Gap solitons in photorefractive medium with PT-symmetric optical lattices

• Gap solitons in photorefractive media with parity and time reversal symmetric optical lattices.
• The existence condition for semi-infinite bandgap solitons is found.
• The dynamical and linear stabilities of the semi-infinite gap solitons are investigated.
• The gap solitons are unstable above a certain value of the model parameter.

We find the existence and stability conditions of semi-infinite gap solitons in photorefractive media with parity and time (PT) reversal symmetric complex optical lattices. When the strength of the gain/loss term of complex potential is below the critical value, where the PT-symmetry of the system is unbroken, both the finite and semi-infinite bandgap solitons can exist. The dynamical propagation, Vakhitov–Kolokolov (VK) stability criterion, and linear perturbation stability analysis confirm the stability of the semi-infinite bandgap solitons. All gap solitons in the finite bandgap are found to be dynamically unstable even though they satisfy the VK criterion for stability. We reveal that for the complex potential strength above the critical value only unstable semi-infinite bandgap solitons exist due to the presence of complex propagation constant as a result of the broken PT-symmetry.