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Strong coupling between light and molecular matter is currently attracting interest both in chemistry and physics, in the fast-growing field of molecular polaritonics. The large near-field enhancement of the electric field of plasmonic surfaces and their high tunability make arrays of metallic nanoparticles an interesting platform to achieve and control strong coupling. Two dimensional plasmonic arrays with several nanoparticles per unit cell and crystalline symmetries can host topological edge and corner states. Here we explore the coupling of molecular materials to these edge states using a coupled-dipole framework including long-range interactions. We study both the weak and strong coupling regimes and demonstrate that coupling to topological edge states can be employed to enhance highly-directional long-range energy transfer between molecules., Comment: 26 pages, 4 figures

We provide a simple method that enables readily acquired experimental data to be used to predict whether or not a candidate molecular material may exhibit strong coupling. Specifically, we explore the relationship between the hybrid molecular/photonic (polaritonic) states and the bulk optical response of the molecular material. For a given material this approach enables a prediction of the maximum extent of strong coupling (vacuum Rabi splitting), irrespective of the nature of the confined light field. We provide formulae for the upper limit of the splitting in terms of the molar absorption coefficient, the attenuation coefficient, the extinction coefficient (imaginary part of the refractive index) and the absorbance. To illustrate this approach we provide a number of examples, we also discuss some of the limitations of our approach.

Strong coupling of molecular vibrations with light creates polariton states, enabling control over many optical and chemical properties. However, the near-field signatures of strong coupling are difficult to map as most cavities are closed systems. Surface-enhanced Raman microscopy of open metallic gratings under vibrational strong coupling enables the observation of spatial polariton localization in the grating near-field, without the need for scanning probe microscopies. The lower polariton is localized at the grating slots, displays a strongly asymmetric lineshape, and gives greater plasmon-vibration coupling strength than measured in the far-field. Within these slots, the local field strength pushes the system into the ultrastrong coupling regime. Models of strong coupling which explicitly include the spatial distribution of emitters can account for these effects. Such gratings form a new system for exploring the rich physics of polaritons and the interplay between their near- and far-field properties through polariton-enhanced Raman scattering (PERS).

The strong coupling of molecules with surface plasmons results in hybrid states which are part molecule, part surface-bound light. Since molecular resonances may acquire the spatial coherence of plasmons, which have mm-scale propagation lengths, strong-coupling with molecular resonances potentially enables long-range molecular energy transfer. Gratings are often used to couple incident light to surface plasmons, by scattering the otherwise non-radiative surface plasmon inside the light-line. We calculate the dispersion relation for surface plasmons strongly coupled to molecular resonances when grating scattering is involved. By treating the molecules as independent oscillators rather than the more typically-considered single collective dipole, we find the full multi-band dispersion relation. This approach offers a natural way to include the dark states in the dispersion. We demonstrate that for a molecular resonance tuned near the crossing point of forward and backward grating-scattered plasmon modes, the interaction between plasmons and molecules gives a five-band dispersion relation, including a bright state not captured in calculations using a single collective dipole. We also show that the role of the grating in breaking the translational invariance of the system appears in the position-dependent coupling between the molecules and the surface plasmon. The presence of the grating is thus not only important for the experimental observation of molecule-surface-plasmon coupling, but also provides an additional design parameter that tunes the system.

Topological insulators (TIs) present a neoteric class of materials, which support delocalised, conducting surface states despite an insulating bulk. Due to their intriguing electronic properties, their optical properties have received relatively less attention. Even less well studied is their behaviour in the nanoregime, with most studies thus far focusing on bulk samples - in part due to the technical challenges of synthesizing TI nanostructures. We study topological insulator nanoparticles (TINPs), for which quantum effects dominate the behaviour of the surface states and quantum confinement results in a discretized Dirac cone, whose energy levels can be tuned with the nanoparticle size. The presence of these discretized energy levels in turn leads to a new electron-mediated phonon-light coupling in the THz range. We present the experimental realisation of Bi$_2$Te$_3$ TINPs and strong evidence of this new quantum phenomenon, remarkably observed at room temperature. This system can be considered a topological quantum dot, with applications to room temperature THz quantum optics and quantum information technologies., Comment: 7 pages, 6 figures

Topological photonic systems, with their ability to host states protected against disorder and perturbation, allow us to do with photons what topological insulators do with electrons. Topological photonics can refer to electronic systems coupled with light or purely photonic setups. By shrinking these systems to the nanoscale, we can harness the enhanced sensitivity observed in nanoscale structures and combine this with the protection of the topological photonic states, allowing us to design photonic local density of states and to push towards one of the ultimate goals of modern science: the precise control of photons at the nanoscale. This is paramount for both nano-technological applications and also for fundamental research in light matter problems. For purely photonic systems, we work with bosonic rather than fermionic states, so the implementation of topology in these systems requires new paradigms. Trying to face these challenges has helped in the creation of the exciting new field of topological nanophotonics, with far-reaching applications. In this prospective article we review milestones in topological photonics and discuss how they can be built upon at the nanoscale.