commercial software package based on the finite-difference time-domain (fdtd) method  (ANSYS inc)

Journal: Nature Communications

Article Title: Experimental verification of field-enhanced molecular vibrational scattering at single infrared antennas

doi: 10.1038/s41467-024-50869-x

Figure Lengend Snippet: a Experimental (s-SNOM) amplitude spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${s}_{3}\left(\omega \right)$$\end{document} s 3 ω , obtained with a PDMS-contaminated AFM tip (O) that interacts with a metal nanorod (A) of different lengths, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L$$\end{document} L (solid lines). Shaded areas show the numerically calculated near-field spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${s}_{3}^{{{\rm{bkg}}}}\left(\omega \right)$$\end{document} s 3 bkg ω , from (b) but scaled to the experimental data (Supplementary Note ). b Numerically calculated (FDTD) amplitude spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${s}_{3}\left(\omega \right)$$\end{document} s 3 ω , (solid lines), where the AFM tip is described as a core-shell nanoparticle with a 50 nm radius Au core and a 10 nm thick PDMS shell, and aspects of tip vibration and signal demodulation were taken into account (Supplementary Note ). Shaded areas show the calculated amplitude spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${s}_{3}^{{{\rm{bkg}}}}\left(\omega \right)$$\end{document} s 3 bkg ω , assuming a non-absorbing dielectric shell. Dashed lines show the magnitude of field-enhanced molecular scattering, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|{E}_{{{\rm{AOA}}}}\left(\omega \right)|$$\end{document} ∣ E AOA ω ∣ , (Eq. , no demodulation considered, scaled to the calculated data). c , d Isolated spectral signature of the molecular vibrations, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {s}_{3}\left(\omega \right)={s}_{3}\left(\omega \right)-{s}_{3}^{{{\rm{bkg}}}}\left(\omega \right)$$\end{document} Δ s 3 ω = s 3 ω − s 3 bkg ω , from the data in ( a , b ) (curves are offset for clarity). The magnitude of the polarizability of the core-shell nanoparticle considered in ( b ), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|{\alpha }_{{{\rm{O}}}}\left(\omega \right)|$$\end{document} ∣ α O ω ∣ , is shown for reference (black solid line in ( d )). e Parametric representation of the spectral signature of the 1258 cm −1 (Si-CH 3 ) molecular vibration of PDMS, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {s}_{3}^{{{\rm{pp}}}}$$\end{document} Δ s 3 pp , as obtained from panels ( a , b ), normalized to maximum and plotted against the calculated field enhancement, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${|f|}$$\end{document} ∣ f ∣ , at 1258 cm −1 . f Experimental (s-SNOM) and g numerically calculated (FDTD) phase spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi }_{3}\left(\omega \right)$$\end{document} φ 3 ω , (solid lines). The dotted lines in ( g ) show the calculated phase spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi }_{3}^{{{\rm{bkg}}}}\left(\omega \right)$$\end{document} φ 3 bkg ω , assuming a non-absorbing dielectric shell. Black dashed lines show the phase of field-enhanced molecular scattering, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi }_{{{\rm{AOA}}}}\left(\omega \right)$$\end{document} φ AOA ω (Eq. ). h , i Baseline-corrected phase spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {\varphi }_{3}\left(\omega \right)={\varphi }_{3}\left(\omega \right)-{\varphi }_{3}^{{{\rm{bkg}}}}\left(\omega \right)$$\end{document} Δ φ 3 ω = φ 3 ω − φ 3 bkg ω from the data in ( f , g ) (curves are offset for clarity). The phase of the polarizability of the core-shell nanoparticle, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{Arg}}}\{{\alpha }_{{{\rm{O}}}}\left(\omega \right)\}$$\end{document} Arg { α O ω } , is shown for reference in (i) (black solid line). j Parametric representation of the spectral signature of the molecular vibration (Si-CH 3 ) of PDMS, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi }_{3}^{{{\rm{pp}}}}$$\end{document} φ 3 pp , as obtained from panels ( h , i ), plotted against the calculated field enhancement, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f$$\end{document} f , at 1258 cm −1 . Error bars in ( e , j ) describe the uncertainty owing to experimental noise (see Methods). Supplementary Fig. shows the spectra for each antenna individually, Supplementary Note details the corresponding spectrally integrated near-field images. The PDMS shell of the core-shell nanoparticle in ( b ) was modeled using tabulated data, and the non-absorbing dielectric shell with constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon=1.8$$\end{document} ε = 1.8 . The polarizability of the core-shell nanoparticle was evaluated analytically using Eq. in Supplementary Note .

