Surface Plasmon Resonance Spectroscopy of Dielectric Coated Gold and Silver Films on Supporting Metal Layers: Reflectivity Formulas in the Kretschmann Formalism

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Abstract
In surface plasmon resonance (SPR) studies of thin films, a binder metal (Cr, W, or Ti) is often used to support the SPR-active gold or silver substrate on a glass prism. The optical response of the SPR device is affected by such binder layers, and in the analysis of experimental data, it is necessary to account for these effects. The present report examines the theoretical considerations for SPR spectroscopy involving these types of supported substrates. It is shown that usually, the binder effects are weak in the neighborhood of the resonance angle. In the same region, the SPR plot exhibits an approximately Lorentzian behavior and is characterized here by extending the previously known Kretschmann formalism to a five-phase system. The calculations lead to a set of analytical formulas, indicating the limiting factors of the binder metal and expressing the reflectivity of the multilayer structure in terms of the thickness and dielectric function of the sample layer. In addition, these formulas explicitly show how the characteristic features of SPR plots are governed by certain experimental variables. The calculations provide a relatively simple framework for analyzing the results of SPR studies that focus primarily on resonance angle measurements.