Abstract
We address the properties of nonlinear localized gap modes supported by the width-modulated Fibonacci lattices, including their existence and stability. Linear system with the width-modulated Fibonacci lattices has multiple gaps. We find the existence of different families of nonlinear localized modes in two relatively large gaps. One of the nonlinear localized gap modes originates from the upper band-edge linear mode. Such gap modes are mostly stable in their entire existence domain, except for a small region in the middle of their existence. The other two families of nonlinear modes localized in the relatively large gap are pure nonlinear modes, and they have a narrow stable region near their upper cutoff. The results of the linear stability analysis are in good agreement with that of the propagation simulations.
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