Abstract
Alldielectric nanoantennas, consisting of high refractive index semiconductor material, are drawing a great deal of attention in nanophotonics. Owing to their ability to manipulate efficiently the flow of light within subwavelength volumes, they have become the building blocks of a wide range of new photonic metamaterials and devices. The interaction of the antenna with light is largely governed by its size, geometry, and the symmetry of the multitude of optical cavity modes it supports. Already for simple antenna shapes, unraveling the full modal spectrum using conventional farfield techniques is nearly impossible due to the spatial and spectral overlap of the modes and their symmetry mismatch with incident radiation fields. This limitation can be circumvented by using localized excitation of the antenna. Here, we report on the experimental nearfield probing of optical higher order cavity modes (CMs) and whispering gallery modes (WGMs) in amorphous silicon nanoantennas with simple, but fundamental, geometrical shapes of decreasing rotational symmetry: a disk, square, and triangle. Tapping into the nearfield using an aperture type scanning nearfield optical microscope (SNOM) opens a window on a rich variety of optical patterns resulting from the local excitation of antenna modes of different order with even and odd parity. Numerical analysis of the antenna and SNOM probe interaction shows how the nearfield patterns reveal the node positions of – and allows us to distinguish between – cavity and whispering gallery modes. As such, this study contributes to a richer and deeper characterization of the structure of light in confined nanosystems, and their impact on the structuring of the light fields they generate.
1 Introduction
Alldielectric nanostructures are becoming key elements in modern nanophotonics R&D, allowing efficient control of the phase, polarization, and direction of light [1]. Twodimensional arrangements of subwavelength nanoparticles make it possible to create ultrathin metasurfaces [2] operating as efficient lenses [3], polarizers [4], nonlinear [5–9] and magnetooptical devices [10, 11], ultrafast switches [12, 13], light emitting devices [14–16], directional light scatterers [17–20], and photonic topological insulators [21, 22]. A single alldielectric nanoparticle in such metasurfaces operates as an optical nanoantenna that manipulates light through the excitation of various electric and magnetic optical modes [23].
The full mode spectrum of a nanoantenna can be significantly expanded by giving it a nonspherical shape. It enables the excitation of higher order modes and thereby offers opportunities for more elaborate light flow manipulation and tunability compared to low order modes. Depending on the spatial field distribution, the higher order modes are localized either inside the whole volume of the nanoantenna – cavity modes (CMs), or around the nanoantenna’s edge – whispering gallery modes (WGMs). Spatial and spectral overlapping of higher order CMs and WGMs in nanoantennas complicates their analysis using conventional farfield optical techniques. Moreover, the presence of mirror symmetry planes of complex shaped nanoantennas splits optical modes in ones with even or odd parity (symmetry). As the electromagnetic field of a plane wave source at normal incidence possesses even and odd parity with respect to the two symmetry planes, it allows coupling with only specific modes [24–28]. Whereas modes with mismatching symmetry are forbidden for excitation, inclined illumination is able to break this symmetry coupling rule [29–32]. Numerical works have shown, nevertheless, that a point dipole source can efficiently couple to both even and odd parity modes and as such modify its emission [33–35]. Therefore, local excitation within the nearfield becomes a crucial approach to excite and visualize higher order modes in alldielectric nanoantennas of increasingly complex shapes.
Various optical techniques exist for the local excitation and visualization of optical modes in photonic structures at the nanoscale. The visualization of plasmonic charge density waves in gold microstructures was realized by scanning a plasmonic antenna with a highly focused light beam while recording the scattered intensity [36]. Angularresolved cathodoluminescence using a high energy electron beam allows the local excitation and mapping of high and low order radial and azimuthal resonant modes in silicon (Si) nanodisks [37], and hybridized symmetric and antisymmetric modes in Si bar dimers [38]. A wide variety of even and odd surface plasmon modes have been mapped using electron beams in metallic nanoantennas of different shapes: rod [39], disk [40], square [41], triangle [42], and their coupled systems [43–45].
Alternatively, the mapping of optical mode distributions with subwavelength resolution can be achieved using scanning nearfield optical microscopy (SNOM). Here, either a sharp metal coated needlelike (apertureless) probe or a hollow, metal coated probe with a subwavelength hole at its apex (aperture) is scanned over the surface of the nanophotonic systems. An SNOM measurement is typically performed with one of two conventional approaches: the collection or illumination scheme.
