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Abstract
Astronomical interferometry is a unique technique that allows observation with angular resolutions on the milliarcsec scale by combining the light of several apertures hundreds of meters apart. The PIONIER and GRAVITY instruments at the Very Large Telescope Interferometer have demonstrated that silica-based integrated optics (IO) provide a small-scale and highly stable solution for the interferometric beam combination process. Yet, important science cases such as exoplanet hunting or the spectroscopic characterization of exoplanetary atmospheres are favorable for observation in the mid-IR, namely the atmospheric windows L and L’ band (3–4 µm), a wavelength range that is not covered by conventional silica-based IO. Here, we propose laser-inscribed IO 2×2 couplers in ZBLAN and experimentally assess the critical properties of the component for broadband mid-IR interferometry. We measure the splitting ratio over the 2.5 to 5.0 µm range and find excellent broadband contrast over the L (3.1–3.6 µm) and L’ (3.6 – 4.0 µm) bands. Furthermore, we quantify the dispersion properties of the coupler and find a phase variation as low as 0.02 rad across the L and L’ band, respectively. By optimizing the NA of our injection beam, we measured a very high total throughput of 58% over the L band including Fresnel reflection and coupling losses. We also compare our findings to recent advances in mid-IR IO in GLS and discuss its advantages and disadvantages for the implementation in future mid-IR interferometers.
© 2017 Optical Society of America
1. Introduction
Achieving high angular resolution observations in astronomy is key to a large number of science cases encompassing, for instance, the investigation of planet formation in circumstellar disks [1, 2], the spectroscopic characterization of exoplanetary atmospheres [3, 4], stellar physics [5,6], or the study of the innermost regions in active galactic nuclei [7,8]. Ground-based seeing-limited observations typically reach about an angular resolution of 1″. Significantly finer resolution can be obtained with adaptive optics or with interferometric techniques as implemented at the VLTI, CHARA, NPOI observatories, or from space [9]. An astronomical interferometer consists of several apertures tens to hundreds meters apart, whose light is simultaneously coherently combined to create an interferogram from which the spatial structure of the observed object can be constrained/imaged with milliarcsecond resolution. The heart of an infrared interferometer is the beam combiner, whose role is to coherently combine the beams from the individual telescopes. Recent progress in optical instrumentation and photonics has permitted to develop innovative solutions such as multi-beam single-mode integrated optics combiners to replace classical bulk optics designs in long-baseline interferometry. This offers unique improvement in terms of stability of the instrumental transfer function, which is a prerequisite to measuring calibrated interferometric visibilities with the highest accuracy and hence accessing a high dynamic range for image reconstruction [10]. Such a technology could play a great role in future multi-aperture interferometric instruments such as the planet formation imager (PFI) [11].
Fiber-fed single-mode interferometric integrated optics (IO) beam combiners are now scientifically operational on instruments like PIONIER and GRAVITY at the VLTI (cf. [12] for a review). Unfortunately, a limitation of current IO beam combiners with respect to bulk optics solutions resides in their insufficient wavelength coverage beyond ∼ 2 µm, i.e. the transparency cut-off wavelength of silica. Using OH-free silica, the transparency range can be greatly increased up to 3.5 µm, which would potentially allow to apply well-established lithographic methods. This was tested for the GRAVITY beam combiner but resulted in strong dispersion, hampering high interferometric contrasts (Laurent Jocou, personal communication). Also, the important astronomical L’ band cannot be accessed and out-of-plane waveguides cannot be easily achieved by this technique.
Considering the richness of the mid-infrared range for high-angular resolution astrophysics and the instrumental benefit of the integrated solution in interferometry, this has motivated further developments of multi-telescope IO beam combiners using alternative dielectric substrates transparent in the 2–12 µm range [13]. Such mid-IR IO would hold application potential not only in astronomy but also in other areas such as medicine [14] or environmental monitoring [15]. The basic need is to benefit from a stable technological platform capable of producing high-throughput single-mode waveguides in mid-infrared materials, in a comparable manner to what the telecom-driven photo-lithographic platform has provided for forty years for silica-based integrated optics and fibers. At longer wavelengths beyond 2 µm, several technologies tested over the last decade succeeded in manufacturing proof-of-concept mid-infrared waveguides and combining functions: the used platforms included chemical etching/lithography, laser-inscription in glass substrates, ion-exchange and diffusion in glasses [16–29].
