Diode lasers with optical feedback and injection: similarities and differences

The question is addressed as to whether the dynamical behaviour of a single-mode semiconductor laser subject to delayed optical feedback can be understood in terms of the behavioural properties of its optical injection counterpart. The relevance of this problem stems from the fact that the injection laser, being a three dimensional dynamical system, is much simpler to deal with than the infinitely dimensional feedback system. The wealth of literature available on the injection laser makes it very tempting to try and apply the knowledge and insights on injection properties to the feedback laser. Therefore we consider the feedback laser as a laser with self-injection. The striking difference in dynamical dimensionality is reflected in the fixed point (FP) properties. A FP of the dynamical system corresponds to monochromatic (DC) operation of the laser. A FP can be stable or unstable. The specific manner in which a stable FP is approached or an unstable FP is left, is physically important, since that will determine to a large extent the system´s dynamical properties.. We consider the dynamics in the neighbourhood of these FPs. For the feedback laser the number of FPs (the external cavity modes and anti-modes) can easily assume values as large as 1000 - even at low feedback levels -, in striking contrast with the injection laser where for any combination of detuning and injection strength at most three FPs exist. Our analysis has revealed that for each FP (whether stable or unstable) of the feedback laser, we can find a corresponding FP of the injection laser and v.v. These corresponding FPs may still differ in their stability. Performing a small signal analysis reveals the stability properties of a given FP