Heterodyne interferometry at ultra-high frequencies with frequency-offset-locked semiconductor lasers

Modern broadband telecommunications require microelectromechanical filters which mechanically vibrate at ultra-high frequencies up to several gigahertz. Heterodyne interferometers, so-called laser-Doppler vibrometers (LDVs), provide a sensitive and contactless measurement technique for vibrations in such filters, but are limited in GHz heterodyning by the efficiency drop of acousto-optic frequency shifters. Heterodyning by frequency-offset locking of two lasers in an optoelectronic phase-locked loop (OPLL) overcomes this limitation. This is demonstrated with our LDV setup with heterodyning up to $1.4\ \mathrm{GHz}$ via offset locking of two semiconductor lasers at visible wavelength. The experiments show a vibration-amplitude resolution of less than $1 \ \mathrm{pm}$ per $\sqrt{\mathrm{Hz}}$ for frequencies higher than $50\ \mathrm{MHz}$ up to $700\ \mathrm{MHz}$. The bandwidth is only limited by our photodetectors. This amplitude resolution already qualifies our LDV for vibration measurement of microelectromechanical filters at ultra-high frequencies. We present a comprehensive model for the vibration-amplitude resolution of a LDV with this technique including the laser linewidths, the OPLL transfer function, and interferometer delays. The experiments with our LDV validate the model predictions from numerical simulations. Finally, we discuss the collapse of the heterodyne carrier at vanishing mutual coherence due to interferometer delays, the transition to shot-noise-limited detection, and provide design recommendations.