Polarization-resolved extinction and scattering cross-section of individual gold nanoparticles measured by wide-field microscopy on a large ensemble

We report a simple, rapid, and quantitative wide-field technique to measure the optical extinction $\sigma_{\rm ext}$ and scattering $\sigma_{\rm sca}$ cross-section of single nanoparticles using wide-field microscopy enabling simultaneous acquisition of hundreds of nanoparticles for statistical analysis. As a proof of principle, we measured nominally spherical gold nanoparticles of 40\,nm and 100\,nm diameter and found mean values and standard deviations of $\sigma_{\rm ext}$ and $\sigma_{\rm sca}$ consistent with previous literature. Switching from unpolarized to linearly polarized excitation, we measured $\sigma_{\rm ext}$ as a function of the polarization direction, and used it to characterize the asphericity of the nanoparticles. The method can be implemented cost-effectively on any conventional wide-field microscope and is applicable to any nanoparticles

Resonant state expansion applied to planar open optical systems

The resonant state expansion (RSE), a novel perturbation theory of Brillouin-Wigner type developed in electrodynamics [Muljarov, Langbein, and Zimmermann, Europhys. Lett., 92, 50010(2010)], is applied to planar, effectively one-dimensional optical systems, such as layered dielectric slabs and Bragg reflector microcavities. It is demonstrated that the RSE converges with a power law in the basis size. Algorithms for error estimation and their reduction by extrapolation are presented and evaluated. Complex eigenfrequencies, electro-magnetic fields, and the Green's function of a selection of optical systems are calculated, as well as the observable transmission spectra. In particular we find that for a Bragg-mirror microcavity, which has sharp resonances in the spectrum, the transmission calculated using the resonant state expansion reproduces the result of the transfer/scattering matrix method

Resonant state expansion applied to two-dimensional open optical systems

The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is applied to two-dimensional open optical systems. The analytically solvable homogeneous dielectric cylinder is used as unperturbed system, and its Green's function is shown to contain a cut in the complex frequency plane, which is included in the RSE basis. The complex eigenfrequencies of modes are calculated using the RSE for a selection of perturbations which mix unperturbed modes of different orbital momentum, such as half-cylinder, thin-film and thin-wire perturbation, demonstrating the accuracy and convergency of the method. The resonant states for the thin-wire perturbation are shown to reproduce an approximative analytical solution

Polariton states bound to defects in GaAs/AlAs planar microcavities

We report on polariton states bound to defects in planar GaAs/AlAs microcavities grown by molecular beam epitaxy. The defect types relevant for the spatial polariton dynamics in these structures are cross-hatch misfit dislocations, and point-like defects extended over several micrometers. We attribute the latter defects to Ga droplets emitted occasionally by the Ga cell during the growth. These defects, also known as oval defects, result in a dome-like local modulation of surface, which is translated into the cavity structure and leads to a lateral modulation of the cavity polariton energy of up to 15\,meV. The resulting spatially localized potential landscape for the in-plane polariton motion creates a series of bound states. These states were characterized by spectrally resolved transmission imaging in real and reciprocal space, and reveal the spatial potential created by the defects. Interestingly, the defect states exhibit long lifetimes in the 10ps range, which we attribute to a spatially smooth confinement potential

Resonant state expansion applied to planar waveguides

The resonant state expansion, a recently developed method in electrodynamics, is generalized here to planar open optical systems with non-normal incidence of light. The method is illustrated and verified on exactly solvable examples, such as a dielectric slab and a Bragg reflector microcavity, for which explicit analytic formulas are developed. This comparison demonstrates the accuracy and convergence of the method. Interestingly, the spectral analysis of a dielectric slab in terms of resonant states reveals an influence of waveguide modes in the transmission. These modes, which on resonance do not couple to external light, surprisingly do couple to external light for off-resonant excitation

Quantum complementarity of microcavity polaritons

We present an experiment that probes polariton quantum correlations by exploiting quantum complementarity. Specifically, we find that polaritons in two distinct idler-modes interfere if and only if they share the same signal-mode so that "which-way" information cannot be gathered. The experimental results prove the existence of polariton pair correlations that store the "which-way" information. This interpretation is confirmed by a theoretical analysis of the measured interference visibility in terms of quantum Langevin equations

Parametric scattering of microcavity polaritons into ghost branches

Polaritons of defined momentum and energy are excited resonantly on the lower polariton branch of a planar semiconductor microcavity in the strong coupling regime, and the spectrally and momentum resolved emission is analyzed. We observe ghost branches from scattering within the lower polariton branch, as well as from scattering to the middle polariton branch, showing the nonlinear mixing between different branches. Extending the theoretical treatment of spontaneous parametric luminescence developed in Ciuti et al. [Phys. Rev. B 63, 041303 (2001)], the eigenmodes of the driven polariton system and its photoluminescence are modeled. A quantitative agreement with the measured branch positions and a qualitative agreement with the branch intensities is found