Abstract
Multiple beam interferometry (MBI) evolved as a powerful tool for the simultaneous evaluation of thin film thicknesses and refractive indices in Surface Forces Apparatus (SFA) measurements. However, analysis has relied on simplifications for providing fast or simplified analysis of recorded interference spectra. Here, we describe the implementation of new optics and a generalized fitting approach to 4 × 4 transfer matrix method simulations for the SFA. Layers are described by dispersive complex refractive indices, thicknesses, and Euler angles that can be fitted, providing modeling for birefringent or colored layers. Normalization of data by incident light intensities is essential for the implementation of a fitting approach. Therefore, a modular optical system is described that can be retrofit to any existing SFA setup. Real-time normalization of spectra by white light is realized, alignment procedures are considerably simplified, and direct switching between transmission and reflection modes is possible. A numerical approach is introduced for constructing transfer matrices for birefringent materials. Full fitting of data to the simulation is implemented for arbitrary multilayered stacks used in SFA. This enables self-consistent fitting of mirror thicknesses, birefringence, and relative rotation of anisotropic layers (e.g., mica), evaluation of reflection and transmission mode spectra, and simultaneous fitting of thicknesses and refractive indices of media confined between two surfaces. In addition, a fast full spectral fitting method is implemented for providing a possible real-time analysis with up to 30 fps. We measure and analyze refractive indices of confined cyclohexane, the thickness of lipid bilayers, the thickness of metal layers, the relative rotation of birefringent materials, contact widths, as well as simultaneous fitting of both reflection and transmission mode spectra of typical interferometers. Our analyses suggest a number of best practices for conducting SFA and open MBI in an SFA for increasingly complex systems, including metamaterials, multilayered anisotropic layers, and chiral layers.
Highlights
Thin film studies using multiple-beam interferometry (MBI) evolved as a powerful tool for measuring absolute thicknesses and complex refractive indices, ñ, of nanometer confined thin films between apposing surfaces
Our analyses suggest a number of best practices for conducting Surface Forces Apparatus (SFA) and open Multiple beam interferometry (MBI) in an SFA for increasingly complex systems, including metamaterials, multilayered anisotropic layers, and chiral layers
Implemented in the Surface Forces Apparatus (SFA), which was pioneered by Tabor, Winterton, and Israelachvili,2–4 MBI provided direct quantification of fundamental interaction forces across surfaces and thin-film properties down to separation distances D below 1 nm, including the first measurement of van der Waals forces,5 hydration layering,6 or hydrophobic interactions
Summary
Thin film studies using multiple-beam interferometry (MBI) evolved as a powerful tool for measuring absolute thicknesses and complex refractive indices, ñ, of nanometer confined thin films between apposing surfaces. The resulting thin-film modifications have defined thicknesses (Λm and/or Λ′m) and refractive indices (ñm and n′m) and can be applied using a number of approaches including formation of supported lipid bilayers as well as self-assembled silane monolayers.13,14 Another frequently used interferometer layout is formed by facing one back-silvered mica surface against a smooth metal surface (usually, e.g., gold, platinum, and palladium) templated from mica or evaporated by magnetron sputtering or physical vapor deposition (PVD). This work explicitly already includes partial transfer matrices for a slab of a continuously twisted biaxial material at normal incidence, and arbitrary isotropic and randomly distributed anisotropic slabs, as well as incident and exit matrices We previously applied this approach to model only a few monolayer-thin, oxide layers formed electrochemically on various noble metals.. Implementation of Schubert’s approach, which is well established and tested in other fields, will open MBI for increasingly complex systems, e.g., with transfer matrices readily at hand for metamaterials, arbitrarily multilayered and anisotropic layers or chiral layers
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