In this paper, we concentrate on using Ultrafast laser inscription (ULI) [30] to inscribe and characterize interferometric couplers in fluoride glasses. A great advantage of laser inscription is that waveguides can be inscribed in all three dimensions, which then allows to experiment with novel beam combination schemes such as all-in-one discrete beam combiners [31, 32]. Two- and three-port couplers for the mid-IR range were successfully laser-inscribed in GLS (Gallium Lanthanum Sulfide) and GCIS glasses [19]. Propagation losses on the order of 0.8 dB/cm and balanced monochromatic splitting ratios were reported [24]. ULI has also been used to inscribe depressed cladding waveguides in crystals. Nguyen et al 2016 [33] has presented a heuristic theoretical analysis of laser writing in Lithium Niobate along with experimental results at 3.68 µm. Yet, the reported measured propagation losses of 2.9 dB/cm for TE and no guidance for TM modes, are still impractical for astronomical applications. Recently, a comprehensive interferometric study on laser-inscribed couplers in GLS glass evidenced low dispersion properties and low differential birefrigence and showed for the first time high broadband instrumental contrast well above 90% over the L and M band [34]. The ULI technique has also been applied to ZBLAN, a fluorozirconate glass, showing propagation losses as low as 0.3 dB/cm and a functioning evanescent coupler over the 3.75 – 4.2 µm range [25]. Although this work has evidenced the great potential of the ZBLAN platform, no further interferometric characterization has been reported yet.
This paper experimentally measures the critical properties of the laser-inscribed ZBLAN couplers for interferometry applications over the L and L’ bands (3 to 4 µm). It includes the total throughput, spectral splitting ratio, dispersion properties and most importantly the instrumental interferometric contrast. In order to move forward to a science qualified mid-IR IO interferometric instrument, it is essential to obtain a detailed picture on the experimental performance achievable with promising mid-IR IO technologies. With this work, we contribute to this objective and, in particular, provide a comparative study to the ULI-GLS platform.
2. Design and fabrication of the sample
The waveguides were inscribed into a ZBLAN substrate using ULI, a technique pioneered 20 years ago by Glezer et al 1996 [35] and Davis et al 1996 [36]. An intense femtosecond laser is tightly focused inside the substrate and causes a local and permanent change in refractive index. By translating the substrate waveguides can be inscribed into the sample. An extensive review of the ULI technique is found in Gross & Withford (2015) [30].
In the case of ZBLAN, the laser-induced change in refractive index is negative, i.e. the cladding of the waveguides is inscribed. The writing laser is a Ti:sapphire oscillator with a 5.1 MHz repetition rate and <50 fs pulses at 800 nm. The laser is focused 300 µm below the polished surface of the substrate using a 1.25 NA objective. The substrate is then translated with a speed of 1000 mm/min and the energy per pulse is 65 nJ. The achieved contrast in refractive index is about −(6 ± 1) · 10−4. The 60 µm wide cladding of each waveguide consists of 108 laser modifications around a 50 µm diameter circular core. Figure 1(a) shows the waveguide cross section of a channel waveguide inscribed with similar parameters. The sample at hand contains 12 straight waveguides and six couplers and measures a total length of 33.6 mm. The properties of the coupler used in this paper are depicted in Fig. 1(b). The coupler has an interaction length of 0 mm, i.e. the two waveguides converge and directly depart, and a raised sine length of 16 mm. The separation between the two waveguides in the interaction area is 39.9 µm (measured as the distance between the centers of the two cores), i.e. the waveguides overlap. More information on the fabrication of the sample can be found in Gross et al 2015 [25].
Fig. 1 Figure 1(a) shows the cross-section of a laser-inscribed channel waveguide written with similar parameters as used for the coupler. In Fig. 1(b), the design parameters of the coupler studied in this paper are depicted. The terms Cross and Bar are used to distinguish the originally excited and the coupled waveguide. Left and right orientation is used as seen from the camera.
