Abstract
In this paper, the scattering properties of two-dimensional quasicrystalline plasmonic lattices are investigated. We combine a newly developed synthesis technique, which allows for accurate fabrication of spherical nanoparticles, with a recently published variation of generalized multiparticle Mie theory to develop the first quantitative model for plasmonic nano-spherical arrays based on quasicrystalline morphologies. In particular, we study the scattering properties of Penrose and Ammann- Beenker gold spherical nanoparticle array lattices. We demonstrate that by using quasicrystalline lattices, one can obtain multi-band or broadband plasmonic resonances which are not possible in periodic structures. Unlike previously published works, our technique provides quantitative results which show excellent agreement with experimental measurements.
Highlights
The cut-and-project method constructs QC lattices as lower-dimensional slices of higher-dimensional periodic hyper-lattices[17]
generalized multiparticle Mie theory21 (GMT) is far superior to the discrete dipole approximation (DDA) method which tends to be less accurate for closely packed metal spheres in the plasmonic regime
There is a close relationship between diffraction patterns and the Fourier transform (FT)
Summary
The cut-and-project method constructs QC lattices as lower-dimensional slices of higher-dimensional periodic hyper-lattices[17]. Analyzing plasmonic structures using traditional full-wave finite-difference and finite-element techniques requires considerable computational resources even for relatively simple configurations[19] For this reason, there has been recent interest in developing more efficient analytical tools which offer solutions several orders of magnitude faster than is possible with finite-difference and finite-element methods. GMT is a transfer matrix method based on an extension of Mie theory to a system with multiple spheres This is a rigorous multiparticle approach which provides a complete solution to Maxwell’s equations and takes into account all the multipolar scattering orders. It has been shown that in order to obtain accurate results for gold (Au) spheres with diameters on the order of 100 nm, in the near-IR region using the DDA method, about 107 dipoles per sphere are required[24] This renders the method impractical for analysis of arrays due to the demanding computational burden. The second issue had to do with the incident field used in the GMT simulations in ref
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