Generalized Dimers and their Stokes-variable Dynamics

Abstract: In the present work, we generalize the setting of dimers with potential gain and loss which have been extensively considered recently in $\mathcal{P T}$-symmetric contexts. We consider a pair of waveguides which are evanescently coupled but may also be actively coupled and may possess onsite gain and loss, as well as (possibly non-uniform) nonlinearity. We identify (and where appropriate review from earlier work) a plethora of interesting dynamical scenaria ranging from the existence of stable and unstable fixed points and integrable dynamics, to the emergence of pitchfork or Hopf bifurcations and the generation of additional fixed points and limit cycles, respectively, as well as the potential deviation of trajectories to infinity. Thus, a catalogue of a large number of possible cases is given and their respective settings physically justified (where appropriate).