Gap solitons in PT-symmetric optical lattices with higher-order diffraction

Abstract

The existence and stability of gap solitons are investigated in the semi-infinite gap of a parity-time (PT)-symmetric periodic potential (optical lattice) with a higher-order diffraction. The Bloch bands and band gaps of this PT-symmetric optical lattice depend crucially on the coupling constant of the fourth-order diffraction, whereas the phase transition point of this PT optical lattice remains unchangeable. The fourth-order diffraction plays a significant role in destabilizing the propagation of dipole solitons. Specifically, when the fourth-order diffraction coupling constant increases, the stable region of the dipole solitons shrinks as new regions of instability appear. However, fundamental solitons are found to be always linearly stable with arbitrary positive value of the coupling constant. We also investigate nonlinear evolution of the PT solitons under perturbation.

Nonlinear waves inPT-symmetric systems

“…Finishing this review of generalized PT -symmetric lattice models, we also mention other possibilities such as chirped (quasi-periodic) PT lattices (Chun-Yan, Chang-Ming, and Liang-Wei, 2013) and effects of higher-order diffraction on PT models (Ge et al, 2014).…”

Energy levels for $\mathcal{PT}$-symmetric deformation of the Mathieu equation

“…We intend to explore the consequences of a non-Hermitian, but PT -symmetric, deformation on the Mathieu equation. In the past few years, different approaches were considered in the literature which proposed some kind of deformation [9,10,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. In the context of PT symmetry, the first works to discuss a periodic potential were Refs.…”

Gap solitons supported by two-dimensional parity-time-symmetric optical lattices in saturable media with fourth-order diffraction

“…For the ultra-short optical pulse propagation, the higherorder diffraction or dispersion should be considered and the fourth-order dispersion can play a key role in photonic crystal fiber cavity [35,36]. Fundamental and out-of-phase dipole gap solitons have been studied in 1D PT-symmetric optical lattices [37] and PT-symmetric mixed linear-nonlinear optical lattices [38] with Kerr nonlinearity and a fourth-order diffraction property. Variations in the coupling constant of the fourth-order diffraction cannot change the critical threshold of the 1D PTsymmetric optical lattices but these variations can affect the stability regions of the fundamental [38] and out-of-phase dipole [37,38] solitons significantly.…”

“…Fundamental and out-of-phase dipole gap solitons have been studied in 1D PT-symmetric optical lattices [37] and PT-symmetric mixed linear-nonlinear optical lattices [38] with Kerr nonlinearity and a fourth-order diffraction property. Variations in the coupling constant of the fourth-order diffraction cannot change the critical threshold of the 1D PTsymmetric optical lattices but these variations can affect the stability regions of the fundamental [38] and out-of-phase dipole [37,38] solitons significantly. When the coupling constant of the fourth-order diffraction is increased, the stability region of the out-of-phase dipole solitons in 1D PT-symmetric optical lattices with focusing Kerr nonlinearity decreases in size [37].…”