We employ an off-axis pumped Nd:YVO4 laser and control the reflectance of output coupler to directly generate asymmetrical Hermite-Gaussian (HG) modes with various transverse orders. By using an astigmatic mode converter, the generated asymmetrical HG modes are straightforwardly transformed into asymmetrical Laguerre-Gaussian (LG) modes with a crescent-like shape. The average output power of all the crescent-shaped LG modes can exceed 1W at the pump power of 4W. Furthermore, experimental results are theoretically verified by resonant modes derived from the inhomogeneous Helmholtz equation with the localized source distribution. Theoretical resonant modes are also used to explore the dependence of the phase structures of LG modes on the system loss. As the loss increases, it is found that the singularities at the origin will be rearranged and new singularities are formed in the outside region with average orbital angular momentum remaining unchanged.