We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain.
We demonstrate that periodic self-imaging of light patterns with certain input periods can be effectively realized in one-dimensional and two-dimensional helical waveguide arrays. The band structure is drastically dependent on the helix radius and period, and the complete collapse of quasi-energy bands occurs for a certain helix radius and period, which strongly affects the intensity carpet and the Talbot length of the Talbot self-imaging effect. Talbot length would extend to infinity, as the helix radius and period approach the corresponding critical values corresponding to the band collapse, where the inversion of intensity distribution between even and odd waveguides is observed for the binary input pattern with phase shift between the adjacent waveguides.
Linear dynamics of an accelerating wave packet, which is produced by adding shifted copies of the fundamental Airy beam, due to parabolic optical potentials are investigated. A new type of self-imaging phenomenon, referred to as period-reversal accelerating self-imaging, is demonstrated theoretically and numerically. Unlike ordinary Talbot effects, where optical field pattern reappears at constant intervals and follows a straight line, here, the field pattern of this new self-imaging effect propagating along a periodic oscillating trajectory, can self-reproduces itself at nonconstant intervals, and begins to invert after the phase transition points, where the superposition of fundamental Airy beams forms multi-beams interference fringes. A completely spatially reversal replica of the initial field distribution is observed at odd multiplies of the period halves. Moreover, the properties of the multi-beams interference fringes are discussed in detail and can be used for the measurement of the system parameter. The above results can be generalized in the case of two transverse dimensions, where it can be treated as a product of two independent one-dimensional cases. The theoretical calculations and numerical simulations verify each other completely.
16 October 2018 in Journal of the Optical Society of America B
We investigate the propagation dynamics of Airy beams in competing nonlocal nonlinear media featuring focusing cubic and defocusing quintic nonlocal optical nonlinearities. By means of numerical methods, it has been shown that the solitons shedding from Airy beams and their interaction are strongly dependent on the strength of nonlinearity and degree of nonlocality. In a highly nonlocal regime, anomalous interaction of two Airy solitons with high intensity leads to the formation of stable bound states in both in-phase and out-of-phase cases.