Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties.

The plasmonic nanostructures are widely used to design sensors with improved capabilities. The position of the localized surface plasmon resonance (LSPR) is part of their characteristics and deserves to be specifically studied, according to its importance in sensor tuning, especially for spectroscopic applications. In the visible and near infra-red domain, the LSPR of an array of nano-gold-cylinders is considered as a function of the diameter, height of cylinders and the thickness of chromium adhesion layer and roughness. A numerical experience plan is used to calculate heuristic laws governing the inverse problem and the propagation of uncertainties. Simple linear formulae are deduced from fitting of discrete dipole approximation (DDA) calculations of spectra and a good agreement with various experimental results is found. The size of cylinders can be deduced from a target position of the LSPR and conversely, the approximate position of the LSPR can be simply deduced from the height and diameter of cylinders. The sensitivity coefficients and the propagation of uncertainties on these parameters are evaluated from the fitting of 15500 computations of the DDA model. The case of a grating of nanodisks and of homothetic cylinders is presented and expected trends in the improvement of the fabrication process are proposed.