Fig. 1. (a) Scheme of FWAs. Light blue and dark red denote waveguides with different n. F₁ to F₆ indicate the first to sixth orders of the Fibonacci sequences. (b) Schematic of the experimental setup used for verifying QWs in different waveguide arrays; both of the propagation dynamics and end-face energy distributions can be acquired by corresponding high-resolution microscopic observation systems with an sCMOS camera and CCD, respectively. Note that the centermost waveguide is extended from the whole array for easy injecting light. (c) Geometrically symmetrical FWAs designed with all basic elements from F₁ to F₆. The red arrow denotes the specific waveguide for injecting light.

Fig. 2. (a) Relationship between mode field diameters (black cubes), coupling coefficients between two evanescently coupled waveguides, where one is scanned at 40 mm/s and the other at 10 to 50 mm/s, respectively (red triangles), and the scanning speeds. Mode field distributions of certain scanning speeds are shown. The scale bar is 2 µm. (b) Relationship between splitting ratio and coupling length for a symmetry DC (both arms are scanned at 40 mm/s) and an asymmetry DC (one arm is scanned at 10 mm/s, and the other is scanned at 40 mm/s); black cubes and yellow triangles denote experimental data at the scanning speeds of 10 and 40 mm/s, respectively, and the corresponding sinusoidal lines are fitted results.

Fig. 3. Propagation dynamics of single excitation. (a1) Theoretical and (a2) experimental results for periodic waveguide arrays, where F₁ and F₂ are identical. (b1) Theoretical and (b2) experimental results for FWAs, where F₁ and F₂ are different. The total length of the propagation is 20 mm, and the coordinate y denotes the propagation direction.

Fig. 4. Propagation dynamics in the waveguide arrays without/with nonlinear perturbation excitation. (a1), (b1), and (c1) show simulated results for injecting linear (γ = 0), nonlinear (γ = 0.2), and strongly nonlinear (γ = 0.5) lights, respectively. (a2), (a4), and (a6); (b2), (b4), and (b6); and (c2), (c4), and (c6) are experimental results of the end-face energy distributions for the waveguide arrays at different coupling lengths (3, 11, and 18 mm), while (a3), (a5), and (a7); (b3), (b5), and (b7); and (c3), (c5), and (c7) are the extracted normalized strengths for the energy distributions. The nonlinear coefficient γ is in the unit of m^-1 W^-1, and we choose the dimensionless quantities for simulations. The coordinate y denotes the propagation direction.