Relationship between the relaxation oscillation frequency of a laser diode and its external cavity length

A laser diode (LD) with external feedback can generate undamped relaxation oscillation (RO) under a certain operational condition. The RO frequency is highly sensitive to the external cavity condition. This work is to study the relationship between the RO frequency of an LD with optical feedback and its external cavity length. We firstly numerically solve the Lang-Kobayashi (L-K) equations to theoretically determine the relationship, then, experimentally verify the theoretical results. Both the simulation and experiment show that the RO frequency is quasiperiodic function of the external cavity length with the period of half laser wavelength when the cavity length is varied in micro scale. The results obtained at this work is useful for sensing and measurement using a laser feedback interferometry at relaxation oscillation.