Staggered parity-time-symmetric ladders with cubic nonlinearity

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 Schrodinger 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.