The principal design of the component is the one of a 2×2 directional coupler which has two inputs and two outputs. In the interaction area the two channels are brought in proximity or to overlap where the two fields mix [37]. Ideally, the two outputs contain each a mixed field with a π phase shift with respect to each other due to the conservation of energy. The advantage of this design is that the losses are only determined by the propagation and bending losses, whereas the Y-Junction inherently reflects 50% of the light. Also, such a design is the building block of an ABCD combiner [38]. Yet, the directional coupler naturally exhibits a chromatic splitting ratio, which will be discussed in this paper.
3. Experimental setup
We use a two-arm interferometric setup for the characterization of the sample as depicted in Fig. 2. For the broadband measurements, we use a fibre-coupled blackbody source that is spatially filtered by a 20 µm pinhole and collimated by an f=50mm achromat. In addition, a spatially filtered HeNe Laser at 3.39 µm is inserted into the setup which can be positioned with respect to the broadband source by a beamsplitter. The beam is split into two beams using a thin pellicle beamsplitter (Thorlabs, BP145B4) in order to avoid differential dispersion in the beamsplitter. The two beams are then reflected by two mirrors: one mirror is mounted on a delay line (Thorlabs, Z812B) in order to control the optical path difference (OPD), the other mirror can be tilted in order to fine-position the beam with respect to the other. The two beams are then injected by an f=50mm achromat into the IO chip. The chip is mounted on a translational stage which can be fine-positioned in three dimensions. The outputs of the chip are collimated by another f=50mm achromat and re-imaged by the infrared camera (Infratech 5360S) with an f=50mm lens. A bandpass filter can be inserted in order to test the performance over the L and L’ band. Our camera adds an intrinsic noise at about 25 kHz (corresponding to 0.5 µm), which we filtered out, as this can lead to falsely measuring too high interferometric contrasts [39].
Fig. 2 Design of the experimental setup for interferometric characterization of the ZBLAN integrated optics chip. Bandpass filters L and L’ can be inserted.
We also use this setup to perform Fourier transform spectroscopy. Therefore, it is critical to precisely record the OPD of the interferometric measurements. The delay line, however, does not provide a highly accurate or repeatable translation. Therefore, we record the interferometric signal of the HeNe laser at 3.39 µm simultaneously to the broadband measurement. As the fringe spacing of the laser is known, we use it to calibrate the OPD. The advantage of the Fourier Transform approach, as opposed to a fiber-coupled spectrometer, lies in the possibility to measure the two chip outputs separately as they are imaged onto the detector of the camera.
4. Results
4.1. Splitting ratio
The spectral shape of the splitting ratio of the directional coupler is crucial to its interferometric performance in broadband operation. When the coupler operates with monochromatic light, an unbalanced splitting (i.e. not 50/50) can be easily calibrated by photometric correction. On the contrary, when operating with polychromatic stellar light within a bandpass filter, the chromatic unbalance of the splitting ratio across the band will result into a degradation of the instrumental contrast, which cannot be compensated photometrically. The degradation effect of the chromaticity of the splitting ratio will occur even if the coupler exhibits a balanced (50/50) splitting ratio integrated over the filter bandwidth.
The sample contains six couplers, each inscribed with varying the parameters. The coupler which showed the most balanced integrated splitting ratio across the L band was chosen to be eventually characterized. After testing the available couplers for photometric unbalance, the selected sample exhibits an integrated splitting ratio of 45% and 34% over the L and L’ band, respectively. The design parameters of this coupler are depicted in Fig. 1(b).
In order to measure the splitting ratio as a function of wavelength, we inject the two arms of the interferometric setup into the same input. Scanning the OPD, each output yields one interferogram, from which the respective spectrum can be derived through Fourier transform spectroscopy. We performed this measurement for the left and right input, from which we yield an average splitting ratio. For this measurement, we initially do not insert any bandpass filter, so that the bandwidth covers the whole accessible spectral range (2.5 – 5 µm) offered by the infrared fiber, the optical setup and the ZBLAN component. Figure 3 shows the mean spectral splitting ratio along with the standard deviation as error bars. We find a quasi linear dependency ranging from about 25% to 80% from 2.5 to 5.0 µm with a slope of about 0.3µm−1. Over the L (3.1–3.5 µm) and L’ (3.6–4.0 µm) band the splitting ratio varies, from edge to edge of the respective band, from 40% to 57% and from 57% to 70%. The 50/50 crossing point is at 3.3 µm.
