Gap solitons in parity-time-symmetric lattices with fractional-order diffraction
Lei Li, Huagang Li, Wen Ruan, Feng-Chun Leng, Xiaobing Luo
Abstract
We investigate new types of gap solitons in a periodic parity-time (PT)-symmetric lattice with fractional-order diffraction. Both the fundamental and dipole solitons in the first and second gaps are discussed. It is found that fractional-order diffraction can not only stabilize low-power dipole PT solitons in the first gap under focusing nonlinearity, but also help to get stable dipole PT solitons in the second gap under defocusing nonlinearity. Additionally, the influence of the strength <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>w</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:mrow> </mml:math> of the gain–loss component on the properties of solitons is also analyzed. It is shown that increasing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>w</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:mrow> </mml:math> is unfavorable to the stability of fractional fundamental solitons, especially for the second gap, while for fractional dipole solitons, the increase of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>w</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:mrow> </mml:math> may lead to their destabilization in the first gap, but stabilization in the second gap.