In the collection scheme, the modes of the nanoantennas are excited from the farfield, and an aperture or apertureless probe picks up their nearfield. Such nearfield studies have been performed on plasmonic nanoantennas of different shapes including disks, rods, triangles, YagiUda antennas [46–51] and alldielectric nanoantennas with, e.g., the visualization of electric quadrupole [52] and anapole [53, 54] modes in Sinanodisks, and the magnetic field in the gap of Sinanodisk dimers [55]. However, such a technique allows coupling only to a limited number of modes available for plane wave excitation, and tilted illumination should be used in order to access both even and odd parity modes.
In the SNOM illumination scheme, a localized nearfield light source is generated around the apex of an aperture or apertureless probe by illuminating it from the farfield. In this case, we obtain a unique subwavelength polarized light source. This localized source can provide a symmetry breaking effect that allows an efficient excitation of even and odd parity modes. As such, multiple plasmonic modes in various antenna shapes [56–59] and optical Fabry–Pérot modes with odd and even parity in amorphous silicon nanorods [60] have been mapped. Notwithstanding that such a variety of higher order optical modes has been observed in plasmonic structures of various shapes, nearfield probing of alldielectric nanoantennas was performed only in disk and rod shapes where several higher order spectrally and spatially separated optical modes have been studied. The modification of a dielectric antenna shape expands the set of higherorder CMs and WGMs with high Qfactor. The spectral and spatial overlapping of CMs and WGMs can be exploited to increase the optical density of states which is crucial for lightemitting and nonlinear devices. However, the coexistence of multiple spectrally overlapped higher order modes at a single wavelength significantly complicates the analysis and interpretation of SNOM data as compared to a single optical mode.
In the current work, we used the aperture type scanning nearfield optical microscopy for the probing of higher CMs and WGMs in alldielectric nanoantennas with basic geometries of different rotational symmetry. We show experimentally and numerically that the SNOM aperture probe in the illumination scheme excites higher order transverse electric and magnetic modes in disk, square, and triangular antennas consisting of amorphous silicon (αSi). Due to the coexistence of a rich variety of modes at a single wavelength, the SNOM maps do not necessarily represent the field distribution of individual optical modes but rather a superposition. Therefore, to provide a thorough analysis of the intensity contrast in SNOM maps, the scanning process of each nanoantenna was simulated with a finitedifference timedomain (FDTD) solver. From these simulations, we can expose the coincidence of features in the SNOM maps and the antennas’ electric or magnetic field modal distributions. At the same time, the wavelengths and probe positions that result in resonant excitation of the different modes can be identified by maxima of the electric field localization.
2 Results and discussion
The experimental scheme for the nearfield mapping is illustrated in Figure 1(a). The local excitation of the optical modes is obtained by focusing polarized supercontinuum laser light in the wavelength range from λ = 600 nm to λ = 750 nm on a subwavelength hole at the apex of 100 nm Alcoated aperture SNOM probe (see the Measurements and simulations in Methods section, Supplementary Materials for more details). The full SNOM map of each nanoantenna is obtained by scanning its surface with the probe in contact mode and recording the transmitted light intensity (T) collected by the objective lens shown at the bottom.
