Multipole gap solitons in fractional Schrodinger equation with parity-time-symmetric optical lattices

We investigate the existence and stability of in-phase three-pole and four-pole gap solitons in the fractional Schrodinger equation supported by one-dimensional parity-time-symmetric periodic potentials (optical lattices) with defocusing Kerr nonlinearity. These solitons exist in the first finite gap and are stable in the moderate power region. When the Levy index decreases, the stable regions of these in-phase multipole gap solitons shrink. Below a Levy index threshold, the effective multipole soliton widths decrease as the Levy index increases. Above the threshold, these solitons become less localized as the Levy index increases. The Levy index cannot change the phase transition point of the PT-symmetric optical lattices. We also study transverse power flow in these multipole gap solitons. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement