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 Schrodinger 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.

中文翻译：

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二维分形纳米结构的光学特性：谢尔宾斯基三角形和谢尔宾斯基地毯的比较

摘要 在目前的研究中，我们首次对固定表面积谢尔宾斯基三角形和谢尔宾斯基地毯的光学特性进行了数值研究。我们在笛卡尔坐标系中采用三点中心差分法求解二维薛定谔方程。通过使用提议的谢尔宾斯基系统，波函数工程现在成为可能。我们说明了谢尔宾斯基三角形和地毯限制势中的波函数对称破缺和对称守恒。我们还评估了所研究系统的光学特性的可调性，并确定了更可调的一个。我们表明，在谢尔宾斯基地毯和三角形中，吸收系数的行为是完全不同的。