Optic pulse propagation in inhomogeneous nonlinear waveguides can be described by nonlinear Schrodinger equation with (2+1) dimension variable coefficients. Similarity transformation is used to construct exact optical rogue wave solutions of (2 + 1) dimensional nonlinear Schrodinger equation with varying coefficients. Moreover，the dynamic of the first- order optical rogue waves in the optical fiber amplifier is investigated by the nonlinear Schrodinger equation with an external harmonic potential. Manipulating propagate conditions of two- dimensional optical rogue waves are given. In the suitable regulation of parameters, the properties of the optical rogue waves are found, such as amplitude and position, which are controllable in the nonlinear media. In the controllable parameters, the propagation behaviour of the controllable light waves in the nonlinear media are discussed, including delayed excitation, annihilation and maintaining. These results give edification in theory and practical application.