6 nm super-resolution optical transmission and scattering spectroscopic imaging of carbon nanotubes using a nanometer-scale white light source

Optical hyperspectral imaging based on absorption and scattering of photons at the visible and adjacent frequencies denotes one of the most informative and inclusive characterization methods in material research. Unfortunately, restricted by the diffraction limit of light, it is unable to resolve the nanoscale inhomogeneity in light-matter interactions, which is diagnostic of the local modulation in material structure and properties. Moreover, many nanomaterials have highly anisotropic optical properties that are outstandingly appealing yet hard to characterize through conventional optical methods. Therefore, there has been a pressing demand in the diverse fields including electronics, photonics, physics, and materials science to extend the optical hyperspectral imaging into the nanometer length scale. In this work, we report a super-resolution hyperspectral imaging technique that simultaneously measures optical absorption and scattering spectra with the illumination from a tungsten-halogen lamp. We demonstrated sub-5 nm spatial resolution in both visible and near-infrared wavelengths (415 to 980 nm) for the hyperspectral imaging of strained single-walled carbon nanotubes (SWNT) and reconstructed true-color images to reveal the longitudinal and transverse optical transition-induced light absorption and scattering in the SWNTs. This is the first time transverse optical absorption in SWNTs were clearly observed experimentally. The new technique provides rich near-field spectroscopic information that had made it possible to analyze the spatial modulation of band-structure along a single SWNT induced through strain engineering.


