In this paper, we propose a novel method to measure the free spectral range (FSR) of a Fabry-Perot cavity (FPC) using single-frequency modulation (FM) with one electric optical modulator (EOM) and the null method. A laser beam modulated by the EOM, to which a cosine-wave signal is supplied from a radio frequency (RF) oscillator, is incident on the FPC. The transmission light from the FPC is observed and converted to an RF signal by a highspeed photodetector, and the RF signal is synchronously demodulated with a lock-in amplifier (LIA) by referring to the oscillator. We theoretically and experimentally demonstrate that the LIA signal become null with a steep slope, when the modulation frequency equals the FSR under the condition that the carrier frequency is slightly detuned from the resonance of the FPC. The experimental results show that the proposed method has the capability to determine the FSR by the null method with a small measurement uncertainty.

In this paper, we discuss a method to measure the free spectral range (FSR) of a Fabry–Perot cavity (FP-cavity) using frequency modulation with one electric optical modulator (EOM) and the null method. A laser beam modulated by the EOM, to which a sine wave signal is supplied from a radio frequency (RF) oscillator, is incident on the FP-cavity. The transmitted or reflected light from the FP-cavity is observed and converted to an RF signal by a high-speed photodetector, and the RF signal is synchronously demodulated with a lock-in amplifier by referring to a cosine wave signal from the oscillator. We theoretically and experimentally demonstrate that the lock-in amplifier signal for the transmitted or reflected light becomes null with a steep slope when the modulation frequency is equal to the FSR under the condition that the carrier frequency of the laser is slightly detuned from the resonance of the FP-cavity. To reduce the measurement uncertainty for the FSR, we also discuss a selection method for laser power, a modulation index and the detuning shift of the carrier frequency, respectively.