Solitons in PT-symmetric ladders of optical waveguides

Abstract

We consider a PT-symmetric ladder-shaped optical array consisting of a chain of waveguides with gain coupled to a parallel chain of waveguides with loss. All waveguides have the focusing Kerr nonlinearity. The array supports two co-existing solitons, an in-phase and an antiphase one, and each of these can be centred either on a lattice site or midway between two neighbouring sites. We show that both bond-centred (i.e. intersite) solitons are unstable regardless of their amplitudes and parameters of the chain. The site-centred in-phase soliton is stable when its amplitude lies below a threshold that depends on the coupling and gain-loss coefficient. The threshold is lowest when the gain-to-gain and loss-to-loss coupling constant in each chain is close to the interchain gain-to-loss coupling coefficient. The antiphase soliton in the strongly-coupled chain or in a chain close to the PT-symmetry breaking point, is stable when its amplitude lies above a critical value and unstable otherwise. The instability growth rate of solitons with small amplitude is exponentially small in this parameter regime; hence the small-amplitude solitons, though unstable, have exponentially long lifetimes. On the other hand, the antiphase soliton in the weakly or moderately coupled chain and away from the PT-symmetry breaking point, is unstable when its amplitude falls in one or two finite bands. All amplitudes outside those bands are stable.

32 pages, 13 figures. To appear in New Journal of Physics

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Cited by in corpus (4)

• Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric systems with spin-orbit coupling and critical nonlinearity
• Dynamical control of solitons in a parity-time-symmetric coupler by periodic management
• Stable solitons in a nearly PT-symmetric ferromagnet with spin-transfer torque