Validity of Machine Learning in the Quantitative Analysis of Complex Scanning Near-Field Optical Microscopy Signals Using Simulated Data

Scattering-type scanning near-field optical microscope (s-SNOM) is a modern technique for subdiffractional optical imaging and spectroscopy. Over the past two decades, tremendous efforts have been devoted to modeling complex tip-sample interactions in s-SNOM, aimed at understanding the electrodynamics of materials at the nanoscale. However, due to complexities in analytical methods and the limited computation power for fully numerical simulations, compromises must be made to facilitate the modeling of tip-sample interaction, such as using quasistatic approximation or unrealistic tip geometries. $\mathrm{In}$ this paper, we apply a variety of widely utilized machine-learning methods, including k nearest neighbor and feed-forward neural network etc. to study the phase-resolved spectroscopic near-field response. With only a small set of training data, which is simulated using the finite-dipole model, we demonstrate that the relation between the experimental near-field signal and sample optical constant can be one to one mapped without the need for tip modeling: for a given material with a moderate dielectric function, its complex near-field spectrum can be accurately determined within the mid-IR spectral range, and vice versa. Our preliminary study sets the stage for future exploration using real experimental data. Our method is beneficial for processing the increasing amount of data accumulated across many research groups and especially useful for user facilities such as synchrotron-based national laboratories where a large amount of data is generated on a daily basis.

Figure 1

(a) Schematics of a typical broadband s-SNOM setup. BS, beam splitter; PM, parabolic mirror. (b) Schematics of the finite-dipole model where the tip is approximated as an elongated spheroid of 1 µm length and 30 nm apex radius. The tip oscillates at its mechanical resonance frequency $\mathrm{\Omega }$ with a 50 nm amplitude. (c), (d) Population distribution of all the training data in the $\epsilon$ space.

Figure 2

IR and THz dielectric functions of sample materials obtained from Ref. [43] and the corresponding near-field spectra calculated by the finite-dipole model. Gold is used as the reference for normalizing the spectra.

Figure 3

(a), (b) Predicted real part and imaginary part of $S_2\mathrm{using}k\mathrm{NN}$ with $k=15$. $S_2$ is encoded as the color map, whereas ${\epsilon }_1$ and ${\epsilon }_2\mathrm{are}$ the x and y axis, respectively. (c), (d) Analytically calculated real and imaginary part of $S_2$, respectively. (e), (f) Difference between the prediction by ML and the analytical solution.

Figure 4

(a) Schematics of the FFNN architecture. (b) A typical SSR as a function of epoch. (c), (d) Predicted real part and imaginary part of $S_2\mathrm{using}$ FFNN trained with noiseless data, respectively. (e), (f) Absolute difference between the prediction and the analytical solution.

Figure 5

(a), (b) Predicted real part and imaginary part of $S_2\mathrm{using}$ FFNN trained with noisy data, respectively. (e), (f) Absolute difference between the prediction and the analytical solution.

Figure 6

Nominal dielectric function, predicted dielectric function using noiseless training data, and predicted dielectric function using noisy training data for (a) ${\mathrm{Si}\mathrm{O}}_2$, (b) PMMA, (c) $\mathrm{K}\mathrm{Br}$, and (d) $\mathrm{Mg}\mathrm{O}$.

Figure 7

(a) Noiseless amplitude and phase spectra of ${\mathrm{Si}\mathrm{O}}_2$ in the pseudodataset. (b) Artificially generated random noise centered at 0 with a standard deviation of 0.025. (c) Amplitude and phase spectra of ${\mathrm{Si}\mathrm{O}}_2$ with added random noise to mimic real data.

Figure 8

Predicted real part and imaginary part of $S_2\mathrm{using}$ random-forest regression and decision-tree regression.

Figure 9

Nominal dielectric function and predicted dielectric function using kNN on noiseless training data for PMMA.