Article Snippet: We used a commercial software package based on the Finite-difference time-domain (FDTD) method to calculate the relevant quantities of SEIRA spectroscopy (Ansys Lumerical FDTD, Ansys, Inc).

Techniques: Isolation

Journal: Nature Communications

Article Title: Experimental verification of field-enhanced molecular vibrational scattering at single infrared antennas

doi: 10.1038/s41467-024-50869-x

Figure Lengend Snippet: a Experimental (s-SNOM) amplitude spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${s}_{3}\left(\omega \right)$$\end{document} s ω , obtained with a PDMS-contaminated AFM tip (O) that interacts with a gap antenna (A) (pair of single rods identical to those in Fig. , of rod length, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L$$\end{document} L , and separated by a 100 nm gap) (solid lines). Shaded areas show the numerically calculated near-field spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${s}_{3}^{{{\rm{bkg}}}}\left(\omega \right)$$\end{document} s bkg ω , from ( b ), but scaled (Supplementary Note ). b Numerically calculated (FDTD) amplitude spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${s}_{3}\left(\omega \right)$$\end{document} s ω , (solid lines), where the AFM tip is described as a core-shell nanoparticle as in Fig. . Shaded areas show the calculated amplitude spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${s}_{3}^{{{\rm{bkg}}}}\left(\omega \right)$$\end{document} s bkg ω , assuming a non-absorbing dielectric shell. Dashed lines show the magnitude of field-enhanced molecular scattering, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|{E}_{{{\rm{AOA}}}}\left(\omega \right)|$$\end{document} ∣ E AOA ω ∣ . c , d Isolated spectral signature of the molecular vibrations, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {s}_{3}\left(\omega \right)={s}_{3}\left(\omega \right)-{s}_{3}^{{{\rm{bkg}}}}\left(\omega \right)$$\end{document} Δ s ω = s ω − s bkg ω , from the data in ( a , b ) (curves are offset for clarity). d The magnitude of the polarizability of the core-shell nanoparticle considered in ( b ), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|{\alpha }_{{{\rm{O}}}}\left(\omega \right)|$$\end{document} ∣ α O ω ∣ , is shown for reference (black solid line). e Experimental (s-SNOM) and ( f ) numerically calculated (FDTD) phase spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi }_{3}\left(\omega \right)$$\end{document} φ ω , (solid lines). f The dotted lines show the calculated phase spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi }_{3}^{{{\rm{bkg}}}}\left(\omega \right)$$\end{document} φ bkg ω , assuming a non-absorbing dielectric shell. Black dashed lines show the phase of field-enhanced molecular scattering, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi }_{{{\rm{AOA}}}}\left(\omega \right)$$\end{document} φ AOA ω (Eq. ). g , h Baseline-corrected phase spectra, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {\varphi }_{3}\left(\omega \right)={\varphi }_{3}\left(\omega \right)-{\varphi }_{3}^{{{\rm{bkg}}}}\left(\omega \right)$$\end{document} Δ φ ω = φ ω − φ bkg ω (curves offset for clarity) from the data in ( e , f ). The phase of the polarizability of the core-shell nanoparticle, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{Arg}}}\{{\alpha }_{{{\rm{O}}}}\left(\omega \right)\}$$\end{document} Arg { α O ω } , is shown for reference in ( h ) (black solid line).

Article Snippet: We used a commercial software package based on the Finite-difference time-domain (FDTD) method to calculate the relevant quantities of SEIRA spectroscopy (Ansys Lumerical FDTD, Ansys, Inc).

Techniques: Isolation