficients. ► We demonstrate theoretically a method to control the dynamics of optical rogue waves via a lens-type transformation. ► By properly choosing the distributed coefficients, various controllable sceneries have been realized. ► Rogue waves can be annihilated, emerge periodically and sustain forever.