Abstract
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.
Highlights
In Eq (1), we consider that the PT-symmetric periodic potential is given by the functions v (x) = V 0 cos2(x + φ) and w (x) = ω0 sin(2x + 2φ), where V0 and ω0 are amplitudes of real and imaginary parts of periodic potential, respectively; φ = 0, π/2 correspond to two different complex refractive index distributions, namely on-site and off-site nonlinearity, depending on whether the real part of modes is symmetric and antisymmetric, in x
I.e., on-site and off-site solitons supported by the PT-symmetric periodic potential can be formed for both the self-focusing nonlinearity and varied nonlinearity
On-site lattice solitons belonging to the semi-infinite band gap can propagate stably in whole existence domain, but off-site lattice solitons belonging to this band gap are unstable in the entire domain of their existence
Summary
We address the existence and stability of solitons in PT-symmetric periodic systems with a saturable nonlinearity, the perturbed index nonlinear change of which varies logarithmically incident optical beam normalized intensity I and is scales with ln(σ +I), where σ = 1 and 0 is an relevant saturable parameter, corresponding to the self-focusing nonlinearity and changing nonlinearity (i.e., the logarithmic function is positive at I > 1 and negative at I < 1), respectively. We investigate solitons and their stability supported by PT-symmetric periodic lattice with logarithmical self-focusing nonlinearity (σ = 1).
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