Gouy phase shift measurement in a high finesse cavity by optical feedback frequency locking

We demonstrate a simple and robust scheme to measure the relative position of transverse cavity modes with high precision. This is based on robust optical-feedback frequency locking of a diode laser to a cavity resonance. A fraction of the laser power is then frequency shifted and used to re-inject other cavity resonances to obtain their positions relative to the locking resonance. This delivers the Gouy phase shift of the cavity modes with precision down to \SI{6,4E-8}{\radian}, comparable to previous state of the art based on a more complex setup. This should also be of interest for high precision/accuracy measurement of distance and displacement.