Analysis of laser modes in high power unstable resonators with intra-cavity wavefront aberrations

A semi-analytical calculation framework is proposed to calculate the eigenmodes of a general laser resonator with arbitrary intra-cavity wavefront aberrations. By solving a linear eigenvalue equation in the complex space, the mode intensity distributions of the eigenmodes in high power unstable resonators are obtained, indicating that due to the aberrations the area of fundamental mode significantly shrinks to form the localized mode with extremely high power intensity. The beam quality, mode area, threshold gain, and operation reliability are compared between the traditional unstable resonator and the one with a graded reflectivity mirror. The simulation results disclose that with a graded reflectivity mirror more high-order modes participate in mode competition and the localized mode effect of fundamental mode is weakened. (paper)