Metamorphosis of the monochromatic spectrum in a double-cavity laser as a function of the feedback rate

We discuss the changes in the spectrum of monochromatic modes in a double-cavity laser showing how the characteristic frequencies change from those proper of a short cavity into those proper of a long cavity using as control parameter the reflectivity of an "external" mirror. The problem is cast into the language of bifurcations in a nonlinear eigenvalue problem. The results show that the transition is mostly dictated by the boundary conditions and occurs regardless of the laser model. Hence, the study presented can be extended to other optical cavities and boundary value problems. Limits of validity of simpler double-cavity loser models, such as the Lang-Kobayashi, are drawn.