Transfer matrix analysis of the birefringent fiber Fabry–Perot cavity and laser frequency locking

The Fiber Fabry–Perot (FFP) cavities are reported as various types of sensors in conventional experiments while rarely reported in application of frequency stabilization. We fabricated 10 cm, 30 cm, 50 cm Single Mode Fiber Fabry–Perot (SMF-FP) cavity with parallel end faces to serve as a frequency reference. The thermoelectric cooler (TEC) and piezoelectric transducer (PZT) are configured on the cavity structure for frequency coarse tuning and fine tuning. By establishing the transfer matrix model of light resonant process in the SMF-FP, the birefringence and thermal effect of resonance peak is explained, and the relationship between the locking error signal and the input polarization is analyzed. It provides a method to improve the precision and stability of frequency locking by optimizing the input polarization performance. Finally, The Allan variance after the frequency locking reached 2.8×10⁻¹⁰ at 10s of the integral time, which is higher half an order magnitude than the stability of free running. The research work is of great significance to the compact frequency reference with low cost and high precision.