Eigenmodes of large-mode-field laser resonators with intra-cavity phase aberrations

A eigenmode expansion method (EME) is proposed to solve the laser eigenmode of optical resonator with intra-cavity phase aberration (ICPA) semi-analytically. In this model, the eigen-equation of OR, so called self-reappearance condition is translated to be a linear eigen-value problem, and it is proved that all eigen-modes can be obtained for any resonators. The linear eigen-value problem is solved numerically, and it gives out the transverse distribution and corresponding eigen-value of each eigenmode, which describe the light field and diffraction loss, respectively. Compared with traditional methods, EME is a semi-analytical method which is unlimited by the order of phase aberration, and it can be solved without numerical iteration. The existing of local modes (LM) in OR with ICPA is proved with EME, which may be the source of local damage on solid medium. And the use of output coupler with transmission, such as graded reflectivity mirror (GRM), can prevent the appearance of LM and improve beam quality. Specially, for the ICPA coupled with laser extraction, the linear eigen-value equations become a nonlinear problem, which are numerically solved by the finite-difference Jacobian method. The result shows that the optical resonator exhibits transverse modal instability (TMI) with certain cavity parameters.