Quasi-analytical model for scattering infrared near-field microscopy on layered systems

Abstract

We present a quantitative quasi-analytical model to predict and analyze signals on layered samples measured by infrared scattering-type scanning near-field optical microscopy. Our model predictions are compared to experimental data and to fully retarded calculations based on a point dipole approximation of the tip. The model is used to study the influence of the tip vibration amplitude and of the tip radius on the near-field contrasts of samples with particularly small variations in the layer thickness. Additionally the influence of a dielectric capping layer on the tip-substrate coupling is analyzed. When inversely applied, our calculation opens the possibility to extract the local layer thickness of thin films or the dielectric functions that allow one to draw conclusions on the material composition, conductivity or crystal structure on the nanoscale.

Model for quantitative tip-enhanced spectroscopy and the extraction of nanoscale-resolved optical constants

“…A function of both frequency ω and in-plane momentum q, the Fresnel coefficient describes the relative magnitude and phase of p-polarized light reflected from the surface of material with frequency-dependent dielectric function (ω). While important theoretical advances have brought near-field spectroscopy beyond qualitative descriptions [27][28][29][30][31][32] , available models describing the probesample near-field interaction remain beset by critical limitations:…”

“…9,32,34,35 One can show that such series are divergent beyond modest values of r p (the "strong coupling" regime), leaving this method inapplicable for the analysis of crystalline solids and strongly resonant plasmonic systems. 31 3. A number of tunable geometric parameters with ad hoc or empirical values are introduced to quantitatively fit measured data.…”

“…A number of tunable geometric parameters with ad hoc or empirical values are introduced to quantitatively fit measured data. These include fractional weights of relevant probe surface charge, 30,31 effective probe size and geometry, [28][29][30] the bare tip polarizability, etc. 20 The multitude of ad hoc tunable parameters provides an unreliable recipe for predictive modeling or quantitative interpretation of data.…”

“…We first present a new model of probe-sample near-field interaction, the lightning rod model, whose generality allows exploring the influence of both probe geometry and electrodynamic effects, while remaining formally exact in both theory and implementation. Mathematical reduction of this formalism back to the point dipole model will make clear that unnecessary ad hoc assumptions underpin prevailing models 30,31 , and that geometric and electrodynamic considerations must ultimately play a role in their vindication.…”

Center and pseudo-isochronous conditions in a quasi analytic system

“…For example, an axis-symmetric quasi-analytical model was presented in order to simulate the behavior of a RFEC system during its operation [23]. A quasi-analytical model to predict and analyze signals on layered samples measured by infrared scattering type scanning near-field optical microscopy was modeled in [5]. A simple quasi-analytical model was developed to study the response of ice-sheets to climate change in [24].…”