2.1 Disk
We start the discussion with the study of an αSi nanodisk on a glass substrate. The disk diameter is 515 nm and thickness is 96 nm (see the SEM image in Figure 1(b)). For details on the sample fabrication, we refer to the sample fabrication in Methods section and atomic force microscopy section in Supplementary Materials. Experimental SNOM maps at different wavelengths in the range from λ = 600 nm to λ = 750 nm are shown in Figure 1(c). SNOM maps consist of the bright and dark areas corresponding to high and low light transmittance through the SNOM probe–antenna system. The transmittance is modified due to the excitation of higher order optical modes in the nanodisk. The strong wavelength dependence of the patterns in these SNOM maps is similar to the frequency dependence of acoustic Chladni patterns observed on a metallic plate covered by sand and locally driven by a bow [61]. Using fullfield 3D FDTD simulations, the experimental maps can accurately be reproduced, as is demonstrated by comparing panel (c) with (d) in Figure 1. The full scanning nearfield microscopy configuration is taken into account for these simulations, including the nanoantenna, the substrate, and the probe (see SNOM simulations in the Methods section, Supplementary Materials for more details). To show how the excited antenna modes modify the probe transmittance T, the color scale is normalized to the transmittance at the glass substrate, T
_{sub}, recorded at 3 μm distance from the disk boundary. The nanodisk resonator with high aspect ratio supports a rich variety of coexisting optical modes at the same wavelength. Determining the order and type of the excited modes requires figuring out the probe positions and wavelengths at which resonant excitation occurs. To this end, we calculated the integral of the electric field localized inside the antenna volume, W_{
a
} = ∫E^{2}dV, recorded at each position of the SNOM probe on the nanoantenna (see SNOM simulations in the Methods section, Supplementary Materials). The spectral dependence of 2D maps of W_{
a
} normalized to the electric field localization without antenna W_{0} is presented in Figure 1(e). The maxima on these W_{
a
}
/W_{0} maps are located both inside the disk and near its edges. For λ = 610 nm they are negligible, while for longer wavelengths from λ = 630 nm to λ = 730 nm, they are clearly distinguished. The circle, square, diamond, and triangle purple symbols in Figure 1(e) mark the prominent W_{
a
}/W_{0} maxima located near and far from nanodisk’s edge. The nearfield distributions of the optical modes shown in the top row of panels (f–i) present FDTD simulations of the dominant field component along zdirection at the wavelengths corresponding to W_{
a
}/W_{0} maxima. These wavelengths were identified from the spectral dependence of the field localization W_{
a
}/W_{0} (blue curves in panels (f–i)) recorded at the probe positions marked with the purple symbols on the 2D SNOM (panel (d)) and W_{
a
}/W_{0} (panel (e)) maps. To categorize the different optical modes supported by the dielectric nanodisk cavity, we follow the nomenclature of microwave dielectric cylindrical resonator antennas and waveguides [63].
When the probe locates near the edge of the disk (circle symbol marking in Figure 1(f)), the W_{
a
}/W_{0} spectrum has three maxima which correspond to the excitation of the following WGMs:
Next, we discuss the optical modes excited at other probe positions. When the probe locates in the disk center (square mark in Figure 1(g)), the type of modes changes from WGMs, which are mostly concentrated near the disk edge, to CMs, which cover the full disk volume. The maximum at λ = 685 nm of the corresponding W_{
a
}/W_{0} spectrum is associated with the
The positions of the SNOM probe, at which the resonant excitation takes place, coincide with nodes of the H
_{
z
} distribution for all excited optical modes. Figure 1(j) shows in more detail the coupling of the probe nearfield with
Now we discuss the transmission intensity contrast that is observed in the SNOM maps. For this, we focus on the most prominent W_{
a
}/W_{0} maxima positions in Figure 1(e) and superimpose them on the simulated SNOM maps in Figure 1(d) (purple marks). As such, we can associate the excitation of specific optical modes with the resulting transmittance features. A quick look at Figure 1(d) and (e) already reveals that there is no straightforward onetoone correlation between the excitation of a mode and the SNOM contrast. Indeed, the maxima of the field localization can coincide with both local dark or bright spots, or even somewhere in between. This leads us to conclude that the SNOM intensity contrast is the result of a more intricate interplay between multiple coexisting optical modes that can be excited at the same wavelength. The scattering intensity of each optical mode can be high or low, which results in bright or dark spots, respectively. For the SNOM map at λ = 630 nm (Figure 1(d)),
Figure 1(g)–(i) depicts the spectral dependence of the transmittance T/T
_{sub} (black curves) and field localization W_{
a
}/W_{0} (blue curves), for fixed positions of the SNOM probe as indicated with the purple dots in Figure 1(d) and (e). Also here, it is seen that there is no straightforward link between the local excitation of a mode and the resulting T/T
_{sub} behavior, i.e., there is no spectral match between peaks and dips. A closer look, however, reveals that the T/T
_{sub} curves possess asymmetric Fano lineshapes in the spectral vicinity of resonant modes excitation (the W_{
a
}/W_{0} maxima). The asymmetric lineshape arises from the interference of the two radiative contributions reaching the objective: the first one being the resonant radiation of an optical mode (E
