Solution structure and dynamics of a semiconductor laser subject to feedback from two external filters

We present an analysis of a semiconductor laser subject to filtered optical feedback from two filtering elements (2FOF). The motivation for this study comes from applications where two filters are used to control and stabilise the laser output. Compared to a laser with a single filtered optical feedback loop, the introduction of the second filter significantly influences the structure of the basic continuous-wave solutions, which are also known as external filtered modes (EFMs). We compute and represent the EFMs of the underlying delay differential equation model as surfaces in the space of frequency ωs and inversion level N_s of the laser, and feedback phase difference dC_p. The quantity dC_p is a key parameter since it is associated with interference between the two filter fields and, hence, controls the effective feedback strength. We further show how the EFM surface in (ωs, dC_p,Ns)-space changes upon variation of other filter parameters, in particular, the two delay times. Overall, the investigation of the EFM-surface provides a geometric approach to the multi-parameter analysis of the 2FOF laser, which allows for comprehensive insight into the solution structure and dynamics of the system.