Novel insight into the physics of short-range ordered nanoholes: Newly defined lattice model and transmittance response related to lattice parameters and ordering evolution

This paper presents unforeseen conceptualization, methods and results on the physics of short-range ordered (SRO) gold nanohole (NH) distributions, fabricated by a recent protocol developed by the authors. The straightforward extension to SRO-NHs of the existing knowledge about periodic NH arrays is confuted and an alternative interpretative picture is proposed and discussed based on three main advancements. First, it is set up a so-called short-range lattice (SR-Lat) method to rigorously and fully characterize the coverage-dependent short-range ordering through the determination of local coordination and periodicity length (aSR) of the NH arrangement. Second, it is demonstrated the failure of the common assumption that the average center-to-center distance of nearest neighbor colloids/nanoholes (dNN) is the characteristic length-scale of SRO-NHs and aSR is set as the proper periodicity parameter. Third, a predictive relationship is formulated between the wavelength of the propagating plasmon modes and aSR that highlights inherent differences with respect to periodic NHs. The presented results lay rigorous foundation for studying systems with correlated diosrdering in general and for making predictions useful not only in design and applications of SRO-NHs, but also on the surface physics in the photonics and sensing fields.