Journal or Book Title
PHYSICAL REVIEW E
We introduce a ladder-shaped chain with each rung carrying a parity-time- (PT -) symmetric gain-loss dimer. The polarity of the dimers is staggered along the chain, meaning alternation of gain-loss and loss-gain rungs. This structure, which can be implemented as an optical waveguide array, is the simplest one which renders the system PT -symmetric in both horizontal and vertical directions. The system is governed by a pair of linearly coupled discrete nonlinear Schrödinger equations with self-focusing or defocusing cubic onsite nonlinearity. Starting from ¨ the analytically tractable anticontinuum limit of uncoupled rungs and using the Newton’s method for continuation of the solutions with the increase of the inter-rung coupling, we construct families of PT -symmetric discrete solitons and identify their stability regions. Waveforms stemming from a single excited rung and double ones are identified. Dynamics of unstable solitons is investigated too.
D'Ambroise, Jennie; Kevrekidis, Panayotis G.; and Malomed, B. A., "Staggered Parity-Time-Symmetric Ladders With Cubic Nonlinearity" (2015). PHYSICAL REVIEW E. 1249.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1249