1. Introduction

Hollow core waveguides represent a special class of optical waveguides with unique properties, since they allow to guide the light inside a hollow or low refractive index (RI) core having found applications in fields such as nonlinear frequency conversion [1], ultrashort pulse compression [2], sensing [3], nano-biophotonics [4] and spectroscopy [5]. Due to the fact that the RI of the core material is lower than that of the cladding, mode formation in such waveguides demands sophisticated microstructured claddings employing effects such as photonic band gap guidance [6], omni-reflection [7] or anti-resonance guidance [8,9]. In particular, the latter has been successfully employed during recent times within the scope of microstructured optical fibers [10], suggesting the possibility to break the current loss benchmark set by solid telecommunication fibers [8,11].

However, such an advancement has not yet been achieved in planar waveguide technology. Here, the most widely used hollow-core approach are anti-resonant reflecting optical waveguides (ARROWs), confining the light via dielectric multilayers inside the hollow core [12]. Even though planar on-chip ARROWs are used within biofluidics [13] and atomic spectroscopy [14], extensive fabrication procedures and incompatibility with fiber circuitry remain key challenges.

One common feature of all discussed waveguides is their tubular geometry, allowing liquids or gases to access the domain of the core only via the open ends. This can lead to impractically long diffusion times, with one example being the diffusion of low-pressure alkali vapour into a few centimetre long hollow core fiber requiring weeks or months of filling time [15,16].

Recently, a new type of on-chip hollow-core waveguide—the light cage—was introduced by the authors providing lateral access to the core region using an open cage structure [17–19]. This concept relies on a freely suspended ring of high aspect ratio dielectric strands surrounding a central hollow core, implemented via 3D laser nanoprinting (Fig. 1(a)). By accessing all three spatial dimensions with nanoscale resolution on the basis of a straightforward two-step procedure [20], this implementation approach allows to overcome the mentioned challenges associated with planar hollow-core waveguides. Light confinement in this structure is enabled by the anti-resonance effect allowing for efficient leaky mode formation and light guidance across centimetre distances. Specifically, the propagating optical modes of the isolated polymer cylinder (i.e., strands) couple together due to the spatial overlap of their modal fields, creating ring-like cladding supermodes. Within one transmission band (regions of high transmission), the central core mode cannot couple to these supermodes due to strong wave vector mismatch, leading to low optical attenuation and forming the underlying principle of the anti-resonance guidance scheme. One unique feature of the light cage geometry is the open space between the strands, providing side-wise access to the core in contrast to other hollow-core waveguide schemes. This novel design drastically reduces diffusion times providing a platform for optical sensing devices with short response times.

 

Fig. 1. The concept of the light cage. (a) Illustration of the light cage including its main features. The upper-right inset shows the measured mode image of the 3 cm long light cage in case white light is launched into the waveguide. A sketch of the light cage cross section is shown in the bottom left corner. (b) Photographic image of three light cages nanoprinted onto a silicon chip (length: 3 cm). (c) Measured transmission spectrum through one of the 3 cm long light cages. The right-hand side images represent a selection of scanning electron micrographs (SEMs) related to light cages showing (d) an oblique view of a single light cage, (e) a top view and (f) an oblique view of three light cages on one chip.

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Even though the capabilities of the light cage concept were already demonstrated [17–19], open questions regarding the overall limits in fabrication of this approach have not been addressed in greater depth. Fully investigating the capabilities and limits of this concept represent the motivation of the present work which features a detailed experimental study of various light cage properties. Specifically we reveal the current limit of maximally feasible device length that can be implemented, unlock the fabrication accuracy of the nanoprinting from optical measurements and discuss the mechanical stability of the light cage geometry.

2. Working principle and design

The construction of the light cage has similarities with revolver-type antiresonant fibers [21]. Both consist of dielectric elements in the micrometre range, which surround a hollow core. In the case of the light cage, these consist of solid polymer strands that are distributed in a hexagonal arrangement. However, unlike fibers, these strands are not fixed by a closed tubular cladding, but are freely suspended, with mechanical stability being ensured by support rings at preselected distances that connect adjacent strands laterally. At the bottom of the hexagon, the waveguide structure is supported by a chain of solid polymer blocks elevating the structure from the substrate.

