Microcavities and nanoresonators are characterized by their quality factors Q and mode volumes V. While Q is unambiguously defined, there are still questions on V and in particular on its complexvalued character, whose imaginary part is linked to the non-Hermitian nature of open systems. Helped by cavity perturbation theory and near field experimental data, we clarify the physics captured by the imaginary part of V and show how a mapping of the spatial distribution of both the real and imaginary parts can be directly inferred from perturbation measurements. This result shows that the mathematically abstract complex mode volume in fact is directly observable.This supplementary Material provides complementary results and discussions to the main text, starting with a Section detailing discussing the reliability of the Δ -measurements, followed by a formal comparison of the classical perturbation formula of Eqs. (1) and (2), a study of the accuracy of Eq. (2) for predicting resonance shifts, and by an analytical study of the domain of validity of Eq. (2) that leads to upper bounds for the maximum perturber strength.

Many of the most advanced applications of semiconductor quantum dots (QDs) in quantum information technology require a fine control of the QDs' position and confinement potential, which cannot be achieved with conventional growth techniques. Here, a novel and versatile approach for the fabrication of site-controlled QDs is presented. Hydrogen incorporation in GaAsN results in the formation of N-2H and N-2H-H complexes, which neutralize all the effects of N on GaAs, including the N-induced large reduction of the bandgap energy. Starting from a fully hydrogenated GaAs/GaAsN:H/GaAs quantum well, the NH bonds located within the light spot generated by a scanning near-field optical microscope tip are broken, thus obtaining site-controlled GaAsN QDs surrounded by a barrier of GaAsN:H (laterally) and GaAs (above and below). By adjusting the laser power density and exposure time, the optical properties of the QDs can be finely controlled and optimized, tuning the quantum confinement energy over more than 100 meV and resulting in the observation of single-photon emission from both the exciton and biexciton recombinations. This novel fabrication technique reaches a position accuracy <100 nm and it can easily be applied to the realization of more complex nanostructures.

The optical behavior of coupled systems, in which the breaking of parity and time-reversal symmetry occurs, is drawing increasing attention to address the physics of the exceptional point singularity, i.e., when the real and imaginary parts of the normal-mode eigenfrequencies coincide. At this stage, fascinating phenomena are predicted, including electromagnetic-induced transparency and phase transitions. To experimentally observe the exceptional points, the near-field coupling to waveguide proposed so far was proved to work only in peculiar cases. Here, we extend the interference detection scheme, which lies at the heart of the Fano lineshape, by introducing generalized Fano lineshapes as a signature of the exceptional point occurrence in resonant-scattering experiments. We investigate photonic molecules and necklace states in disordered media by means of a near-field hyperspectral mapping. Generalized Fano profiles in material science could extend the characterization of composite nanoresonators, semiconductor nanostructures, and plasmonic and metamaterial devices.

Photonic and plasmonic devices rely on nanoscale control of the local density of optical states (LDOS) in dielectric and metallic environments. The tremendous progress in designing and tailoring the electric LDOS of nano-resonators requires an investigation tool that is able to access the detailed features of the optical localized resonant modes with deep-subwavelength spatial resolution. This scenario has motivated the development of different nanoscale imaging techniques. Here, we prove that a technique involving the combination of scanning near-field optical microscopy with resonant scattering spectroscopy enables imaging the electric LDOS in nano-resonators with outstanding spatial resolution (l/19) by means of a pure optical method based on light scattering. Using this technique, we investigate the properties of photonic crystal nanocavities, demonstrating that the resonant modes appear as characteristic Fano line shapes, which arise from interference. Therefore, by monitoring the spatial variation of the Fano line shape, we locally measure the phase modulation of the resonant modes without the need of external heterodyne detection. This novel, deep-subwavelength imaging method allows us to access both the intensity and the phase modulation of localized electric fields. Finally, this technique could be implemented on any type of platform, being particularly appealing for those based on non-optically active material, such as silicon, glass, polymers, or metals.

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