Abstract
The propagation of surface plasmon–polaritons is investigated in a metallic, fractal-like structure based on Cantor set. The dynamic of plasmonic modes generating on the Cantor structure is discussed in the context of the setup geometry. The numerically obtained reflection spectra are analyzed with the box-counting method to obtain their dimension, which is shown to be dependent on the geometry of the plasmonic structure. The entropy of the structure is also calculated and shown to be proportional to the dimension. Presented analysis allows for extracting information about fractal plasmonic structure from the reflectance spectrum. Predictions regarding the experimental observation of discussed effects are presented.
Highlights
Over the past decades, the study of electromagnetic waves propagating at the interface between a metal and dielectric has been of significant interest
The study of electromagnetic waves propagating at the interface between a metal and dielectric has been of significant interest. In such a physical system the energy of the electromagnetic field is confined to sub-wavelength size supporting localized surface plasmon polariton (SPP) modes
The presented relations are repeatable across different systems and hold in the presence of noise. These results suggest that the proposed approach is viable for realistic, random and semi-random fractal-like structures
Summary
The study of electromagnetic waves propagating at the interface between a metal and dielectric has been of significant interest In such a physical system the energy of the electromagnetic field is confined to sub-wavelength size supporting localized surface plasmon polariton (SPP) modes. Their unusual properties depend on the metal and geometry of the material structure, which plays a crucial role in local electromagnetic enhancement and tuning the resonance positions. Such interdependences have been recently studied regarding the impact of the nonlocality of the surface structure on the dispersion relation of SPP [1]. In recent years there has been continuous interest in the development of fractal metamaterials, which could be used in high-gain, compact, multiband antennas [7,8,9]
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