A unified theory to construct exact optical rogue wave solutions of (1+1)-dimensional nonlinear Schrdinger equation with varying coefficients is proposed. The dynamics of the first-order optical rogue waves in nonlinear graded-index waveguide amplifiers exhibiting self-focusing or self-defocusing Kerr nonlinearity are also investigated. Moreover, under the suitable parameter condition, the propagation characteristics of the rogue waves in the nonlinear optical media are discussed. The properties of the optical rogue waves, such as width, amplitude, and position, can be controlled in the nonlinear optical media. A unified theory to construct exact optical rogue wave solutions of (1 + 1) -dimensional nonlinear Schrödinger equation with varying coefficients is proposed. The dynamics of the first-order optical rogue waves in nonlinear graded-index or self-defocusing Kerr nonlinearity are also investigated. Moreover, under the appropriate parameter condition, the propagation characteristics of the rogue waves in the nonlinear optical media are discussed. The properties of the optical rogue waves, such as width, amplitude, and position, can be controlled in the nonlinear optical media.