Periodic physical systems, where a finite band gap in the underlying linear spectrum always opens, have aroused a concern in the studies of wave localizations and dynamics properties, in past decades.

Recent studies have pushed the periodic physical systems to their nonlinear counterparts, namely, the systems with a nonlinear lattice — the periodic potential acts merely on the nonlinear term (the coefficient in front of nonlinearity) wherein the strength and even the sign could be changed periodically.

Besides the fundamental gap solitons, another novel type of self-trapped localized states that are being viewed as truncated nonlinear Bloch waves (TBWs) or gap waves, which reside in the band gap of the linear Blochwave spectrum too, were also found in periodic systems.

The studies of gap solitons have so far mainly focused on defocusing (repulsive) nonlinearity, while their properties under focusing (attractive) nonlinearity have not been well understood (only few papers focused on this topic), and the experimental verification remains a blank.

In this article, a research team led by Prof. Dr. ZENG Jianhua from Xi'an Institute of Optics and Precision Mechanics (XIOPM) of the Chinese Academy of Sciences (CAS) aim to find the self-trapped spatially localized wave structures of gap types, in the forms of aforesaid gap solitons and TBWs, in one- and two- dimensional (1D and 2D) focusing nonlinear periodic system consisted of (linear) optical and nonlinear periodic lattice potentials — the combined linear-nonlinear lattices model.

（Original research article " Frontiers of Physics volume 15, Article number: 12602(2020) https://doi.org/10.1007/s11467-019-0930-3"）