A scanning cavity microscope

Imaging the optical properties of individual nanosystems beyond fluorescence can provide a wealth of information. However, the minute signals for absorption and dispersion are challenging to observe, and only specialized techniques requiring sophisticated noise rejection are available. Here we use signal enhancement in a high-finesse scanning optical microcavity to demonstrate ultra-sensitive imaging. Harnessing multiple interactions of probe light with a sample within an optical resonator, we achieve a 1,700-fold signal enhancement compared with diffraction-limited microscopy. We demonstrate quantitative imaging of the extinction cross-section of gold nanoparticles with a sensitivity less than 1 nm2; we show a method to improve the spatial resolution potentially below the diffraction limit by using higher order cavity modes, and we present measurements of the birefringence and extinction contrast of gold nanorods. The demonstrated simultaneous enhancement of absorptive and dispersive signals promises intriguing potential for optical studies of nanomaterials, molecules and biological nanosystems.

compared to the beginning of the cavity length scan changes, and thus the resonances of interest can shift out of the data recording window.
To compensate this, we use a second laser (homebuilt external cavity diode laser) at a wavelength of 969 nm. At this wavelength the finesse of the resonator has dropped below 1. Thus, the resonator is not sensitive to weak absorbers. By comparing the actual position of a cavity resonance with a target value, we can readjust the start position of the length scan and thereby stabilize the average length of the cavity to within a few nanometers over days.

Supplementary Figure 3: Plane Mirror
-10 -5 0 5 10 Cext [nm²] The plane mirrors used as sample holders in our experiments are superpolished fused silica substrates, coated with a high reflective dielectric coating (R=99.9914%, T=60 ppm, L=26 ppm) with SiO 2 as terminating layer, while the back side is antireflection coated. The coatings were manufactured by LAYERTEC, Mellingen.
The figure shows a map of extinction cross sections measured for a clean plane mirror. The typical variation of the mirror loss amounts to 0.2 ppm rms, corresponding to an extinction cross section of 0.5 nm 2 for the cavity parameters used in the experiments. We observe that each mode of the cavity is split up into two orthogonally polarized modes. Uphoff et al. [1] show that the small ellipticity of the micromachined mirror on the fiber endfacet leads to a differential phaseshift between light polarized along the two half axes of the resonator. Thus each mode of the cavity is split up into a doublet. We exploit this for measuring anisotropy of extinction and cavity lineshift of single gold nanorods. For our theoretical considerations, we calculate the extinction cross section and the cavity line shift using a projection of the polarizability tensor of the particle onto the corresponding polarization axis.
We do not observe a rotation of the orientation of the cavity eigenaxes in the presence of particle birefringence, as predicted e.g. by Moriwaki et. al. [2] or Brandi et. al. [3]. If rotation would be induced, a second resonance peak would appear at the output ports of the polarizing beamsplitter, which is aligned with respect to the unperturbed cavity modes.
In order to prove this effect, we first fit the sum of both ports to get the position and width of each peak. In a second step, we fit each signal separately with a double Lorentzian, using the positions and widths from the first step in order to get the amplitudes of the two peaks, if they would appear.
The figure shows the measured difference of the two amplitudes of peaks for the two output ports of the beamsplitter. The values are normalized to the sum of both amplitudes. The data agree quite well with a model assuming no change of the polarization inside the cavity, while they obviously deviate from a model that assumes the nanoparticle changing the polarization orientation inside the cavity.

Supplementary Figure 5: SEM Image of Gold Nano-Spheres
Scanning electron microscope image of mirror with gold nanospheres used in the experiments.

Supplementary Note 1: Optical Properties of a Metal Nanoparticle
For the interpretation of the experiments shown in this work, a detailed understanding of the optical properties of the metal nanoparticles is crucial. In the following, different effects that influence the properties are discussed.
The dielectric constants of the particle, its surrounding and the surfaces in the vicinity of the particle are denoted as follows: 1 denotes the dielectric constant of the surrounding environment, 2 the dielectric constant of a surface close to the particle and 3 gives the dielectric constant of the particle it self. 0 is the vacuum dielectric constant.

Polarizability of a nanoparticle
Polarizability is the key quantity to describe the optical properties of a particle. In the following, basic formulas are presented: Spherical particles For spherically symmetric and isotropic particles, the polarizability is given by the Clausius-Mossotti law: where V p is the volume of the particle.
Ellipsoids For ellipsoidal nanoparticles, the polarizability is described by a tensor.
The main values of the tensor can be calculated as follows [4]: where j denotes the axis, V p the volume of the particle and L j is a dimensionless parameter depending on the ratios of the semiaxes a 1 , a 2 and a 3 of the particle. For arbitrary ratios of those axes, L 1 is given by L 2 and L 3 are obtained by cyclical permutation. Furthermore, the relation has to be fulfilled. For prolate ellipsoids like nanorods, where a 1 > a 2 , a 3 and a 2 = a 3 , the problem simplifies to For nanorods that are not aligned along the polarization of the probe light, we rotate the polarizability tensor and project it onto the polarization axes. We do the projection for the imaginary and real part separately.

Correction of the dielectric constant because of the small size
It turns out that the dielectric constant of gold 3 has to be modified with respect to the bulk value ( bulk ) [5] in order to describe very small particles accurately [6]: with the metal plasma frequency ω p and the electron scattering rates in the bulk (γ bulk ) and confinded metal (γ), where with v F the Fermi velocity, D the particle diameter and g a proportionality factor in the order of 1. At a wavelength of 780 nm and g = 1.4 we find an extinction cross section of 22.3 nm 2 .

Correction of the polarizability for particles on a dielectric surface
As the nanoparticles in our experiments lie on the surface of a dielectric mirror, also the effect of a surface close to the particle has to be considered. For metal nanospheres far away from plasmon resonance and for an incident light field with a polarization parallel to the surface, like in the case discussed in this paper, Wind et al. [7] give the following solution: with the depolarization factor

Scattering and Absorption
When light interacts with an object it either gets absorbed or scattered. For nanoparticles smaller than a wavelength of light, this is described by Rayleigh scattering. The corresponding cross sections are given by: and As both effects attenuate the probe beam, the measured quantity in all our experiments is the extinction of a nanoparticle:

Size-and g-factor distribution for gold nanospheres
The size of the nanoparticles varies as well as the g-factor, a heuristic value characterizing damping effects for small nanoparticles. In order to compare our measured distribution of extinction cross sections, we take a Gaussian diameter distribution measured by the manufacturer of the particles with central diameter 41.1 nm and a standard deviation of 3.3 nm. In addition, we adopt a gaussian distribution of the g-factor found by Muskens et. al. [6] around 1.4 with a standard deviation of 0.25.

Calculations for nanorods
For all calculations concerning the polarizability of nanorods, we use the calculus described above for ellipsoids. We correct 3 for small-size effects of the particle.
In equation 6, we use the size of the long (short) axis as particle diameter for the calculation of the polarizability along the respective axis. As we are interested in differences, we do not consider surface effects, which we assume to be equal for both axes.