Frequency response measurement of electro-optic phase modulators using the time-frequency analysis method

We propose a novel method for the frequency response measurement of electro-optic phase modulators by time-frequency analyzing the instantaneous frequency of a sinusoidal frequency-modulated (SFM) signal. The SFM signal is generated by a frequency-shifting loop (FSL) in which the electro-optic phase modulator under test generates a dual-sideband frequency shift per roundtrip. And the bandwidth of the generated SFM signal is dozens of times of the input radio-frequency (RF), which makes it a precise method to measure the frequency response of electro-optic phase modulators at lower cutoff frequencies. Based on the previously proposed time-delayed interference model [H. Yang et al., J. Lightwave Technol. 39 , 3112 ( 2021 ) 10.1109/JLT.2021.3059875 ], we establish the relationship between the “peak-to-peak” frequency of the SFM waveforms and the modulation index of the phase modulators. And a short-time Fourier transformation (STFT) is adopted to characterize the time-frequency properties of output waveforms. Experimental results are well supported by the simple theoretical model. Finally, the accuracy of the half-wave voltage measurement is discussed.