Abstract:
Optical transmission and scattering spectroscopic microscopy at the visible and adjacent wavelengths denote one of the most informative and inclusive characterization methods in material research. Unfortunately, restricted by the diffraction limit of light, it cannot resolve the nanoscale variation in light absorption and scattering, diagnostics of the local inhomogeneity in material structure and properties. Moreover, a large quantity of nanomaterials has anisotropic optical properties that are appealing yet hard to characterize through conventional optical methods. There is an increasing demand to extend the optical hyperspectral imaging into the nanometer length scale. In this work, we report a super-resolution hyperspectral imaging technique that uses a nanoscale white light source generated by superfocusing the light from a tungsten-halogen lamp to simultaneously obtain optical transmission and scattering spectroscopic images. The colors of nanomaterials are determined by the optical absorption and scattering processes strongly correlated with their local optical and electronic structures, which can be radically different from the bulk. Single-walled carbon nanotubes (SW-CNTs), for example, comprise a family of more than 200 different structures that are characterized by different chiral indices, endeavored with distinct electronic structures 1,2 , and known to show different colors as individuals [3][4][5] . On the contrary, in bulk, they are the darkest material that absorbs nearly all incident light 6,7 . Like other nanomaterials, SW-CNTs have electronic and optical properties closely related to the environmental influence, such as local strain, defects, dielectric screening, the quantum effect from particle size, etc. There is a strong drive for optical hyperspectral imaging techniques that can provide multidimensional information with nanometer resolution to decipher the local optical and electronic properties noninvasively.
Conventional optical spectroscopic microscopy has its spatial resolution restricted to hundreds of nanometers due to light diffraction. Although near-field scanning optical microscopy (NSOM) offers nanometer-scale resolution by using the plasmonic effect on an optical antenna to scan at the vicinity of the sample surface and has been widely applied absorption/scattering imaging via single-wavelength excitations [8][9][10][11] , its applications in spectroscopy analysis in the visible region have been primarily restricted to inelastic light-matter interaction processes 12-14 , such as tip-enhanced photoluminescence (TEPL) or Raman scattering (TERS), where sufficiently high signal-to-noise ratios can be achieved by removing the excitation light with a spectral filter.
Recently, the NSOM-based nano-spectroscopic imaging has been demonstrated in the infrared (IR) regime, using spatially coherent light sources such as tunable mid-IR lasers [15][16][17] , or a synchrotron radiation beam if a broad bandwidth is desired [18][19][20] . Extending the nano-spectroscopy imaging technique to the absorption and elastic scattering processes in the visible (VIS) and near-infrared (NIR) range will allow direct probing of band structures of a much wider variety of semiconductors with nanoscopic details, without requiring sample luminesces or advanced light sources.
Here, we report a strategy to extend the VIS-NIR scattering and transmission spectroscopic microscopy down to the nanometer length scale. The light from a tungsten-halogen lamp is compressed to the tip apex of a silver nanowire (AgNW) probe through high-external-efficiency broadband nanofocusing 21 to create a broad-spectrum ('white') point light source for nanoscale near-field sample illumination. The two-step nanofocusing process, as described previously 21 , involves the mode coupling from the optical fiber (OF) to the AgNW waveguide and the adiabatic nanofocusing of the surface plasmon polaritons (SPPs) in the AgNW at its gradually narrowing tip. Since neither of the two steps requires spatial or spectral coherency in light, a tungsten-halogen light source can provide sufficient light intensity for hyperspectral imaging. We image both the transmission and scattering spectra of SW-CNTs with a 6-nm spatial resolution and analyze the longitudinal and transverse optical electronic transitions with this approach. The intrinsic electronic structure variation along a structured SW-CNT prepared by the local strain engineering is also studied.
The working mechanism of the nanoscale VIS-NIR hyperspectral microscopy can be considered as a dark-field NSOM configuration, as illustrated in Fig. 1a. The radially polarized SPP in the AgNW waveguide probe is quasi-adiabatically focused by the gradually narrowing tip ( Fig. 1a zoom-in), forming a plasmonic hotspot at the tip apex (tip radius ~ 5nm) with enhanced electric field components in both parallel and perpendicular directions to the sample surface. The far-field radiation pattern of the superfocused mode forms a radially polarized ring 22 , with its 1 storder lobe as small as around 15° in the E-plane ( Fig. 1a-i, inside of the dashed circle). The further k-space measurement confirms its radial polarization over the working wavelength range (Details in the supplementary text). As the probe approaches the sample surface, the superfocused electrical dipole at the tip apex starts to interact with its image dipole in the substrate, leading to the emerging of the 2 nd -order lobes ( Fig. 1a-ii, outside of the dashed circle). A k-space filter (NA = 0.7) is inserted into the optical path to block the low-k component ( Fig. 1a-iii), leaving the high-k part to form a radially-polarized ring pattern in the spectrometer image plane for spectrum analysis ( Fig.   1a-iv).
The intensity profile along the azimuthal direction of the ring pattern is highly sensitive to the nanoscale optical anisotropy distribution. Conventionally, optical anisotropy results in the polarization variation in the transmitted or scattered light 5,23 . In a radially-polarized beam, the polarization variation causes intensity variation along the azimuthal direction of the beam after focus [24][25][26] . Specifically, a SW-CNT placed along the x-direction, as shown Fig. 1b, has a strong depolarization effect due to the longitudinal electronic transition that weakens the x-direction far-field radiation (noted as ∥ ). This variation can be measured by selecting the corresponding region of interest in the spectrometer camera ( Fig. 1a-iv, red dashed area, noted as ROI ∥ ). Meanwhile, the longitudinal electronic transition generates longitudinal diploes that enhance the far-field radiation along the y-direction (defined as " ), leading to an increase of light intensity in ROI " . The spectroscopic information acquired from the two ROIs can reconstruct the nanoscale transmission and scattering images of the sample. As shown in Fig. 1c, the true-color pictures of two individual SW-CNTs are calculated from their spectra using the CIE 1931 color matching function. The separation distance between the two SW-CNTs is ~100 nm, well below Abbe's diffraction limit.
It is worth noting that the low-k light from the probe can be scattered by sample surface roughness and become the major source of the noise, which influences the scattering image more severely than the transmission image due to the already weak signal level. Increasing the NA of the k-space filter can improve the image quality (Details in the supplementary text).  CNT reconstructed from the spectra of ROI ∥ and ROI " , respectively. The spatial resolution of both images can be estimated from a set of adjacent spectra across the SW-CNT. As shown in Fig. 2d, for the 2.3 nm-in-diameter SW-CNT, the spatial resolution is ~ 6 nm for the 510 nm transmission valleys, calculated from fitting its 2D Gaussian surface in the wavelength-displacement space (Details in the supplementary text). This resolution is roughly the same as the AgNW tip radius (~ 5nm).
SW-CNT is one of the ideal quasi-one-dimensional systems and has highly anisotropic optical properties. Due to their one-dimensional characteristic, SW-CNTs have strong optical transitions when the incident light polarization is parallel to their axes, which has been intensively investigated through inelastic (e.g. photoluminescence excitation spectroscopy [27][28][29] ) and elastic scattering measurements (e.g. Rayleigh scattering microscopy 1,30,31 ). The Rayleigh scattering with a perpendicular polarization, however, is difficult to characterize due to the small scattering cross section and has only been investigated theoretically 32  These two scenarios have different influences on the far-field radiation patterns, distinguishable from the two ROI spectra. Specifically, the longitudinal transition (Fig. 3a)  . We take an (8, 6) SW-CNT as an example. The DFT calculated band structure (Fig. 3c) indicates that both the *% ' (or %* ' ) and %% ' transitions have quasi-direct bandgaps with a small mismatch in momentum (~ 3% and 7% of the Brillouin zone, respectively), which can be efficiently excited by the superfocused light at the probe apex and appear in both transmission and scattering spectra as evident valleys/peaks. The *( ' transition is across an indirect bandgap with a more considerable momentum mismatch (~ 60% of the Brillouin zone), making it more challenging to excited. Nonetheless, since its unit length (2.6 nm) is comparable with the probe tip radius (~ 5 nm), this momentum mismatch can still be partially compensated by the sharp tip.
Therefore, *( ' transition gives a shallow yet measurable valley in both spectra of Fig. 3d.

Similar characteristics for longitudinal and transverse transitions can be identified in all
SW-CNT scan results.  (Fig. 4g-h), equivalent to ~ 1% of strain according to the DFT calculation. We also notice that the (* ' peak intensity slightly increased under strain (Fig. 4f and g), which may result from the reduction in momentum mismatch between the corresponding valance and conduction bands, as shown in the DFT calculation (Fig. 4a).
In summary, the super-resolution optical transmission and scattering spectroscopic