Hierarchical Plasmon Resonances in Fractal Structures

Abstract

An equilateral triangular prism is used as the fundamental building block to construct additive Sierpiński fractals, enabling new surface plasmon resonances (SPR) in the first three generations of Sierpiński triangles, as well as topological intermediaries between generations. The modes are characterized using electron energy loss spectroscopy accompanied by eigenmode calculations and optical finite-difference time-domain simulations. The complex fractal geometries present a predictable hierarchy of new resonances, each arising from the previous generational building blocks used to construct the fractal. Intermediate structures break the polarization degeneracy of the equilateral fractals while maintaining a rich multiband spectral response. Engineering defects in the narrow conductive channels of the fractal allows further manipulation of the SPR response, emphasizing higher order SPR modes over the lowest energy peak. The knowledge gained is used to develop guidelines for engineering the response of more complex fractal-based structures, including the spectral response and hotspot distribution.

Surface Plasmon Resonances in Sierpinski-Like Photonic Crystal Fibers: Polarization Filters and Sensing Applications

“…Moreover, the interaction between nearby metallic scatterers increases the number of allowed resonances through plasmonic hybridization [ 46 , 47 ], i.e., the overlap of plasmonic near-fields between adjacent metallic scatterers, which resembles the electronic bands from well-localized atomic orbitals in solid state physics [ 48 , 49 ]. The fractional sizes of different nearby scatterers, i.e., the fractal-like geometry, also introduce a broadening of the frequency range for SPR excitation [ 38 , 41 ]. In Figure 2 , we plot the and -values (confinement loss) for ranging from 630 nm to 1700 nm.…”

“…Importantly, using this fractal design we found a set of 34 plasmonic modes in the frequency range from 630 nm to 1700 nm, which enable applications from the visible to the infrared regime. These multiple resonances are explained by self-similar effects, which as recently demonstrated for triangular Sierpinski fractals are due to self-similar hierarchy of metallic scatterers in the structure [ 38 , 41 ]. Calculations in this work were made using the finite element method (FEM), through the commercial software COMSOL Multiphysics ® .…”

“…The use of fractal geometries, on the other hand, has been successfully exploited during the last decades for the realization of multiband (or broadband) compact and high-performance antennas [ 34 , 35 , 36 ]. More recently, these self-similar geometries have also enabled multispectral compatibility and multiple applications when used for patterning one- and two-dimensional plasmonic superlattices [ 37 , 38 , 39 , 40 , 41 ]. In contrast, self-similar plasmonic properties in SPR-PCFs remain unexplored.…”

Aluminum Cayley trees as scalable, broadband, multiresonant optical antennas

“…This unprecedented range of tunability is experimentally evidenced using electron energy loss spectroscopy (EELS), a powerful tool allowing us to simultaneously obtain a spectrum analogous to an unpolarized optical extinction spectrum ( 25 ) and perform a spatial mapping of the resonances with nanoscale resolution ( 26 ). As such, EELS is well suited to the experimental study of optical antennas and has been applied to the characterization of antennas of various geometries ( 14 , 17 , 18 , 27 ), including fractals ( 24 , 28 , 29 ). In order to unveil all the electromagnetic resonances sustained by the Al Cayley trees, it is necessary to probe the mid-IR regime.…”

Aluminum Cayley trees as scalable, broadband, multi-resonant optical antennas

“…This unprecedented range of tunability is experimentally evidenced using electron energy loss spectroscopy (EELS), a powerful tool allowing to simultaneously obtain a spectrum analogous to an unpolarized optical extinction spectrum [25], and to perform a spatial mapping of the resonances with nanoscale resolution [26]. As such, EELS is well-suited to the experimental study of optical antennas and has been applied to the characterization of antennas of various geometries [14,17,18,27], including fractals [24,28,29]. In order to unveil all the electromagnetic resonances sustained by the Al Cayley trees, it is necessary to probe the mid-IR regime.…”