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arXiv:1912.06023 · Journal of the Optical Society of America B

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

Clément Majorel, Christian Girard, Aurélien Cuche, Arnaud Arbouet, Peter R. Wiecha

Published Mar 30, 2020• 7 citations
arXivHTMLPDF

Abstract

Scanning near-field optical microscopy (SNOM) using local active probes provides 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 and the electric 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 paper, 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 approach 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 such as the laser intensity, the polarization and wavelength, the SNOM probe size, and the nature of the sample.

DOI
10.1364/josab.385918

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Scanning near-field optical microscopy (SNOM) using local active probes provides 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 and the electric 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 paper, 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 approach 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 such as the laser intensity, the polarization and wavelength, the SNOM probe size, and the nature of the sample.
Earlier an idea to use controlled with modern Scanning Probe Microscopy (SPM) technique resonant interaction of dipoles (fluorescent rare earth (RE) ions in crystals) was put forward. Here we discuss the possibility to exploit nanolocal Stark effect, caused in such systems by strong inhomogeneous electric fields of sharp SPM electrodes (tips), to engineer the dark - bright states of resonantly interacting dipoles: their energies and decay (decoherence) rates can be strongly influenced by such fields.
We experimentally demonstrated that the lifetime of quantum emitters with strongly mixed electric dipole (ED) and magnetic dipole (MD) transitions can directly probe the combined electromagnetic local density of optical states. OCIS codes: (250.0250) Optoelectronics; (260.2510) Fluorescence; (260.3160) Interference. Purcell effect shows the spontaneous decay rate of a quantum emitter depends on its local density of optical states (LDOS), which indicates that the spontaneous decay rate can be selectively enhanced or suppressed by properly engineering its local optical environment. As demonstrated in Drexhage's pioneering experiments, the electric LDOS oscillates as a function of the separation distance between the emitter and metal-dielectric interface (red line in Fig. 1(a)), thus leading to the measurable oscillations of corresponding lifetimes (red line in Fig. 1(b)). The lifetime oscillations refer to the enhancement and suppression of spontaneous decay rate of light emitters at varied locations. In the literature, the fitting to the oscillations has been employed to infer quantum efficiency of light emitters. However, these oscillations are not a fundamental nature of electromagnetic mode density. The measured electric LDOS using the common purely ED or ED-dominant emitters is only the projection of the combined electromagnetic LDOS onto an isotropic electric dipole (Fig. 1(a)). In the past decade, the magnetic light matter interaction has drawn great attention thanks to the advance of metamaterials. In addition to those magnetic resonators (e.g., split-ring resonators and parallel nanorods), strong MD transitions exist as well in transition-metal and lanthanide ions [1]. In order to probe the combined electromagnetic LDOS, strongly mixed ED-MD emitters are required to access to electric and magnetic LDOS simultaneously. Here we experimentally investigated the lifetimes of two strongly mixed ED-MD emitters: divalent nickel ions in magnesium oxide (Ni 2+ :MgO) and trivalent erbium ions in yttrium oxide (Er 3+ :Y 2 O 3) [2]. Staircaselike samples with 44 distinct regions (i.e., with varied spacer thicknesses d and/or top interfaces) were fabricated for the two quantum emitters, respectively. Time-dependent photoluminence was then measured for all distinct areas of the samples to extract the corresponding lifetimes. The measured lifetime of the mixed ED-MD emitter does not solely depend on electric or magnetic LDOS, but rather follows the combined electromagnetic LDOS. Almost no lifetime oscillations was observed in the measured lifetimes of 3 T 2 → 3 A 2 transitions in Ni 2+ :MgO, as shown in Fig. 1(c) (black dots). This is further confirmed by a technologically and scientifically important emitter Er 3+ :Y 2 O 3. Of great interest, the complex electronic levels of Er 3+ make it support both purely ED transitions (4 S 3/2 → 4 I 15/2) at visible regime and strongly mixed ED-MD transitions (4 I 13/2 → 4 I 15/2) at telecom wavelengths [3]. The measured lifetime of strongly mixed ED-MD transitions 4 I 13/2 → 4 I 15/2 in Er 3+ :Y 2 O 3 at telecom wavelengths follows the combined electromagnetic LDOS. In contrast, the measured lifetime of the purely ED transitions at visible regime (4 S 3/2 → 4 I 15/2) originating from the same Er 3+ emitters solely depends on the electric LDOS. The extracted MD contributions from the theoretical fitting of measured lifetimes match the results obtained by the recently developed energy-momentum spectroscopy [3,4]. The findings here show that, for emitters with strongly mixed ED-MD transitions as well as characterized quantum efficiency and bulk lifetime, a single lifetime measurement can probe the combined electromagnetic LDOS at the point of interest in a complex optical system, such as metamaterials, epsilon-near-zero materials, and topological photonics.
The change of intensities of optical transitions of atoms, molecules, and their ions in the near field of nanoobjects is of interest for researchers from both basic and applied points of view. The concept of a near field was used as early as the 1960s to study the mechanisms of hypersensitive transitions of rare-earth (RE) ions. In this work, it is once more emphasized that, precisely for these transitions, changes in characteristics under the action of local properties of the medium are especially strong and, correspondingly, these transitions are especially promising for use. The Judd method for the calculation of the intensities of hypersensitive transitions of RE ions taking into account the inhomogeneous ligand field is extended to RE ions in the near field of nanoobjects. A simple analytical expression for the Judd-Ofelt intensity parameter Ω 2 for RE ions in the field of spherical nanoparticles of a subwavelength size is derived.
We study the behavior of electric fields in and around dielectric and metal nanoparticles, and prepare the ground for their applications to a variety of systems viz. photovoltaics, imaging and detection techniques, and molecular spectroscopy. We exploit the property of nanoparticles being able to focus the radiation field into small regions and study some of the interesting nonlinear, and quantum coherence and interference phenomena near them. The traditional approach to study the nonlinear light-matter interactions involves the use of the slowly varying amplitude approximation (SVAA) as it simplifies the theoretical analysis. However, SVVA cannot be used for systems which are of the order of the wavelength of the light. We use the exact solutions of the Maxwell's equations to obtain the fields created due to metal and dielectric nanoparticles, and study nonlinear and quantum optical phenomena near these nanoparticles. We begin with the theoretical description of the electromagnetic fields created due to the nonlinear wavemixing process, namely, second-order nonlinearity in an nonlinear sphere. The phase-matching condition has been revisited in such particles and we found that it is not satisfied in the sphere. We have suggested a way to obtain optimal conditions for any type and size of material medium. We have also studied the modifications of the electromagnetic fields in a collection of nanoparticles due to strong near field nonlinear interactions using the generalized Mie theory for the case of many particles applicable in photovoltaics (PV). We also consider quantum coherence phenomena such as modification of dark states, stimulated Raman adiabatic passage (STIRAP), optical pumping in 444-level atoms near nanoparticles by using rotating wave approximation to describe the Hamiltonian of the atomic system. We also considered the behavior of atomic and the averaged atomic polarization in 777-level atoms near nanoparticles. This could be used as a prototype to study any n−n-n−level atomic system experimentally in the presence of ensembles of quantum emitters. In the last chapter, we suggested a variant of a pulse-shaping technique applicable in stimulated Raman spectroscopy (SRS) for detection of atoms and molecules in multiscattering media. We used discrete-dipole approximation to obtain the fields created by the nanoparticles.
A scanning optical microscope whose active element (the tip) consists of a crystal containing impurity ions or color centers, which are excited by laser radiation, is proposed. The excitation energy from a single impurity center located at the point of the tip is transferred to the fluorescence centers of the experimental sample by the mechanism of resonant dipole-dipole exchange. It is shown that this approach can give nanometer spatial resolution with high sensitivity, which in many cases is much higher than the sensitivity of the “standard” near-field fluorescence microscopy.