Application of convolutional fitting in Fabry-Perot (F-P) resonator linewidth measurement experiments

To address measurement inaccuracies in traditional swept-frequency methods caused by laser linewidth effects, this study proposes a convolution-based signal analysis approach that accounts for the convolutional relationship between Gaussian-shaped laser spectra and Lorentzian-type Fabry-Perot (F-P) resonator responses. An experimental platform employing two F-P cavities (one custom-built and one commercial) demonstrated three key advancements: 1) Quantitative simulations established laser linewidth impacts on signal profiles, coupled with a dedicated fitting algorithm; 2) Beat-frequency characterization revealed a Gaussian laser lineshape with 11.59 ± 1.23 kHz linewidth; 3) Comparative analysis of Lorentzian versus convolutional fitting across different linewidth regimes showed critical performance differences. For Cavity 1 (204.1 kHz nominal), both methods yielded comparable results (Lorentzian: 204.1 ± 11.2 kHz; Convolutional: 203.9 ± 11.2 kHz), while for Cavity 2 (4.17 kHz reference), convolutional fitting achieved superior accuracy (4.42 ± 0.50 kHz vs. Lorentzian's 8.97 ± 0.42 kHz). The methodology effectively recovers true linewidths when laser and cavity linewidths are spectrally comparable, and converges with Lorentzian fitting when laser linewidth (11.59 kHz) $\ll $ cavity linewidth (204.1 kHz). This approach significantly expands the applicability range of narrow-linewidth F-P cavity measurement systems by relaxing laser source requirements.