Hyperfine Intrinsic Magnitude and Phase Response Measurement of Optical Filters Based on Electro-Optical Harmonics Heterodyne and Wiener–Lee Transformation

An electro-optical heterodyne scheme is proposed and demonstrated for magnitude- and phase-frequency response measurement of optical filters based on harmonics heterodyne and Wiener–Lee transformation. The method consists of an acousto-optic frequency shifter and a phase modulator located in a frequency-shifted heterodyne interferometer. The minimum phase-frequency response is simultaneously extracted from the measured magnitude–frequency response with the help of Kramers–Kronig relations and the Wiener–Lee transformation. As compared with the single-sideband-based or double-sideband-based methods, our method eliminates small-signal assumption and features an immunity to undesired spurious sidebands, enabling harmonic sideband sweeping with even-folded measuring frequency range. Prior to the conventional frequency-shifted heterodyne methods, the method enables simultaneous extraction of intrinsic magnitude and phase frequency responses for most optical filters by introducing the Wiener–Lee transformation. A phase-shifted fiber Bragg grating is measured for extracting the frequency responses in the proof-of-concept experiment with the frequency resolution up to 50 kHz and frequency range of 80 GHz by using a frequency-swept modulation of 20 GHz.