Absolute optical extinction measurements of single nano-objects by spatial modulation spectroscopy using a white lamp.

This article describes a high sensitivity spectrophotometer designed to detect the overall extinction of light by a single nanoparticle (NP) in the 10(-4)-10(-5) relative range, using a transmission measurement configuration. We focus here on the simple and low cost scheme where a white lamp is used as a light source, permitting easy and broadband extinction measurements (300-900 nm). Using a microscope, in a confocal geometry, an increased sensitivity is reached thanks to a modulation of the NP position under the light spot combined with lock-in detection. Moreover, it is shown that this technique gives access to the absolute extinction cross-sections of the single NP provided that the incident electromagnetic field distribution experienced by the NP is accurately characterized. In this respect, an experimental procedure to characterize the light spot profile in the focal plane, using a reference NP as a probe, is also laid out. The validity of this approach is discussed and confirmed by comparing experimental intensity distributions to theoretical calculations taking into account the vector character of the tightly focused beam. The calibration procedure permitting to obtain the absolute extinction cross-section of the probed NP is then fully described. Finally, the force of the present technique is illustrated through selected examples concerning spherical and slightly elongated gold and silver NPs. Absolute extinction measurements are found to be in good consistency with the NP size and shape independently obtained from transmission electron microscopy, showing that spatial modulation spectroscopy is a powerful tool to get an optical fingerprint of the NP.

Optical response of a single spherical particle in a tightly focused light beam: application to the spatial modulation spectroscopy technique.

We develop a new and numerically efficient formalism to describe the general problem of the scattering and absorption of light by a spherical metal or dielectric particle illuminated by a tightly focused beam. The theory is based on (i) the generalized Mie theory equations, (ii) the plane-wave decomposition of the converging light beam, and (iii) the expansion of a plane wave in terms of vector spherical harmonics. The predictions of the model are illustrated in the case of silver nanoparticles. The results are compared with the Mie theory in the local approximation. Finally, some effects related to the convergence of the beam are analyzed in the context of experiments based on the spatial modulation spectroscopy technique.