Quantum theory of near-field optical imaging with rare-earth atomic clusters

Abstract

Scanning near-field optical imaging (SNOM) using local active probes provides in general images of the electric part of the photonic local density of states. However, certain atomic clusters can supply more information by simultaneously revealing both the magnetic (m-LDOS) and the electric (e-LDOS) local density of states in the optical range. For example, nanoparticles doped with rare-earth elements like europium or terbium provide both electric dipolar (ED) and magnetic dipolar (MD) transitions. In this theoretical article, we develop a quantum description of active systems (rare earth ions) coupled to a photonic nanostructure, by solving the optical Bloch equations together with Maxwell's equations. This allows us to access the population of the emitting energy levels for all atoms excited by the incident light, degenerated at the extremity of the tip of a near-field optical microscope. We show that it is possible to describe the collected light intensity due to ED and MD transitions in a scanning configuration. By carrying out simulations on different experimentally interesting systems, we demonstrate that our formalism can be of great value for the interpretation of experimental configurations including various external parameters (laser intensity, polarization and wavelength, the SNOM probe size, the nature of the sample ...).

Control of light emission of quantum emitters coupled to silicon nanoantenna using cylindrical vector beams

“…S 2 ), thus avoiding the PL being governed by the LDOS only. In the low power regime, as previously mentioned, we expect the PL to be dependent mainly on the near-field at the excitation wavelength 12 – 14 .

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“…On the other hand, the influence of the pump has been rarely considered experimentally. In fact, the PL signal of a quantum emitter is either proportional to the LDOS or to the near-field intensity when the excited state is saturated or not, respectively 12 – 14 . In this article, we investigate in the nonsaturated regime the influence of focused cylindrical vector beams on the PL of a rare earth ion-doped thin film deposited on high refractive index dielectric nanostructures.…”

Magnetic and electric Purcell factor control through geometry optimization of high index dielectric nanostructures

“…We have used the Green Dyadic Method (GDM) [39] and especially the python toolkit pyGDM [40,41]. It allows to perform decay-rate calculation inside multi-material nanostructures through a formalism based on field-susceptibilities for the derivation of the LDOS [26,40,42,43]. The GDM is based on a volumic discretization of the nanostructures.…”

“pyGDM” - new functionalities and major improvements to the python toolkit for nano-optics full-field simulations

“…Finally, it is now possible to calculate both, the electric and magnetic decay rates also inside nanostructures. pyGDM uses a formalism based on field-susceptibilities for the derivation of the photonic local density of states (LDOS), as detailed in references [30,67,68,69]. We demonstrate the possibility to calculate magnetic decay rates inside nanostructures by a comparison to Mie theory [70,71].…”