Solitons in a chain of parity-time-invariant dimers

Abstract

Dynamics of a chain of interacting parity-time-invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrödinger (DNLS) equation is demonstrated. Approximate solutions for solitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart of the discrete equations. These solitons are mobile, featuring nearly elastic collisions. Stationary solutions for narrow solitons, which are immobile due to the pinning by the effective Peierls-Nabarro potential, are constructed numerically, starting from the anticontinuum limit. The solitons with the amplitude exceeding a certain critical value suffer an instability leading to blowup, which is a specific feature of the nonlinear parity-time-symmetric chain, making it dynamically different from DNLS lattices. A qualitative explanation of this feature is proposed. The instability threshold drops with the increase of the gain-loss coefficient, but it does not depend on the lattice coupling constant, nor on the soliton's velocity.

Nonlinear switching and solitons in PT‐symmetric photonic systems

“…Continuum versions of such models have been analyzed in the works [164][165][166]. In other cases soliton dynamics is investigated in the two-core systems such as an array of coupled PT-symmetric dimers [85,167] and its continuum version in the form of coupled planar waveguides with gain in one of them and balanced loss in another [77,168]. Two-dimensional generalization of such models was studied in [169].…”

“…The discussed model (29) as well its discrete counterpart do not admit dark soliton solutions [see for example [85]]. However nonlinear coupling between waveguides (cross-phase modulation) can facilitate the formation of dark and bright solitons.…”

Wave scattering on a domain wall in a chain ofPT-symmetric couplers

“…It may be interesting to add nonlinearity to the system. In addition to the formation of solitons [8], the nonlinearity may give rise to spontaneous symmetry breaking [6]. Obviously, these effects may strongly affect the scattering problem.…”

“…[8], with the gain-and loss-carrying units coupled to their neighboring counterparts of the same sign [see Fig. 1(a) below].…”

PT-symmetric dimer of coupled nonlinear oscillators

“…However, one of the major milestones (and a principal thrust of recent activity) regarding the physical and experimental realizability of the corresponding Hamiltonians stemmed from progress in optics both at the theoretical [4,5] and at the experimental [6,7] levels. In particular, the realization that, in optics, the ubiquitous loss can be counteracted by an overwhelming gain in order to create a PT -symmetric setup, e.g., in a waveguide dimer [7], paved the way for numerous developments, especially so at the level of nonlinear systems, as several researchers studied nonlinear stationary states, stability, and dynamics of few site configurations [8][9][10][11][12][13][14][15][16] as well as of infinite lattices [17][18][19].…”