Propagation of elegant Laguerre Gaussian beam through a misaligned optical system

The analytical formula of elegant Laguerre Gaussian beam (ELGB) through the misaligned optical system is derived by using the diffraction integral equation. Based on the formula, the propagation properties of ELGB are studied in detail, the numerical examples are given to confirm the correctness of our calculated results. It is shown that the parameters (La, θa,φ,z,m) will influence the intensity distributions and beam shapes of ELGB, these results are useful in the application of laser beams.