In this work we specifically studied light cage geometries consisting of twelve strands arranged in a single hexagonal ring (note that dual ring light cages have also been realized [17]). Common to all is the strand diameter ($d = 3.65\;\mathrm{\mu} \textrm {m}$) and the dimensions of the support rings (width along waveguide axis: $3 \;\mathrm{\mu} \textrm {m}$, thickness: $1 \;\mathrm{\mu} \textrm {m}$). Parameters investigated here are the pitch $\Lambda$ (centre-to-centre distance, $\Lambda =7\;\mathrm{\mu} \textrm {m}$), support ring spacing ($L_{\textrm {Supp}}=45 \;\mathrm{\mu} \textrm {m}$), support block spacing ($L_{\textrm {Block}}=178 \;\mathrm{\mu} \textrm {m}$) and total waveguide length $L_{\textrm {LC}}$ with the values in brackets corresponding to the standard geometry (Fig. 1). Note that the hexagonal arrangement is not crucial for the light guidance mechanism and was chosen in analogy to conventional photonic crystal fiber designs with simulations suggesting that light cages with circular- or square-shaped arrangements also work.

Light guidance in light cages is provided by the anti-resonant effect [17]. This effect is based on the hybridization of the individual strand modes leading to the formation of cladding supermodes. These supermodes are anti-resonant with the central core mode at certain wavelengths, which ultimately leads to the formation of leaky modes. In the vicinity of the resonances, however, light can escape from the central core. Both effects result in a characteristic distribution of the transmission of the core mode, i.e. to the formation of transmission bands that are limited by areas with very high losses. This behaviour has been experimentally confirmed in a series of works [17–19] (example of such a spectrum in shown in Fig. 1(c)).

The light cages were fabricated on polished silicon substrates by two-photon polymerization of liquid IP-Dip photoresist using a commercial femtosecond direct laser writing system with the built-in galvanometric mirror scanner (Photonic Professional GT, Nanoscribe GmbH). To this end, the dip-in configuration of the system was used where a high numerical aperture objective (Plan-Apochromat 63x/1.40 Oil DIC, Zeiss) is immersed directly into the resist. One example of a prepared silicon chip is presented in Fig. 1(b). A detailed description of the 3D-printing process is available in the Materials and Methods section of [17]. In short, the used printing parameters were 31 mW, 55,000 $\mathrm{\mu}\textrm{m}$/s, 1 V/m$\textrm {s}^{2}$ and 100 nm / 150 nm for laser power, galvanometric mirror scanning speed and acceleration, and hatching / slicing distances, respectively. These settings were chosen to ensure a high accuracy of the printed structures and result in a manufacturing time of 18 minutes per millimeter waveguide length. Drastically shorter fabrication times could potentially be reached by parallelizing the fabrication using multi-focal arrays [22]. After fabrication, the structures are developed in propylene glycol monomethyl ether acetate (PGMEA, Sigma Aldrich) for 20 minutes, and rinsed by methoxy-nonafluorobutane (Novec 7100 Engineered Fluid, 3M) for 2 minutes. Examples of SEM images of the cross section of the light cages can be found in Fig. 2(c) of [17]. In principle, three-dimensional waveguide architectures can also be realized via direct laser writing (DLW) inside bulk glasses through nonlinear absorption of focused femtosecond laser pulses [23–25]. One key difference to the 3D nanoprinting approach discussed in this work is that such waveguides are always created inside a material and therefore DLW in bulk glasses does not offer the possibility to fabricate freely suspended waveguides such as the light cage geometry.

 

Fig. 2. (a)-(d) Spectral distribution of transmitted power through different implemented light cages for samples with various lengths $L_{\textrm {LC}}$ of 5 mm (a), 10 mm (b), 15 mm (c) and 20 mm (d). The propagation loss was calculated from exponential fitting of transmitted power versus sample length at the spectral location of high transmission and is shown in (e). The grey dashed line in (e) is a guide-to-the-eye.

