Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy

The phonon-enhanced near-field response of polar materials is studied in theory and with a broadband midinfrared near-field microscope that generates spectra in real time. Absolute magnitude and phase spectra are determined for SiC, SiO${}_2$, and $a$-SiO${}_2$ at several demodulation orders. The data set is compared with results from two theoretical models of near-field interaction, point dipole and finite dipole. Only the latter produces acceptable agreement with a single parameter choice of all measured quantities (line shape in amplitude and phase, line position, and absolute scattering amplitude). This allows determining for the commercial metal tip used that (i) the dipole representing the near-field interaction has 600-nm effective length and that (ii) its near-field-induced far-field backscattering amplitude efficiency reaches 0.3% at phonon resonance, for the NA ≈ 0.45 objective used. The near-field phonon resonance is a robust and well-understood feature whose bright and sharp ($Q$ ≈ 200) signatures specifically can highlight and can identify polar materials in the nanoscale imaging of heterogeneous composites.

Figure 1

Sketches (a) of two theoretical concepts of s-SNOM and (b) of corresponding interaction regions (dotted) overlaid on the SEM image of the experimentally used probe, which has a 40-nm tip diameter. The tip-enhanced optical field (vector pattern) polarizing the sample (gray) is confined below the apex to a dimension of the tip radius $a$. The field originates in the PD model from a PD at A oriented along the tip axis and in the FD model from a point charge near A that is neutralized by a countercharge at B. The double arrow indicates the incident and the Rayleigh-scattered beams for the experimental back-scattering geometry at 60° incidence.

Figure 2

Theoretical predictions (curves) of scattering amplitude spectra $s_n$ (lower parts) and phase spectra ${\phi }_n$ (upper parts) of a flat sample of either SiC or Au [for $n$ $=$ 1 (blue), 2 (black), and 3 (red)]; the SiC spectra show the phonon resonance while the Au spectra are flat; assumed tip material Pt, curvature radius $a$ $=$ 20 nm, and tapping amplitude Δ$z$ $=$ 10 nm; (a) PD model with Re ($V$) $=$ (190 nm)${}^3$, (b) FD model with Re ($V$) $=$ (700 nm)${}^3$, 2$L$ $=$ 600 nm, and Re ($g$) $=$ 0.7. For the experimental data (points), see Sec. 4.

Figure 3

Optical layout of a coherent broadband midinfrared source based on frequency-difference generation in GaSe illuminating an s-SNOM via a Michelson interferometer.

Figure 4

Experimental data and FD model predictions as in Fig. 2b of crystalline SiO${}_2$; dielectric data from Table .[26]

Figure 5

Experimental data and FD model predictions as in Fig. 4 of ${\sigma }_2$ of SiO${}_2$ varying the tapping amplitude Δ$z$ $=$ 5 nm (blue), 10 nm (black), 20 nm (red), and 40 nm (green).

Figure 6

(a) Experimental data and FD model predictions as in Fig. 4 of $s_2$ of SiO${}_2$ varying the distance $z$ between the sample and the lower turning point of the oscillating tip as indicated.

Figure 7

Experimental data and FD model predictions as in Fig. 4 of ${\sigma }_2$ of SiO${}_2$ varying the fraction of mutual charge induction Re ($g$) $=$ 0.6 (red), 0.7 (black), and 0.8 (blue).

Figure 8

Calculated dielectric function ɛ (black), ${\varepsilon }_1$ (full), ${\varepsilon }_2$ (dotted) of crystalline SiO${}_2$, Reststrahlen reflectivity $R$ (blue), and Fresnel reflection (red), for 60° $p$-polarized incidence, amplitude (full), phase (dotted), after Table .[26]

Figure 9

Experimental data and FD model predictions as in Fig. 2b of ${\sigma }_2$ of amorphous SiO${}_2$ suprasil; dielectric data from Table  with all damping factors multiplied by 4.2.

Figure 10

Experimental data and FD model predictions as in Fig. 2b of ${\sigma }_2$ comparing crystalline SiO${}_2$ [(blue), from Fig. 4], amorphous SiO${}_2$ suprasil [(black), from Fig. 9], and amorphous SiO${}_2$ tempax [(red), dielectric data from Table  with all damping factors multiplied by 8.2].