1. Introduction

In the last two decades, plasmonic structures and metamaterials have attracted the attention due to their novel applications and unconventional physics. Strong modification of photonic modes achieved with these systems makes it possible to control light propagation in unprecedented ways as featured in experimental demonstrations such as optical cloaking, negative refraction, and subwavelength imaging below diffraction limit [1–7]. In addition, it has been predicted and experimentally proved that strongly modified local optical environment provides new possibilities to control quantum processes [5,6]. Among them, the most known phenomenon is an enhancement of the spontaneous emission due to an increased density of photonic modes (so-called Purcell effect, first shown by Purcell in 1946 using the resonant cavity [8]). Multiple demonstrations and applications include use of various resonant structures, such as cavities, plasmonic nanoparticles, nano-antennas, metasurfaces and metamaterials with enhanced densities of photonic modes [9–17], including hyperbolic metamaterials having a nominally infinite density of photonic modes [16,17].

Majority of the theoretical studies and experiments are primarily focused on electric dipole emitters. Similar arguments have been also applied to magnetic dipole transitions which are commonly weak in natural materials but can be enhanced and controlled via modified optical environment (magnetic Purcell effect [18–29]), providing a new playground for fundamental physics and various applications. Various approaches have been taken in order to achieve this, using the structures which provide strong enhancement of the magnetic component of photonic modes, such as plasmonic nanostructures having magnetic resonance at the emission wavelength [20,21], films, metasurfaces, metamaterials [22–27], and high-index dielectric nanostructures [28,29]. However, in the contrary to expectations, experimentally observed enhancements in the magnetic dipole emission are not significant. This can be due to a relatively low quality-factor of resonances in real nanostructures, high loss in metal, or other factors such as a competition between various channels of the relaxation, which are also affected by the environment.

In this work, we test another approach for controlling magnetic dipole emission. We use tri-layer sandwich-like structures consisting of two external metal layers and a dielectric layer between them, which can exhibit the resonances at the emission wavelength. The resonance behavior of such structures is determined by several parameters, including the distance between the metal layers, d, thickness of metal films, dielectric constants of the materials and surrounding dielectrics, with the dispersion relation split to several branches [30]. Here we consider the low frequency range and two types of the resonances, a cavity (Fabry-Perot-type) resonance, Fig. 1 (a), and a low-frequency branch of gap plasmon resonances, Fig. 1(b). In terms of waveguide applications, these modes can be also referred as asymmetric and symmetric modes (regarding to the orientation of fields on interfaces) [31,32]. At relatively large d, both types of resonances occur, while at small gap sizes, $d < \lambda /2,\; $ only the gap plasmon modes survive with strongly confined fields. Since that gap plasmons allow one to achieve strong field confinement, they are of great practical interest for various studies and applications in information transfer technologies, sensing and single-photon sources, nanoantennas, quantum computing, etc. [33,34].

 

Fig. 1. (a,b) Schematics of fields in (a) cavity resonance and (b) gap plasmon modes in metal-air-metal structures at λ = 600 nm, p-polarization. Electric fields are shown with arrows, magnetic fields are shown with color (in arb. u.). The gap size is 270 nm. The dielectric constant of the substrate is assumed to be 3.2.

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The cavity and gap plasmon resonances have different distributions of magnetic and electric fields as illustrated in Fig. 1. We expect the emitters located inside to be affected by the resonant modes. Due to different distributions of the fields, the effects on electric and magnetic emitters can be different.

The cavity modes are decoupled to propagating modes at the condition

2. Experimental

Eu(NO₃)₃.Bpy₂ is a convenient luminescent material for such an experiment, and has been used in the previous studies [17,20,22–25,28] for probing effects of a modified optical environment on both electric and magnetic dipoles. Schematics of the energy levels and excitation and emission in this material are shown in Fig. 2(a). Eu³⁺ can be excited via ligand in the ultraviolet range and demonstrate bright emission in red (Fig. 2(b)) with several well-resolved peaks in the spectrum corresponding to the transitions from ⁵D₀ to ⁷F_i sublevels. The predominantly magnetic dipole (MD) transition ⁵D₀$\to $⁷F₁ is observed around 590 nm, and the strongest ⁵D₀$\to $⁷F₂ transition associated primarily with the electric dipole (ED), is observed at 613 nm, Fig. 2(c).

 

Fig. 2. (a) Energy level diagram; (b) Photo of silver substrates covered with 25 nm-thick emitter layers under UV light illumination; (c) Spontaneous emission spectra of the film on the silver surface; (d) Schematics of the experimental profile-modulated structure.

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Eu(NO₃)₃.Bpy₂ crystals are synthetized using the solution grown technique [22,37]. For fabrication of thin films, ethanol-water solution is prepared with the mixture of Eu(NO₃)₃.Bpy₂ and polyvinylpyrrolidone (PVP) in 1:1 weight ratio.