_{antenna}, see Figure 1(a)) and the second being light nonresonantly transmitted through the antenna (E
_{probe}, see Figure 1(a)). The latter comes from propagating modes of the illuminated probe [64]. Similar spectral behavior of the transmittance spectrum (Fano lineshape) has been observed for plasmonic nanoantennas probed by aperture type SNOM in the illumination mode [65, 66]. The T/T
_{sub} minima (maxima), which are blue(red) shifted from the W_{
a
}/W_{0} maxima in Figure 1(f–i), are the results of the destructive (constructive) interference between the antenna modes and propagating modes of the probe. Consequently, this Fanointerference, along with various scattering intensities of each mode, influences the SNOM map intensity contrast. Each mode can manifest itself as a bright or dark spot depending on the observation wavelength and the transmittance of other coexisting modes. Moreover, the SNOM probe position determines the transmittance properties of the individually excited mode. It is seen from the excitation of the
Compared with other works on SNOM nearfield mapping, the observed SNOM contrast for the αSi nanodisk is different from the contrast observed for the excitation of the spectrally and spatially separated Fabry–Perot modes in alldielectric [60] and plasmonic 1D nanorod [56, 67] antennas. In those nanoantennas, the bright (for dielectric nanorod) and dark (for plasmonic nanorod) spots on the SNOM maps coincide with the probe positions of resonant excitation. However, similar to the obtained SNOM maps for a αSi nanodisk, the coexisting cavity and edge plasmon modes at a single wavelength results in either bright or dark spots on SNOM maps measured on gold nanodisks [68] and graphene nanoresonators with a disk and square shape [69].
To conclude, for the disk antenna geometry, we showed that nearfield light of the SNOM aperture probe locally excites the higher order
2.2 Square
Next, we reduce the antenna rotational symmetry to fourfold and turn our attention to an αSi nanosquare with dimensions similar to the nanodisk above: side length of 515 nm and thickness of 96 nm (see SEM image in Figure 2(a)). The experimental and simulated SNOM maps are shown in Figure 2(b) and (c), respectively, at multiple wavelengths between λ = 600 nm and λ = 750 nm. Also here, very distinct transmission patterns are obtained with a very good agreement between experiment and simulation. Although these patterns present some resemblance to those of the nanodisk, there are some clear differences. The calculated 2D maps of electric field localization W_{
a
}/W_{0} shown in Figure 2(d) reveal the probe positions of resonant mode excitation at the local W_{
a
}/W_{0} maxima. The prominent W_{
a
}/W_{0} maxima positions – near and far from the square’s edges – are again marked in Figure 2(a) and (d) with a purple symbol. To find the exact wavelengths of resonant mode excitation, W_{
a
}/W_{0} (blue curves) spectra taken at fixed probe positions are shown in Figure 2(e–h). The top row depicts the distribution of the dominant field component H
_{
z
} in the nanosquare taken at wavelengths corresponding to W_{
a
}/W_{0} maxima in the plots at the bottom row. The H
_{
z
} distributions reveal that the probe excites
Similar to the SNOM maps of the nanodisk, superimposing the W_{
a
}/W_{0} maxima in Figure 2(d) onto the SNOM maps in Figure 2(c) highlights the transmittance features associated with the excitation of the optical modes. The excitation of multiple coexisting modes at their various H
_{
z
} nodes results in bright and dark spots on the SNOM maps. In panel (c), e.g., the bright and dark areas at λ = 655 nm are associated with the excitation of
The different T/T
_{sub} values, associated with excitation of optical modes, are also demonstrated in Figure 2(e–h) by the simulations of the T/T
_{sub} (black curves) and W_{
a
}/W_{0} (blue curves) spectral dependences recorded at individual SNOM probe positions marked with the purple dots. Similar to the disk case, T/T
_{sub} curves present asymmetric Fano lineshapes near the vicinity of optical mode excitation (W_{
a
}/W_{0} maxima) caused by interference of the antenna mode radiation and nonresonantly transmitted light. This again shows that the different modes result in various T/T
_{sub} Fano lineshapes. Even for the individual modes,
To summarize for the square geometry, SNOM maps of the αSi nanosquare reveal the excitation of higher order
2.3 Triangle
Reducing the rotational symmetry of the nanoantenna further expands the modal spectra. In contrast to the disk and square shape, for the equilateral triangle possessing mirror symmetry only with respect to the σ _{ x }plane, a 90° change in the excitation polarization allows the SNOM probe to couple to a different set of modes [70]. Therefore, the polarization directions parallel and perpendicular with respect to the triangle’s height (yaxis) are studied separately in Figures 3 and 4, respectively. Starting with parallel polarization in Figure 3, the experimental SNOM maps of an equilateral αSi nanotriangle with a side length of 700 nm and thickness of 100 nm (see SEM image in panel (a)) are shown in panel (b) together with the simulated results in panel (c). Again, the simulated SNOM maps demonstrate a good agreement with the experimental results. Maxima on the 2D W_{ a }/W_{0} maps in Figure 3(d) marked with the purple symbols indicate probe positions that result in resonant mode excitation. For the triangle antenna, we limit our discussion to probe positions on the triangle’s height from the top corner to the base.
