Fig. 4: Spectral-resolving heterodyne measurement of optomechanical mode conversion process.

a Heterodyne measurement schematic. EDFA erbium-doped fiber amplifier, RSA real-time spectrum analyzer, AOFS acousto-optic frequency shifter. The reference signal is generated by shifting the laser frequency by \(\delta /2\pi=102.9\) MHz using an AOFS. b The beating signals of the heterodyne measurement, the red and blue signals correspond to the counter-propagating anti-Stokes P₀₂\((\varOmega -\delta )\) and co-propagating Stokes P₀₂\((\varOmega+\delta )\) signals of the optomechanical ring resonator (OMR), respectively. The purple signal P₀₂\((\delta )\) is generated by the beating of the static TE₂ mode and reference signal. It thus provides a measure of the TE₀ pump intensity in the OMR. Inset: zoom-in of the signals P₀₂\((\varOmega -\delta )\), P₀₂\((\varOmega )\), and P₀₂\((\varOmega+\delta )\). c Anti-Stokes signal P₀₂\((\varOmega -\delta )\) as a function of acoustic wave frequency. The gray dashed line denotes the 5.1 MHz frequency separation between the two peaks. d TE₀ mode pump depletion signal P₀₂\((\delta )\) as a function of L₂ mode pump power. The purple solid line is the Coupled-mode theory (CMT) fitting. e Anti-Stokes signal P₀₂\((\varOmega -\delta )\) as a function L₂ mode pump power. The red solid line is the CMT fitting. The solid circles within the error bar in (d and e) represent the mean of the measurements.