Displacement sensing using the relaxation oscillation frequency of a laser diode with optical feedback

A laser diode (LD) with external optical feedback can generate undamped relaxation oscillation (RO) under certain operational conditions. The RO frequency can be modified by the external cavity length of the LD and is highly sensitive to the variation of the cavity length (ΔL). This work first investigates the relationship between the RO frequency and ΔL by solving the well-known Lang-Kobayashi (L-K) equations and then verifies the relationship by experiments. Both theory and experiment show that the RO frequency changes in a sawtooth-like quasi-periodic manner with respect to ΔL. The fundamental period is half laser wavelength. This sawtooth feature enables us to achieve period unwrapping and thus extend the measurement range up to a few micrometers. This work shows a possible new solution for achieving high-resolution, large-range displacement measurements.