As profile-modulated substrates we use polycarbonate substrates with the modulation period of 320 nm and height of 20-25 nm derived from digital storage BluRay-R (BR) discs (from Verbatium) following the procedure described in [38]. Silver is deposited with the thermal evaporation method. The first external silver layer is chosen to be thick enough (160 nm) to efficiently reflect the light, and the second silver layer is thin (30 nm) in order to provide efficient excitation of the emitters. Intermediate layers with Eu are fabricated using the spin coating technique. By regulating rotation speed, time and steps, we are able to produce the films with various thicknesses. The quality of the luminescent films is tested before the deposition of the second silver layer observing their luminescence under a UV lamp, Fig. 2(b). Planar structures on glass substrates are fabricated together with the profile-modulated structures; they are used as witness samples for the thickness measurement after each fabrication step. The thickness of the produced layer is measured in the flat structures with DekTekXT surface profilometer. Since particular layers in a profile-modulated structure and a witness sample are produced at the same thermal evaporation run or at the same spin coating parameters, we assume that they have the same thickness.

The schematics of fabricated three-layer systems is illustrated in Fig. 2(d). The silver layers have the same thicknesses for all systems in the series while the size of the emitter layer, d (in the range from 25 nm to 200 nm) is made different for each sample. Visual examination of the produced three-layer systems (under UV light) shows that in flat structures the emission is very weak, however it is significantly brighter in the profile-modulated systems, in particular, in the samples with small d and at large observation angles, where it is predominantly p-polarized.

In the experiment, the profile-modulated structures with various gap sizes are studied using the standard spectrofluorometer (Fluorolog-QM). The samples are placed on the stage with the grooves oriented vertically. The emission spectra are collected in the front-face collection setup, where the angle between the incident light (excitation) and collected light (emission) is 22.5°. We use the incidence angle, θ = 20° for the incident light. The excitation wavelength is 330 nm, which corresponds to the maximum of the excitation band. The emission spectra are recorded in the direction close to normal (2.5°) in the range of 570 nm - 630 nm, which covers both magnetic dipole transition and the strongest electric dipole transition, Fig. 3(a). We use the same orientation (θ = 20°) for all the systems under study and estimate the ratio of the peak intensities of magnetic dipole and electric dipole transitions, I_MD / I_ED as the function of d. Variation in the angle θ does not significantly affect the ratio for a particular system (but affects the intensity of the signal).

 

Fig. 3. (a) Emission spectrum in silver-emitter layer-silver structures with d = 150 nm (blue) and 30 nm (red). Branching ratio of MD and ED transitions in (b) three-layer structures, (c) in the presence of the original BR multilayer. (d) Emission spectra on top of silver with the multilayer. Insets show schematics of the corresponding structures. The materials are indicated.

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The results obtained in the samples with different emitter layer thicknesses are shown in Fig. 3(b). Here, the ratio I_MD /I_ED is normalized to that observed in the emitter films deposited on glass (0.18). The experiment demonstrates the minimum at intermediate d (∼ 150 nm) and an increase in I_MD / I_ED toward a decrease in d. The magnitude I_MD / I_ED do not exceed the ratio observed on glass at any gap thickness.

In addition to these results, we would like to mention an interesting experimental finding. If in the fabrication, we do not remove the original multilayer from BR discs and deposit the luminescent material directly on it, the ratio I_MD / I_ED in such structures is significantly higher than that in our main experimental three-layer structures. It also shows different dependence on the gap size, Fig. 3(c). The ratio is even higher in the structure without the external silver layer, Fig. 3(d). The MD line exceeds the strongest ED line, which was, according to our knowledge, never observed before in or in vicinity of any plasmonic structure. (Typical spectrum of Eu³⁺ on top of silver is shown in Fig, 2(c).)

3. Analysis and discussion

Let us first discuss resonance properties of profile-modulated three-layer structures. We use COMSOL Multiphysics for numerical simulations of the optical fields in three-layered structures with one dimensional (1-D) modulation of profile, corresponding to the geometry of our experimental structures, Fig. 2(d). Since we concentrate on the emission range between 580 nm - 620 nm, the simulations are performed at the wavelength λ = 600 nm which is close to both MD and ED transitions. As a metal we use silver with the dielectric permittivity, ε_M = - 16 + 0.44i at 600 nm. The permittivity of the dielectric layer ε_D = 2.56 corresponds to that of the organic material in our experimental systems.

Note that the resonance behavior of this system having a profile modulation and a relatively thin metal layer is more complex than that in the gap between two semi-infinite flat metals. However, both cavity resonance (Fig. 4(a)) and gap plasmon (Fig. 4(b)) resonances are clearly present. In our geometry (p < λ), the gap plasmons can be excited (or decoupled) at the condition,

 

Fig. 4. (a,b) Distributions of electric (top) and magnetic(bottom) energy in (a) cavity resonance mode at d = 160 nm, and (b) plasmonic mode, d = 75nm. (c) Reflectivity vs incidence angle at d = 25 nm.