The field distribution in Figure 3(e–h) taken at the fixed probe positions (marked by purple symbols in panel (d)) and corresponding to maxima of W_{
a
}/W_{0} spectra (blue curves) in Figure 3(e–h) demonstrate the excitation of both
The positions of resonant excitation coincide with E
_{
z
} nodes for
Figures 4(b) and (c) show that rotation of the excitation polarization by 90° leads to modification of the SNOM maps due to the absence of mirror symmetry of the nanotriangle with respect to the σ
_{
y
}plane (perpendicular to the yaxis). Again, experimental maps (panel (b)) are in very good agreement with simulated results (panel (c)). The selected wavelengths of λ = 642 nm and λ = 704 nm correspond to the maxima on the W_{
a
}/W_{0} maps shown in panel (d). The simulated H
_{
z
} distributions shown in panels (e–h) demonstrate that the type of modes excited along the height of the triangle is transverse electric with odd parity with respect to the σ
_{
x
}plane. The mode parity is opposite to the one observed for ypolarized illumination (Figure 3). The H
_{
z
} field distribution of the modes for xpolarized illumination is transformed as a symmetric function (H
_{
z
}(x, y) = H
_{
z
}(−x, y)). The
The superimposed W_{
a
}/W_{0} maxima positions on the simulated SNOM maps (Figure 4(c)) show the various SNOM probe transmittance features associated with the excitation of coexisting optical modes with different scattering intensity, similar to the disk and square case. For the SNOM map at λ = 642 nm,
Concluding the triangle geometry, the bright and dark spots on the observed SNOM maps are associated with excitation of
2.4 Quality factor and light trapping capabilities of the excited modes
In addition to the farfield radiative properties of the locally excited higher order modes, we estimate their Qfactors and light trapping capabilities, which are important parameters for applications in lightemitting devices, solar cells, and nonlinear light generation. For this, the W_{
a
}/W_{0} spectra of the nanodisk (Figure 1(f) and (g)), nanosquare (Figure 2(e)–(g)), and nanotriangle (Figure 3 (e and g) and Figure 4(e and h)) were fitted with a multipeak Lorentzian. For the nanodisk, the highest quality factor of Q = 68 and highest field localization value of W_{
a
}/W_{0} = 7.5 are obtained for
A slightly lower Q = 45 is observed for
The estimated Qfactors of the nanotriangle modes are generally lower than the maximum values observed for the nanosquare antenna and are compared to the nanodisk CMs. For ypolarized illumination, we obtained Qfactors of Q = 21 for
However, the SNOM probe–antenna interactions can modify the modal excitation boundary conditions as well as the absorption and scattering of the optical modes. To reveal the influence of the SNOM probe on the Qfactor and resonant wavelength, we compared these parameters calculated from the SNOM data (spectral dependence of electric field localization W_{ a }/W_{0}) with eigenmode analysis without the SNOM probe. Tables S1–S3 in Supplementary Materials, Section 5 show results for optical modes in the nanodisk, nanosquare, and nanotriangle, respectively. For optical modes with Q > 40 (obtained from SNOM W_{ a }/W_{0} data), Qfactors obtained from eigenmode analysis are almost two times larger than the results from SNOM spectral data. In contrast, the eigenmode analysis has similar values for the low Q optical modes (Q < 30 obtained from the SNOM data analysis). The more significant difference of the Qfactors for high Q modes (Q > 40) can be associated with the influence of the SNOM probe on excited optical modes. The SNOM probe leads to the additional light scattering and absorption of the optical modes that decrease their Qfactor. Low Q modes already have multiple channels for radiative and absorption losses. Therefore, adding one more channel (an SNOM probe) will not substantially impact the new Qfactor. In contrast, the impact on a high Q mode will be more prominent. Tables S1–S3 also show that the SNOM probe has only a small impact on the resonant wavelengths. This can be explained by the localization of the optical modes inside the volume of the nanoantennas.
