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.

Interferometer techniques for gravitational-wave detection

“… 1992 ; Bochner and Hefetz 2003 ; Day et al. 2014 ; Jerome 2008 ). Both methods contain further approximation, in the addition to assuming paraxial behaviour.…”

Modeling circulating cavity fields using the discrete linear canonical transform

“…Fast Fourier transforms (FFTs) can be used to efficiently compute the diffraction integrals, which has in turn led to this class of models being colloquially called FFT models. The number of iterations is reduced with a better initial guess of the circulating field or by accelerating the rate of convergence by using a modified iteration scheme [8][9][10]. The Fox-Li method has also been used in modelling eigenmodes of unstable resonators [11,12].…”

“…FFT models can be used to model more complicated optical systems involving multiple coupled cavities, such as the Fabry-Perot power recycled Michelson interferometers (FPPRMI) used in Gravitational Wave (GW) detectors as modeled by Bochner et al in 2003 [9]. Bochner et al additionally state that FFT models are difficult to implement in code and that accelerating the rate of convergence of their FFT models often leads to instabilitywhich was also found to be an issue by Day et al [10]. A 2017 review of unstable resonator eigenmode modelling by New [13] showed that the Fox-Li method can be outperformed by general purpose linear algebra algorithms available in MATLAB in cases where the sampling grid resolution is not larger than 512 × 512.…”