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At large gaps,

The Eq. (4) predicts the excitation or decoupling of plasmons at the incidence angle of ∼ 56°. Simulations show that this estimation holds up to the smallest thicknesses of the intermediate layer (d = 25 nm) used in our experiments. In the reflectivity, Fig. 4(c), this is observed as a deep minimum, indicating that our geometry provides conditions for efficient plasmon excitation or decoupling.

Purcell effect [8] predicts the modification of the spontaneous emission rate as

Here $\; \tau _n^{ - 1}$ is the rate for other relaxation channels which are not affected, including non-radiative relaxation. If the affected transition is very weak, $\; \tau _r^{ - 1}$ and $F\; \tau _r^{ - 1}$, are much lower than $\; \tau _n^{ - 1},\; \,G \approx \; F$, and the emission can become F -fold brighter (neglecting losses in metal).

Note in organic systems with Eu³⁺, the luminescence of Eu³⁺ is already very efficient [22,37,41,42]. Depending on the excitation pathways, it can reach up to 50% of quantum yield [42] mostly in ED transitions. Thus, in the very best scenario and extremely high Purcell factor, visible enhancement of the ED emission can be only around two. On the other hand, MD transition is relatively weak (of about 8-18% of the total emission depending on a particular material), leaving a room for a possible enhancement. However, since both ED and MD transitions originate from the same energy level, ED channels of the relaxation may become the main competitors for MD channels.

Let us estimate the change in the branching ratio in our systems following the approach used in [28], involving the Lorentz reciprocity theorem [40,43]. According to the theorem [44,45], the light out-coupling problem can be solved considering light in-coming to the emitter. In our estimations, we consider only probabilities of the emission to propagating waves. Since both ED and MD transitions originate at the same level, contributions of non-propagating modes affect the total relaxation rate and result only in reducing the total emission intensity.

In calculations, we assume the random orientation of the emitters and, average the results over 32 points which are distributed over the modulation period (Fig. 5(a)), since the fields strongly vary inside the gap. The probability of the emission under the angle θ is estimated as $P_\theta ^{ED} \propto \; \mathop \sum \limits_{,TE,TM} {|{E(\theta )} |^2}$ and $P_\theta ^{MD} \propto \; \mathop \sum \limits_{,TE,TM}{|{H\; (\theta )} |^2}$ for electric and magnetic dipole emitters respectively, where E and H are correspondingly electric and magnetic components of the optical modes. Taking into account symmetry of our system and assuming no transmission through the thick silver layer, we vary the incidence angle θ between 0 and 90° and calculate the transitions probabilities in the emitter layer for various sizes of the gap, d = 25 - 280 nm. At a small gap size, the emission is determined by gap plasmons. It is highly directional, showing significant enhancement (more than order of magnitude in comparison with emitters in free space) in the direction corresponding to the plasmon decoupling angle, Fig. 5(b). This is in line with the experimentally observed predominantly p-polarized emission at large observation angles. At larger d, the pattern is more complicated and much broader covering the whole angular range.

 

Fig. 5. (a) Positions of emitters (shown with red dots) in calculations of the emitting properties; (b) Angular dependence of the ED (blue) and MD (red) emission intensity in the structure with d = 25 nm; (c) Branching MD/ED ratio, calculations (circles) and experiment (crosses).

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The total MD or ED emission to free space is estimated with integration over θ . The resulting branching ratio, ${I_{MD}}/{I_{ED}}$ shows the variation with the gap size well corresponding to the experimental data, Fig. 5(c).

In our three-layer resonant structures both electric and magnetic dipoles are affected by plasmons or cavity modes; this restricts the opportunity to fully control or enhance magnetic dipole emission in Eu³⁺ ions. In principle, placing the emitters with nanoscale accuracy to certain places of standing resonance modes can provide for the enhancement, however, would require sophisticated fabrication approaches.

Commonly, in the research devoted to MD enhancement, the main attention is paid to the structures with a strong magnetic response. An alternative approach worth investigating can be in designing the structures primarily targeting decreasing the competitive ED transition rate. This would lead to a natural increase in the MD emission intensity and a better control of it. Our preliminary considerations show that this may be the cause for our surprising accidental finding of MD/ED brunching ratio > 1 in BR substrates with original recording multilayers, Fig. 3(d), and its behavior in complex cavities, Fig. 3(c). Since the composition of the BR discs is a proprietary information, for a proper study we plan to repeat these experiments with our own multilayers and publish in detail elsewhere.

4. Conclusions

In conclusion, profile-modulated three-layer systems consisting of two external silver layers and an intermediate layer with Eu³⁺ emitters are experimentally and theoretically studied, taking into account the competition of ED and MD channels of the relaxation. Strong directionality of the emission is predicted for small gap sizes; it is associated with decoupling of gap plasmons excited by emitters inside the cavity. Since both ED and MD emitters are affected, such structures do not provide for the efficient MD enhancement, and mainly cause the variation in the branching ratio of MD and ED transitions in the dependence of the emitter layer thickness.