Accelerated convergence method for fast Fourier transform simulation of coupled cavities

Abstract

Fast Fourier transform (FFT) simulation was used to calculate the power and spatial distribution of resonant fields in optical cavities. This is an important tool when characterizing the effect of imperfect geometry and mirror aberrations. This method is, however, intrinsically slow when the cavities are of relatively high finesse. When this is the case, an accelerated convergence scheme may be used to calculate the steady-state cavity field with a speed that is orders of magnitude faster. The rate of convergence of this method, however, is unpredictable, as many different factors may detrimentally affect its performance. In addition, its use in multiple cavity configurations is not well understood. An in-depth study of the limitations and optimization of this method is presented, together with a formulation of its use in multiple cavity configurations. This work has not only resulted in consistent improvement in performance and stability of the accelerated convergence method but also allows the simulation of optical configurations, which would not previously have been possible.