Dipolar and quadrupolar excitons coupled to a nanoparticle-on-mirror cavity

Abstract

We investigate plasmon-emitter interactions in a nanoparticle-on-a-mirror cavity. We consider two different sorts of emitters, those that sustain dipolar transitions, and those hosting only quadrupolar, dipole-inactive, excitons. By means of a fully analytical two-dimensional transformation optics approach, we calculate the lightmatter coupling strengths for the full plasmonic spectrum supported by the nanocavity. We reveal the impact of finite-size effects in the exciton charge distribution and describe the population dynamics in a spontaneous emission configuration. Pushing our model beyond the quasi-static approximation, we extract the plasmonic dipole moments, which enables us to calculate the far-field scattering spectrum of the hybrid plasmon-emitter system. Our findings, tested against fully numerical simulations, reveal the similarities and differences between the strong coupling phenomenology for bright and dark excitons in nanocavities.

Strong coupling as an interplay of quantum emitter hybridization with plasmonic dark and bright modes

“…In the strong coupling regime, however, Rabi splitting is relatively robust with respect to quenching when the emitter is spectrally tuned to the bright dipole mode of a plasmonic nanoparticle, as was shown recently [31]. It has also been shown that light-forbidden quadrupolar transitions of excitons coupled to a nanoparticle on mirror system can lead to strong coupling [37,48].…”

“…Alternatively, strong coupling between the QE and the so-called "dark," weakly radiative modes of conventional Ag and Au nanoparticles has been explored [30][31][32][33][34][35][36][37]. Despite the fact these dark modes are not observable using traditional optical techniques (although they can be observed by electron energy loss spectroscopy (EELS) [38][39][40][41][42], or in scattered light by large clusters [43] and anapoles [44]), it might be possible to visualize them by further hybridization of the dark mode-QE state with the bright mode of the resonator.…”

Transformation optics for plasmonics: from metasurfaces to excitonic strong coupling

“…As discussed in Section 1, TO has been used in the past to obtain analytical descriptions of the light collection and concentration by a wide range of nanoparticle geometries. In this section, we discuss the application of similar methods to build 3D [112,113] (Section 3.1) and 2D [114][115][116][117] (Section 3.2) models of the response of similar structures to point-like EM sources, such as quantum emitters (QEs), placed in their vicinity. This way, TO provides analytical insights into the Dyadic Green's function for these systems.…”

“…The spectral densities can be calculated from the 2D model by using the first equality in (9), fed with 2D calculations of the Purcell enhancement P (ω) = (8 0 /µ 2 E )(c/ω) 2 Im{µ E ∇ Φ(r, ω)| r E }, where r = (x, z) and r E is the position of the emitter in the xzplane. This simplified model makes it possible treating quadrupolar exciton transitions in QEs in an analytical fashion as well [117]. Once 2D Purcell factors are known, they are combined with 3D free-space decay rates in (9).…”

“…With this theory refinement, the spectral width of the Lorentzian terms in (9) acquire the form γ l ,σ = γ D + γ r l ,+1 δ σ,+1 . Moreover, using the method of images, the dipolar moment of even SPs can be extracted out of γ r l ,+1 [117]. The top panel of Figure 5 renders the SP dipolar moment versus index l for the NPoM cavity in panel (a).…”