Behavior Study for a Self-mixing Laser Diode with Undamped Relaxation Oscillation and Its Sensing Applications

Self-mixing interferometry (SMI), or also called optical feedback interferometry (OFI) is a promising non-contact sensing technology. It is based on the self-mixing effect which occurs when a fraction of light back-reflected or back-scattered by an external target re-enters the laser internal cavity. A sensing system by using SMI technique consists of a laser diode (LD), a photodiode (PD) packaged at the rear of the LD, a lens and a target. The LD is called self-mixing laser diode (SMLD). This configuration reflects a minimum part-count scheme, which is useful for engineering implementation. Compared to traditional interferometry, e.g., Michelson or Mach-Zehnder interferometry, SMI has the advantages of simplicity in system structure, low cost in implementation, and ease in optical alignment. Using these merits, SMI technology has been developed for various applications, such as measurement of displacement, vibration, velocity, imaging, material related parameters, laser related parameters, etc. Most of the SMI-based applications and behavior study on SMLD system are based on the analytical SMI model, which is derived from the steady-state solution of the Lang and Kobayashi (L-K) equations, or from the classical three-mirror model, by assuming the system operates in stable mode, i.e. both the electric field and carrier density in an LD with a stationary external cavity can reach constant state after transient period. However, undamped relaxation oscillation (RO) may occur under some operation conditions, e.g. it is found an SMLD in moderate feedback regime exhibits undamped RO. The moderate feedback regime is quite commonly employed by researchers. Based on our in-depth study, the behavior of an SMLD system with undamped RO cannot be described by the existing analytical SMI model. The laser intensity (called as sensing signal) from such SMLD system shows some new characteristics. In order to differentiate the conventional SMI signals, we name the SMI signals with un