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The optical properties of the samples were determined by measuring the transmission $T$ across the visible spectral domain using a setup that consists of a broadband light source, coupling opto-mechanics and spectral and imaging diagnostics [17]. Specifically, the white light beam was supplied from the output of a supercontinuum source ($450 \;\textrm {nm} \leq \lambda \leq 2.4 \;\mathrm{\mu} \textrm {m}$; SuperK COMPACT, NKT Photonics). A notch filter was used to remove the pump light at 1065 nm, while a polarizer was employed to create a horizontally polarized beam. The beam was then coupled to the fundamental mode of the light cage (example mode image shown in Fig. 1(a)) by means of a standard microscope objective ($\times$20, NA = 0.5). After transmission through the light cage, the beam was collimated by an objective ($\times$10, NA = 0.3) and guided to a spectrometer ($350 \textrm {nm} \leq \lambda \leq 1.75 \;\mathrm{\mu} \textrm {m}$, $\Delta \lambda = 0.4 \;\textrm {nm}$; AQ6374, Yokogawa test $\&$ measurement Corp.) via a multi-mode fiber (M15L05, core size: $105\;\mathrm{\mu} \textrm {m}$, NA = 0.22).

The optical measurements were performed in two steps: First, the core mode was excited by light focused by the in-coupling objective positioned on a micrometer-precision 3D translational stage. The coupled mode shape and transmitted intensity were optimized while monitoring the mode with a CCD camera. Subsequently, the coupling of the transmitted light to the multi-mode fiber of the spectrometer was maximised. All spectra were normalized to the same reference spectrum which was measured without sample. The off-resonance modal attenuation $\gamma _{\textrm {off}}$ was calculated by fitting the transmission values (given in units of dB) at the center wavelength of one selected transmission band by a linear function, which the slope being the values of the modal attenuation.

As shown in [18], the spectral positions of the resonances $\lambda _R$ are generally described accurately by the cut-off wavelengths $\lambda _{\textrm {co}}$ of the corresponding isolated strand modes in the weakly-guidance approximation $(\lambda _R \approx \lambda _{\textrm {co}})$. In the investigated situation of the light cage being located in air, the cut-off wavelengths of the different guided modes are defined by the condition $J_{l-1} (d \pi /\lambda _{\textrm {co}} \;\textrm {NA})=0$ [26], leading to the following equation for the resonances:

Note that in Eq. (3) it is assumed that the dispersion of the NA is negligible allowing to use the respective value at $\overline {\lambda _R}$. Note that as shown in [27] RI variations resulting from two-photon polymerization of the resist only occur between different fabrication runs and are extremely small with absolute deviations of below 0.005 which allowed us to neglected this influence in the following.

3. Results and discussion

The maximum sample length that has been achieved with the 3D nanoprinting implementation approach mentioned above was $L_{\textrm {LC}}$ = 3 cm, representing the current state-of-the-art in light cage length. This leads to an aspect (length-to-diameter) ratio of a single strand of approximately AR = 8200 which to our knowledge represents the largest AR of a nanoprinted structure that is partially suspended. Examples of freely suspended nanoprinted structures from other groups are presented in Table 1 showing aspect ratios < 500, which is more than ten times smaller than the light cage structure shown here.

Table 1. Comparison of different nanoprinted structures that include suspended-type elements. Examples of non-free-standing waveguides are also shown (gray).

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The spectral characterization shows for all light cages an alternating sequence of regions of low and high loss, thus indicating light guidance via the anti-resonance effect (Figs. 2(a)-(d)). Note that the double dips features within one resonance (i.e., one transmission dip, visible for instance in Fig. 2(b) at $\lambda =890 \;\textrm {nm}$) arise from LP-mode splitting as discussed later in the section. Particularly remarkable is the observation of resonances and high-transmission bands for the 3 cm long light cage (Fig. 1(c)), which indicates a factor of three improvement in achievable light cage length compared to $L_{\textrm {LC}}$ = 10.5 mm reported in previous experiments [17]. The determined off-resonance modal attenuation $\gamma _{\textrm {off}}$ (Fig. 2(e)) shows values close to 0.65 dB/mm at around $\lambda =520 \;\textrm {nm}$ which increase to about 1 dB/mm at near-infrared wavelength.

