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 rad, 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.