Acceleration of Dominant Transversal Laser Resonator Eigenmode Calculation by Vector Extrapolation Methods

Abstract

Field tracing provides the flexible and fully vectorial calculation of the dominant transversal resonator mode. Therefore, the eigenvalue problem formulated in a set of coupled, nonlinear operator equations has to be solved. Up to now, only the iterative power method, also known as Fox and Li algorithm, was used for the eigenvector calculation, where serious convergence problems can occur. We accelerate the convergence speed by applying two polynomial-type vector extrapolation methods, namely, the minimal polynomial extrapolation and the reduced rank extrapolation. Numerical examples show that the convergence speed and, consequently, the computational time required for the calculation of the fully vectorial transversal resonator eigenmode, could be reduced by up to 70% compared with the Fox and Li algorithm. Furthermore, it is shown that the calculated eigenmode is in good agreement with the experimental results.