The overall magnitude of losses is between (0.5$\cdots$ 1.0) dB/mm which lies within the range of commonly used on-chip hollow core waveguides [12,13] and high contrast photonic band gap fibers [36]. The measured losses agree with that of significantly shorter light cages previously reported [17], indicating that the fabrication accuracy is maintained over the increased distance. Therefore, even longer waveguide lengths can principally be realized. Here it is important to note that long writing times lead to a higher probability of contamination and structural deformation due to the weight of the resin. If the writing area is larger than the area where the immersion lens and chip are in contact with the resin, it is difficult to keep the entire writing area well covered with resin throughout the printing process. Future strategies to increase the length of the implemented light cages therefore target reducing the writing time by using other photo resins with a coarser voxel size. The magnitude of the losses leads to an attenuation of several tens of dB over the 3 cm, which indicates that longer light cages have practical limitations for the core radius given here and on the basis of the current implementation scheme. Note that the losses in such antiresonant tube-like geometries can be principally reduced by increasing the core extent as modal attenuation scales proportional to the inverse of roughly the fourth power of the core diameter [37]. Generally the measured loss values are about one to two orders of magnitude higher than the prediction by simulations [17]. In the context of this it is important to reveal the impact of the reinforcement rings on modal attenuation from the experimental perspective. While the rings are required to hold the strands in their hexagonal arrangement, they introduce a non-uniformity along the waveguide axis that might lead to scattering losses. At the same time, the rings reduce the lateral openness of the cage structure and therefore their number should be kept to a minimum. To address this issue, a series of light cages of identical length ($L_{\textrm {LC}}$ = 10 mm) but different longitudinal spacing between the rings ($10\;\mathrm{\mu} \textrm {m}$, $30\;\mathrm{\mu} \textrm {m}$, $50\;\mathrm{\mu} \textrm {m}$, $70\;\mathrm{\mu} \textrm {m}$) have been implemented on one chip and the spectral distribution of the transmission of the fundamental core mode has been determined. These measurements show neither a significant spectral shift of the resonances nor a substantial change of the transmission value (change of transmission values in the transmission bands throughout this measurement series is < 2.5 dB), thus no consistent trend is observable from these measurements, indicating that the impact of the reinforcement rings on the modes is negligible. Simulations of the electric field mode overlap between the modes of the light cage inside and outside the ring domain in the middle of a transmission band reveal an overlap close to unity [38], which supports this experimental observation. These findings suggest that the main origin of the observed modal attenuation results from surface roughness of the strands. The spectral bandwidth of the measured transmission bands is within the order of 20 nm - 40 nm in the visible spectrum. Larger spectral bandwidth can principally be achieved by implementing strands with smaller diameter, potentially allowing broadband applications for dispersion control in nonlinear optical devices or ultrafast spectroscopy.

To specify the structural deviations that are induced by nanoprinting for identical light cages that are located on one chip, we use the above-mentioned data analysis procedure for the situation of an ensemble of five identical light cages of length $L_{\textrm {LC}}$ = 15 mm (N = 5, example of transmission spectrum is shown in Fig. 2(c)), measured with a high resolution spectrometer. Using an automated numerical procedure (Mathematica: FindPeaks), we measured the spectral positions of the transmission dips within the spectral interval $575 \;\textrm {nm} < \lambda < 840 \;\textrm {nm}$ including five different orders of modes. Note that the fundamental mode ($\textrm {HE}_{11}$-mode) of the strands has no cut-off and therefore cannot impose a resonance in the transmission spectrum of the light cage. Several dips include double-dip features, which presumably results from a lift of LP-modal degeneration which is either associated to polarization mode splitting due to a coupling to hybrid HE- and EH- modes (resulting from the large RI contrast between polymer and air) or to a slight ellipticity of the strands (leading to a lifting of the otherwise degenerate modes in the purely cylindrical case). Here it is important to note that the results presented in [18] clearly confirm the validity of the LP-approach within the context of this work and the two resonances within one transmission dip are labeled identically according to the LP-nomenclature. The resulting values (Table 2) show that the implementation via nanoprinting yields highly reproducible structures within one chip since the standard deviation of the determined resonance wavelength is extremely small ($\sigma _{\lambda } < 1 \;\textrm {nm}$), which is supported by the value obtained by averaging over all standard deviations ($\overline {\sigma _{\lambda }} = 0.3 \;\textrm {nm}$). Note that due to the small absolute value of the deviations, a large sample length of $L_{\textrm {LC}}$ = 15 mm was chosen here in order to increase the fringe contrast of the dips (on-off transmission ratio) and therefore allows for a more precise localization of the resonance wavelengths. A preliminary study has shown that samples with different lengths show deviations of a similar order of magnitude. Moreover, the calculated standard deviations of the strand diameter (determined by the procedure mentioned Sec. 2.) yield values within the nanometre range including the corresponding mean value ($\overline {\sigma _d} = 2 \;\textrm {nm}$) additionally confirming the appropriateness of using nanoprinting for implementing highly reproducible light cage structures. Note that the mean of the calculated mean diameter ($\overline {\overline {d}}=3665 \;\textrm {nm}$) matches the diameter used in corresponding dispersion simulations ($d=3.64\;\mathrm{\mu} \textrm {m}$ [18]), a posteriori confirming the appropriateness of the LP-approach. These small numbers show overall extremely small structural variations for light cages located on the same chip, indicating excellent reproducibility, which is close to values known from fiber optics. Note that for microstructured optical fibers, fiber drawing within a drawing process is highly reproducible [39], while fiber structures can vary significantly between fiber runs.

