Electromagnetic Bloch-like oscillations in Fibonacci metamaterial waveguide arrays

In this paper, we present optical transportation in metamaterial waveguide arrays (MMWAs) that exhibit Bloch-like oscillations (BLOs). The metamaterial waveguide array is created by laterally combining the metal and dielectric layers in Fibonacci sequence. By mapping the field distribution of a Gaussian wave packet in the corresponding waveguide arrays, the mechanical evolution is visualized directly in a classical wave environment. On the basis of this approach, three types of oscillation modes are obtained at different incident positions in the ninth generation Fibonacci structure, where no thickness gradient or refractive index gradient is introduced in any layer. Furthermore, the spreading period of the BLOs increases with a redshift of the incident wavelength for both ninth and tenth generation Fibonacci MMWAs, providing a valuable way to manipulate the emergence of BLOs.