Comprehensive model of the optical spectra of carbon nanotubes on a substrate by polarized microscopy

Polarized optical microscopy and spectroscopy are progressively becoming key methods for the high-throughput characterization of individual carbon nanotubes (CNTs) and other one-dimensional nanostructures, on substrate and in devices. The optical response of CNTs on substrate in cross polarization experiments is usually limited by the polarization conservation of the optical elements in the experimental setup. We developed a theoretical model taking into account the depolarization by the setup and the optical response of the substrate. We show that proper modelization of the experimental data requires to take into account both noncoherent and coherent light depolarization by the optical elements. We also show how the nanotube signal can be decoupled from the complex reflection factor of the antireflection substrate, which is commonly used to enhance the optical contrast. Finally, we describe an experimental protocol to extract the depolarization parameters and the complex nanotube susceptibility, and how it can improve the chirality assignment of individual carbon nanotubes in complex cases.