Analysis of the external filtered modes of a semiconductor laser with filtered optical feedback

We present a detailed analysis of the external filter mode (EFM) structure of a semiconductor laser subject to filtered optical feedback (FOF). These EFMs form the ‘backbone’ of the dynamics of the system. Specifically, from the governing delay differential equations, we find analytic, transcendental expressions for both the solution curves, which define the frequency and amplitude of the EFMs, and their envelopes. We use numerical continuation to find and follow solutions of these equations. This approach allows us to show how the structure depends on the key parameters of filter width, filter detuning, and feedback phase. In other words, we identify the external influence of the filter on an otherwise fixed laser