| Abstract: | ![]()
Optical absorption is the most fundamental optical property characterizing light–matter interactions in materials and can be most readily compared with theoretical predictions. However, determination of optical absorption cross-section of individual nanostructures is experimentally challenging due to the small extinction signal using conventional transmission measurements. Recently, dramatic increase of optical contrast from individual carbon nanotubes has been successfully achieved with a polarization-based homodyne microscope, where the scattered light wave from the nanostructure interferes with the optimized reference signal (the reflected/transmitted light). Here we demonstrate high-sensitivity absorption spectroscopy for individual single-walled carbon nanotubes by combining the polarization-based homodyne technique with broadband supercontinuum excitation in transmission configuration. To our knowledge, this is the first time that high-throughput and quantitative determination of nanotube absorption cross-section over broad spectral range at the single-tube level was performed for more than 50 individual chirality-defined single-walled nanotubes. Our data reveal chirality-dependent behaviors of exciton resonances in carbon nanotubes, where the exciton oscillator strength exhibits a universal scaling law with the nanotube diameter and the transition order. The exciton linewidth (characterizing the exciton lifetime) varies strongly in different nanotubes, and on average it increases linearly with the transition energy. In addition, we establish an empirical formula by extrapolating our data to predict the absorption cross-section spectrum for any given nanotube. The quantitative information of absorption cross-section in a broad spectral range and all nanotube species not only provides new insight into the unique photophysics in one-dimensional carbon nanotubes, but also enables absolute determination of optical quantum efficiencies in important photoluminescence and photovoltaic processes.Single-walled carbon nanotubes (SWNTs), a model one-dimensional nanomaterial system, constitute a rich family of structures (1). Each single-walled nanotube structure, uniquely defined by the chiral index (n,m), exhibits distinct electrical and optical properties (2–5). Quantitative information of SWNT absorption cross-section is highly desirable for understanding nanotube electronic structures, for evaluating quantum efficiency of nanotube photoluminescence (5, 6) and photocurrent (7–9), and for investigating the unique many-body effects in 1D systems (10–16). Despite its obvious importance, reliable experimental determination of nanotube absorption cross-section at the single-tube level is still challenging (17). Previous absorption measurements on ensemble nanotube samples only provide averaged behavior (18–20). Recent absorption studies of individual nanotubes, suffering from small absorption signals and/or slow laser-frequency scanning, cannot determine the absolute absorption cross-section and are limited in achievable spectral range (15, 21–23).We demonstrate here a high-sensitivity polarization-based homodyne method to measure nanotube absorption spectra. By manipulating the light polarization, we enhanced the nanotube-induced transmission contrast, ΔI/I, by two orders of magnitude, and this enhanced transmission contrast can be quantitatively related to nanotube absorption cross-section along and perpendicular to the nanotube axis. Using this polarization control together with supercontinuum laser source, we realized high-throughput and broadband absorption measurements at the single-tube level; combined with electron diffraction technique on the same tube, it enables absolute determination of absorption cross-sections of individual chirality-defined nanotubes, to our knowledge for the first time. We obtained quantitative absorption spectra of over 50 SWNTs of different chiralities, and established a phenomenological formula for absorption cross-sections of different nanotubes. The chirality-dependent nanotube absorption spectra reveal unique 1D photophysics in nanotubes, including a universal scaling behavior of exciton oscillator strength and of exciton resonance linewidth. |
