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

Abstract

In the current study, for the first time, we numerically investigate the optical properties of fixed surface area Sierpinski triangles and Sierpinski carpets. We solve the two dimensional Schrödinger equation by using three-point centered difference method in the Cartesian coordinate. By using the proposed Sierpinski systems, wave function engineering is now possible. We illustrate the wave function symmetry breaking and symmetry conservation in the Sierpinski triangle and carpet confining potentials. We have also evaluated the tunability of the optical properties of the studied systems and determined the more tunable one. We showed that the behavior of the absorption coefficient is completely different in the Sierpinski carpets and triangles. We compared two different system shapes of the case I (antidot) and case II (dot) systems and discussed the differences in their optical properties.