The Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport (original) (raw)

We consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there exist finite-power, constant-intensity nonlinear supermodes (NS), resulting from the balance between gain, loss, nonlinearity, coupling and dissimilarity. The system is shown to possess non-reciprocal dynamics enabling directed power transport functionality. Energy transport between coupled systems or different modes of the same system is one of the most fundamental problems in physics and the controlled and directed transport is of great importance in many technological applications such as electronic and optical devices. For the latter, the design and implementation of integrated photonic devices is a major challenge requiring the realization of a set of fundamental elements for photonic circuitry, such as couplers, switches, diodes and isolators for the directed transport of the optical power 1. The nonlinear coherent coupler 2,3 has been widely studied as a basic photonic component allowing for power-sensitive energy transport. The presence of nonlinearity, in principle, allows for the breaking of Lorentz-reciprocity which is a key mechanism for various applications related to unidirectional dynamics and optical isolation 4,5. It has been shown 6,7 that the presence of gain and/or loss in this system renders its dynamics more complex and enriches its functionality. Moreover, in the case where the gain in one channel is exactly equal to the loss in the other channel, the coupler can be considered as a PT-symmetric dimer, and has been shown to possess unidirectional dynamics 8,9 which is the key property for an optical diode. Similar properties have been studied for a large variety of such PT-symmetric photonic structures, extending the theoretical interest on these systems 10-14 , to realistic experimental studies on light propagation in coupled waveguide structures based either on AlGaAs heterostructures 15 or on Fe-doped LiNbO 3 16 at wavelengths of 1550 nm and 514.5 nm, respectively. The PT-symmetric systems have been considered for important applications such as the non-reciprocal light transmission 17-19 , the observation of asymmetric transport 20,21 , the study of active coupling mechanisms 22 , and the synthesizing of unidirectionally invisible media 23. Also, PT-symmetric cavities have been studied with respect to interesting properties of resonant mode control and selection, which is of crucial importance in laser physics 24-26. The presence of gain and loss along with the nonlinearity of a photonic structure has also been shown to support bright and dark solitons in dual-core systems 27-30 and to provide soliton control capabilites in photonic structures with homogeneous gain and loss 31,32 as well as in structures with symmetric 33 or nonsymmetric 34,35 spatially inhomogeneous gain and loss. Finally, we stress the relation of the underlying model of active photonic structures, consisting of coupled mode equations, with similar models used in the study of quantum systems including Bose-Einstein and exciton-polariton condensates 36-38. The PT-symmetric dimer is known to generate unstable dynamics above the parameter threshold which separates the PT-exact phase from the PT-broken phase 39. One way to regain stability is to use the analogy to dissipatively coupled exciton-polariton condensates in the weak lasing regime 36,37. In the optical coupler case this implies to place an active medium in the evanescent wave region of the coupler 22. This is a rather complicated and intricate experimental task, because the pumping in the evanescent wave region can easily lead to an overpumping, which will substantially modify the used underlying model equations.