Resonant frequency and Q factor extraction from temporal responses of ultra-high Q optical resonators

Resonant frequency extraction from time signal simulations of optical resonators is often required to resolve closely spaced resonances in addition to estimating high Q factors. Traditional Fourier transform-based fitting methods thus require very long time signals, limiting their usage. Complex exponential fitting-based methods such as matrix pencil, modified Prony and harmonic inversion provide better accuracy, but each has its own advantages as well as disadvantages. In this study, it is shown that the matrix pencil method is limited by the number of time samples, but provides accurate results, whereas the harmonic inversion method provides less accurate results with high efficiency. The difference formulation of the modified Prony method implemented with multiple precision, while providing the best accuracy, is the least efficient approach and requires careful adjustment of its parameters to obtain a solution.