Vortex Creation without Stirring in Coupled Ring Resonators with Gain and Loss

Abstract

We present study of the dynamics of two ring waveguide structure with space dependent coupling, linear gain and nonlinear absorption -the system that can be implemented in polariton condensates, optical waveguides, and nanocavities. We show that by turning on and off local coupling between rings one can selectively generate permanent vortex in one of the rings. We find that due to the modulation instability it is also possible to observe several complex nonlinear phenomena, including spontaneous symmetry breaking, stable inhomogeneous states with interesting structure of currents flowing between rings, generation of stable symmetric and asymmetric circular flows with various vorticities, etc. The latter can be created in pairs (for relatively narrow coupling length) or as single vortex in one of the channels, that is later alternating between channels.

Two Spot Coupled Ring Resonators

“…We compare these results with the previous results of the article [20]. The similarity is that there is the decrease of modulus of wavefunction at x = ±π when we increase the ratio strength coupling J 0 /a.…”

“…System (1) is simple, but possesses a surprisingly rich and diverse set of stable states (some of them nonstationary). For the limit of very wide coupling (a π), we expect the same results dynamics as for the single-Gaussian coupling (this is described in [20]). On the other hand, very narrow coupling (a π) allows approximating coupling with the delta function.…”

“…The similarity is that there is the decrease of modulus of wavefunction at x = ±π when we increase the ratio strength coupling J 0 /a. The difference is that in our model minimum modulus of wavefunction has the value at x = ±x m for all values of J 0 while in the paper [20] the minimum modulus of wavefunction is achieved at value x = ±x m with x m =≤ π.…”

“…Extended discussion of the model (1) and its applications can be found in a publication [18], where the rings were homogeneously coupled, i.e., where it was assumed that J(x) is constant. We also mentioned that (1) with constant coupling is analogous to the model introduced earlier in [19], with local single-Gaussian coupling modulation [20], where it was considered on the whole axis subject to the zero boundary conditions. In this paper, we focus on expanding the study of the model through introducing double-Gaussian coupling modulation J(x).…”

Route to chaos in a coupled microresonator system with gain and loss

“…2. It was studied by some of us earlier revealing rich dynamical behavior such as the spontaneous symmetry breaking, modulational instability or complex and persistent flow of currents between the rings [27,28]. In the present work we concentrate on the route of chaos, which may be observed in this system as demonstrated numerically in Sec.…”