Table 2. Result of the statistical data analysis procedure to reveal the intra-chip reproducibility of the nanoprinting processes within the context of the light cage geometry.

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The chip-to-chip (i.e., inter-chip) variations of the structural features of the light cages have been analysed in a similar way to the intra-chip analysis presented in the previous section. Here we investigated the spectral positions of five resonances of three light cages located on different chips (details can be found in Table 3, $L_{\textrm {LC}}$ = 5 mm). An approximately ten times larger variation of the spectral positions of the resonance wavelengths $\sigma _{\lambda }$ was observed (mean standard deviation ($\overline {\sigma }_{\lambda } = 2.9 \;\textrm {nm}$), which is reflected in correspondingly higher variations of the strand diameter (mean standard deviation $\overline {\sigma _d} = 15 \;\textrm {nm}$). This value is reasonable given the current experimental circumstances: The dimensions of 3D nanoprinted polymer structures are subject to strong shrinkage during the development process with rates of up to $26 \ \%$ per dimension [40]. Therefore, the actual dimensions of a 3D nanoprinted structure strongly react to fluctuations in the development process (e.g., exact timing, temperature, final concentration of photoresist in developer, humidity), potentially imposing structural changes from sample-to-sample. Therefore the measured larger chip-to-chip variations appear realistic on the basis of the experimental circumstances, which will be improved in future studies. Note that the inter-chip measurement uses a different version of light cages which have a larger mean diameter ($\overline {\overline {d}} = 3841 \;\textrm {nm}$) and were performed with a broadband optical spectrum analyser. The latter has the consequence that only a single dip per resonance could be resolved, leading to a single value of $\lambda _R$ per strand mode (Table 3).

Table 3. Result of the statistical analysis for uncovering the inter-chip reproducibility of the light cage ($L_{\textrm {LC}}$ = 5 mm).

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An important issue needing consideration is the structural collapse of the light cage during the drying stage of development process. When the used solvent evaporates a meniscus is formed between adjacent strands which results in a deformation of the high aspect ratio strands if the capillary forces exceed the elastic restoring force of the polymer. To understand the collapsing effect from the experimental perspective, we fabricated another series of light cages with the same pitch ($\Lambda =7\;\mathrm{\mu} \textrm {m}$) and length ($L_{\textrm {LC}} = 2 \;\textrm {mm}$) but with different spacing between reinforcement rings (Fig. 3). Increasing the spacing from $30\;\mathrm{\mu} \textrm {m}$ to $70\;\mathrm{\mu} \textrm {m}$ does not lead to a visible difference between the light cages (Figs. 3(b)-(d)), while for a spacing of $100\;\mathrm{\mu} \textrm {m}$ a deformation of the light cage cross section in the middle between two rings is observed (Fig. 3(e)). We attribute this phenomenon to radially inward capillary forces (red arrows in Fig. 3(a)) that the strands experience during the drying process.