It should be noted that the excitation of the optical modes near nanoantennas’ edges leads to higher electric field localization than at other probe positions.
The variable coupling efficiency that is observed originates from differences in the field overlap of the optical modes and nearfield around the SNOM probe. This overlap is strongly governed by the spatial distribution of the field antinodes. Depending on the mode spatial structures, the field antinodes can be closer or farther from each other. It also depends on the wavelength of the excitation. For the disk, square, and triangle nanoantennas, the spatial distribution of the excited optical modes is different, which modifies the overlap of the optical modes with the nearfield of the SNOM probe. The coupling efficiency is also governed by their intrinsic losses. The ratio of the radiative and absorption loss of the optical modes determines the coupling efficiency [75, 76]. All incident light can be coupled with the optical antenna modes at the equivalence between these two quantities. In other cases, the SNOM probe nearfield light is more efficiently absorbed or scattered. As each mode has its own radiative loss, different modes possess a different coupling efficiency with the SNOM probe nearfield.
2.5 Plane wave excitation
The higher order CMs and WGMs studied above by the SNOM probe excitation are difficult to be observed by farfield techniques using a plane wave source. For comparison, in Section 6, Supplementary Materials, we applied a plane wave source with normal incidence to drive the optical modes in the nanoantenna. It is shown that for the nanodisk, nanosquare, and nanotriangle such an approach allows the coupling to only a limited number of modes. The inability to excite all antenna supported modes is associated with a symmetry mismatch of the electromagnetic fields of the modes and the plane wave source. Moreover, even for the symmetryallowed modes studied above, low coupling efficiency with a normalincidence plane wave source complicates their excitation and observation.
3 Conclusions
Aperture type scanning nearfield optical microscopy (SNOM) reveals a very rich variety of nearfield optical patterns in amorphous silicon nanoantennas. The subwavelength localized excitation of higher order optical cavity modes (CMs) and whispering gallery modes (WGMs) strongly depends on the nanoantennas shape, probe position, and excitation frequency. This has been demonstrated for some of the most basic geometries with varying rotational symmetries: a disk, square, and triangle. A detailed analysis based on fullfield FDTD simulations allowed us to link the aperture SNOM maps to the field distributions of higher order modes supported by the nanoantennas which have not been previously visualized. The experimental data has been reconstructed based on the decomposition in CMs and WGMs with different order and parity. The insights obtained within this study for basic antenna cavity shapes provide an important foundation for the detailed understanding of the optical behavior of more complex nanocavity systems under local excitation and the interpretation of experimental nearfield data. The local excitation of CMs and WGMs with even and odd symmetry is accompanied by very distinct light scattering and trapping properties that have a direct impact on e.g. the quantum efficiency of nearby emitters, the efficiency of nonlinear effects [77, 78], and directionality of scattered or emitted light [19, 79].
Funding source: Russian Ministry of Education and Science
Award Identifier / Grant number: (14.W03.31.0008, numerical simulations)
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: (190200876, SNOM measurements)
Funding source: Russian Science Foundation
Award Identifier / Grant number: (201200371, sample fabrication)
Funding source: MSU Quantum Technology Centre
Funding source: MSU Development program of the Interdisciplinary Scientific and Educational School
Acknowledgments
The authors like to thank V. D. Malyshev for simulation assistance and Dr. Jiaqi Li for sample fabrication.

Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

Research funding: A.Y.F., V.I.P., and A.A.F. acknowledge financial support by the Russian Ministry of Education and Science (14.W03.31.0008, numerical simulations), Russian Foundation for Basic Research (190200876, SNOM measurements), Russian Science Foundation (201200371, sample fabrication). A.Y.F. also acknowledges MSU Quantum Technology Centre. A.Y.F., V.I.P., and A.A.F. also acknowledge the MSU Development program of the Interdisciplinary Scientific and Educational School “Photonic and Quantum technologies. Digital medicine”. V.V.M. and J.V.V. acknowledge Methusalem support by the Flemish government.

Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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