Optical properties of two dimensional fractal shaped nanostructures: Comparison of Sierpinski triangles and Sierpinski carpets

Sound-scattering properties of Sierpinski triangle fractal structures in the near field

“…The Sierpinski triangle is a self-similar structure with the overall shape of a triangle and subdivided recursively into smaller triangles [29]. We used isosceles right triangles as the base of the fractal pattern to make the designed diffusers easily integrated into the surfaces of buildings (e.g., walls, facades).…”

“…As one of the most famous fractal patterns, the Sierpinski triangle is a self-similar structure discovered by Waclaw Sierpinski in the 1900s [29]. Xu et al [30] investigated the visual acceptance of the Sierpinski fractal multi-level modular diffuser through eye-tracking and semantic differential technique and found a more impressing appearance than conventional QRDs.…”

Photonic band structure in a two-dimensional photonic crystal with a Sierpinski triangle structure

“…Using the TMM, the results reveal that the transmittance spectrum undergoes a peak split as the sequence length increases. For a two-dimensional case, a fractal structure of interest is a Sierpinski lattice, which is used to investigate the optical absorption in semiconductor nanosystems by solving the Schrodinger equation using the finite difference method [40]. Huang et al [41] used the finite element method to determine the elastic wave dispersion relation in a heterostructure with Sierpinski carpet unit cells, which is composed of square Pb cylinders inserted in a rubber matrix.…”