RF-referenced and phase-tracking-based precise measurement of optical resonator free spectral range across a broad wavelength range

The free spectral range (FSR) is a key parameter in the design of optical resonators. However, material dispersion can cause nonuniform FSR variations across a broad wavelength range. To address this drawback, this study proposes a high-precision FSR measurement method that combines an electro-optic modulator with an orthogonal Mach-Zehnder interferometer (MZI). A tunable laser is electro-optically modulated to generate equally spaced sidebands, yielding stable frequency markers. Subsequently, the markers are combined with the unwrapped instantaneous phases obtained from the MZI to determine high-precision FSR. Using a fiber ring resonator as a representative example, the FSR varied by ~51.4 kHz over an 82.4-nm wavelength span. The measured FSR was used as a frequency-interval reference, together with the known absolute wavelength of the R9 line, to determine the center wavelengths of H¹³C¹⁴N gas absorption lines. As a result, an absolute measurement accuracy better than 0.24 pm was achieved, demonstrating the method's high precision and reliability. Thus, the proposed method enables high-precision characterization of optical resonator parameters across a wide spectral range and offers a practical approach to precision spectroscopy.