Abstract
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 nm2 and for the polarizability of α/ϵ0 = (28 000 + 200i) nm3. Our method opens the way to a full characterization of the optical properties of individual nanosystems, with applications ranging from nanomaterial science to biology.
Highlights
BACKGROUND SUBTRACTIONTo obtain the sample extinction, we measure the cavity linewidth for the fundamental mode using similar sidebands on many points on the plane mirror that is boustrophedonically raster scanned with a step size of 200 nm at a measurement speed of around 0.25 s/pixel, mainly limited by the online data processing.In general, the resulting signal of sampling a sparse distribution of particles absorbing or dispersing light with almost 2 orders of magnitude larger resonator modes is a convolution of the sample and the intensity distribution
We simultaneously measure the extinction signal by quantifying the intracavity loss introduced by the sample and measure the real part of the polarizability by observing dispersive frequency shifts of the cavity resonance frequency. The challenge for the latter measurement is to separate frequency shifts due to the sample, which correspond to cavity length changes on a picometer level, from mechanical noise of the widely scannable cavity setup, which shows typical amplitudes on a nanometer-level. To overcome these mechanical limitations, we demonstrate a differential measurement scheme exploiting relative frequency shifts of higher order transverse modes that are differently affected by a nanoparticle inside the cavity
We show spatially resolved simultaneous measurements of the extinction and dispersion of individual 50 nm gold nanoparticles and use it to retrieve the real and imaginary part of the polarizability α
Summary
To obtain the sample extinction, we measure the cavity linewidth for the fundamental mode using similar sidebands on many points on the plane mirror that is boustrophedonically raster scanned with a step size of 200 nm at a measurement speed of around 0.25 s/pixel, mainly limited by the online data processing. The expected peak frequency shift for a 50 nm GNP probed at 780 nm amounts to 3.5 GHz. In the background-subtracted signal, the characteristic bloom-shaped point spread function becomes clearly visible and can be quantitatively evaluated. We have measured the extinction cross section of the same particle for subsequent longitudinal mode orders and repeated this experiment five times This yields a larger variation of 5%, originating from transverse mode mixing effects,[38,43] which is the dominating systematic uncertainty in our measurements and limits the accuracy of the method
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