Fundamental and multipole solitons in amplitude-modulated Fibonacci lattices.

We investigated the existence and stability of fundamental and multipole solitons supported by amplitude-modulated Fibonacci lattices with self-focusing nonlinearity. Owing to the quasi-periodicity of Fibonacci lattices, families of solitons localized in different waveguides have different properties. We found that the existence domain of fundamental solitons localized in the central lattice is larger than that of solitons localized in the adjacent central waveguide. The former counterparts are completely stable in their existence region, while the latter have a narrow unstable region near the lower cut-off. Two families of dipole solitons were also comprehensively studied. We found the outer lattice distribution can significantly change the existence region of solitons. In addition, we specifically analyzed the properties of four complicated multipole solitons with pole numbers 3, 5, 7, and 9. In the Fibonacci lattice, their field moduli of multipole solitons are all asymmetrically distributed. The linear-stability analysis and direct simulations reveal that as the number of poles of the multipole soliton increases, its stable domain is compressed. Our results provide helpful insight for understanding the dynamics of nonlinear localized multipole modes in Fibonacci lattices with an optical nonlinearity.