 

Fig. 3. Study of the mechanical stability of the light cage concept, showing the necessity to include reinforcement rings to support the cage. (a) Sketch showing the capillary force induced collapsing process emerging during the drying process. The SEMs on the right-handed side show light cages of same pitch and length ($\Lambda =7\;\mathrm{\mu} \textrm {m}$, $L_{\textrm {LC}} = 2 \;\textrm {mm}$) but with different distance between the reinforcement rings ((b) $30\;\mathrm{\mu} \textrm {m}$, (c) $50\;\mathrm{\mu} \textrm {m}$, (d) $70\;\mathrm{\mu} \textrm {m}$, (e) $100\;\mathrm{\mu} \textrm {m}$). Scale bars are $10\;\mathrm{\mu} \textrm {m}$.

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Fig. 4. Material dispersion of the developed IP-Dip resist calculated using Eq. (4).

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The results presented clearly indicate the necessity of including reinforcement rings, which distribute the stress from the capillary forces more evenly during the transition from the liquid to the air environment. This consideration applies in particular to situations where the liquid has a high surface tension, such as aqueous solutions. A further improvement of the mechanical stability or conversely, a larger spacing between support rings might be obtained by using photoresists with a higher Young’s modulus such as IP-L780 [41] or by improving the polymerization through an additional curing procedure [40].

4. Conclusion

As previously reported, the light cage represents a novel type of hollow core on-chip optical waveguide with unique properties such as diffraction-less light guidance over centimetre distances, side-wide access to the core and high fraction of optical power inside the core region [17]. As such it is well suited for future integrated sensing applications [42] that demand fast response times and minimal background signal originating from the material of the waveguide. In this work we discuss the current opportunities and limitations of this approach that mainly arise from the implementation approach, i.e., from the nanoprinting. Specifically light cages of a maximal length of 3 cm with a single-strand aspect ratio of 8200 have been achieved. The measured modal attenuation lies within (0.5$\cdots$ 1) dB/mm suggesting that the practically relevant limit of light cage length has been reached here. The investigation of structural intra-chip variations shows extremely small variations ($\overline {\sigma _d} = 2 \;\textrm {nm}$) yielding a very high level of reproducibility that is essential from the application perspective. About ten times larger chip-to-chip variations have been observed ($\overline {\sigma _d} = 15 \;\textrm {nm}$), which mainly result from fluctuations in the development processes, which can be improved by exerting more rigorous control over the sample treatment conditions. Finally the importance of including reinforcement rings to mechanically support the suspended structures particular during exposure of light cages to a liquid environment has been uncovered. Particularly the study on reproducibility conducted in this work is not only relevant for light cages, but can also be transferred to other nanoprinted waveguides, especially towards nanoprinted geometries with suspended structures.

5. Appendix

5.1 Appendix A: Refractive index of the polymer

The material dispersion of the exposed IP-Dip resist has been determined using the following Sellmeier equation:

(4)$$n_{\textrm{IP}} (\lambda) = \left( \frac{1.34246897 \, \lambda^{2}}{\lambda^{2}-0.0164958}+1 \right) ^{1/2}$$

with $\lambda$ given in $\mathrm{\mu} \textrm {m}$. As shown in [19], this approximation excellently describes the spectral distribution of the refractive index of the developed IP-resist due to the match between the calculated resonance position of the central core mode and the measured transmission dips.

5.2 Appendix B: Cut-off values of the LP-modes

The cut-off wavelengths of the LP-modes that are relevant for the discussion of this work have been calculated using the material dispersion of the polymer (Eq. (4)) considering $d=3.64\;\mathrm{\mu} \textrm {m}$. The resulting wavelengths for the $l=0$ and $l=1$ modes are shown in Table 4.

Table 4. Calculated cut-off wavelengths of the LP-modes that are relevant for the discussion of this work ($d=3.64\;\mathrm{\mu} \textrm {m}$).

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Funding

Deutsche Forschungsgemeinschaft (MA 4699/2-1, SCHM2655/11-1, SCHM2655/15-1, SCHM2655/8-1); H2020 Marie Skłodowska-Curie Actions (797044).

Acknowledgments

S.A.M. additionally acknowledges the Lee-Lucas Chair in Physics. J. G. acknowledges funding from the European Commission for the Marie-Skłodowska-Curie action.

Disclosures

The authors declare no conflicts of interest.

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