Quantitative Determination of the Complex Polarizability of Individual Nanoparticles by Scanning Cavity Microscopy

The complex polarizability describes the complete optical properties of a nanoobject in the Rayleigh limit, including its absorption, scattering, and dispersion. A large range of applications would benefit from the capability to infer the polarizability on a single-particle level; however, it requires two complementary measurements to fully determine this quantity, and the smallness of the signals makes this highly challenging. Here we use signal enhancement in a tunable high finesse fiber cavity and apply noise-rejecting differential measurement techniques to simultaneously obtain the extinction cross section and the dispersion of individual gold nanospheres, which allows us to quantitatively obtain the real and imaginary part of the polarizability with high precision. We achieve a detection limit for extinction cross sections of 1.8 nm^2 and for the polarizability of α/ϵ0 = (28 000 + 200i) nm^3. Our method opens the way to a full characterization of the optical properties of individual nanosystems, with applications ranging from nanomaterial science to biology.