Abstract: The phase conjugation technology can correct wavefront aberration of optical radiation in laser system. Based on Helmholtz equation, a conventional phase conjugate reflection equation set about the correction model for wavefront aberration of laser radiation are established. By using the Lie Group analytic procedure, it deduces the multiple groups of allowed infinitesimal Lie symmetries and invariant solution of the partial differential equations, and more importantly, it also points out their detailed analytical expressions and properties. The content and method can provide an effective way for the exact analytical solution of the adaptive laser propagation considering the boundary and initial conditions, and it reveals the inherent principle of the laser wavefront correction, and it also provides a verification for the numerical algorithm of the nonlinear optical wave equations.

Key words: Laser, Wavefront correction, Phase conjugation, Lie symmetries, Invariant solution