Fig. 3 The splitting ratio of the coupler as a function of wavelength. Bar and Cross denote the originally injected and the coupled waveguide, respectively, (cf. Fig. 1(b)). The solid lines depict the measured values and the dashed lines depict the RSoft simulation.
We modeled the splitting ratio by an RSoft simulation with a depressed cladding index of Δn = −7·10−4 and using the geometry of the coupler depicted in Fig. 1(b). The model reproduces the slope across the bandwidth but shows an offset of about 30%, see Fig. 3. The simulation can be matched with the measured splitting ratio by tuning the separation of the waveguides in the coupling region to 36 µm.
4.2. Transmission
In this section, we present both the average total throughput in the L band and the transmission spectrum from 2.5 to 5.0 µm. Maintaining a high throughput in photon-starved applications like astronomy is clearly important if one considers, for instance, that the VLTI transmission from the primary mirror down to the interferometric combination laboratory is only ∼20% at 2 µm before entering any instrument.
In order to estimate the total throughput, it is essential that the numerical aperture (NA) of the injection beam matches the NA of the waveguide. Therefore, we placed an iris in the collimated beam before the injection lens to modify the injection spot size – and the coupling efficiency accordingly – and measured the throughput for different iris diameters D. The results are shown in table 1. We find the highest throughput of 58% for an iris size of 6 mm which corresponds to an NA∼D/2f of 0.06±0.01 (error due to sampling of the beam diameter). If we take into account the attenuation due to Fresnel reflections (4% at the input and output facet for nZBLAN ~1.50) and the maximum coupling efficiency (82%) between the Airy pattern and the Gaussian-like waveguide mode, we are left with an excellent transmission of 76% of the sample including bending and propagation losses, which translates into 1.19dB (0.33 dB/cm). The measured NA is in line with what was measured by [25] for another coupler (but with the same refractive index contrast) in this sample. Table 1 also shows that the transmission for the left and right input are very similar.
Table 1. Throughput of the 33.6 mm long 2×2 combiner in L band (FWHM: 3.1–3.6 µm) for different input beam diameters.
In order to measure the spectral transmission of the sample, we use the data from the interferometric measurements from section 4.1 and performed Fourier transform spectroscopy. The sum of the two output spectra is the totally transmitted spectrum, which can be compared to the spectrum of the setup without component. We find a relatively flat spectral transmission along the measured bandwidth with a slightly lower transmission towards shorter wavelength, see Fig. 4(a). This may be explained by the fact that the coupling cannot be equally optimized for all wavelengths across the spectrum. Figure 4(b) allows to assume that the total throughput will not be significantly less in the L’ than has been measured for the L band.
Fig. 4 Figure 4(a) shows the normalized transmission of the experimental setup compared to the transmission of the ZBLAN sample. The ZBLAN curve was scaled with respect to the bench matching the measured total throughput of 58% over the L band. For each case, three measurements were taken from which the average and the standard deviation is calculated. The dip at 4.2 µm is due to CO2 absorption. Figure 4(b) shows the relative transmission of the ZBLAN sample calculated from the ratio of the curves from Fig. 4(a) over the relevant the L and L’ band up to the CO2 absorption.
4.3. Interferometric characterization
In this section we test the coupler for interferometric beam combination as it is eventually intended to operate in an interferometric instrument. The interferograms presented are photometrically corrected and recorded for unpolarized light. Each interferogram is recorded three times from which a mean and standard deviation are computed.
Using the L band filter with 0.4 µm FWHM, we test the interferometric performance over the 3.1 to 3.5 µm range (see Fig. 5(b) for the spectrum of the measurement). Figure 5(a) shows the two interferometric outputs of the chip with a high broadband contrast of CL =93.0 ± 1.3% in unpolarized light. The near-π phase shift between the two coupler’s outputs is qualitatively visible in the inset. The high contrast evidences the small level of differential birefringence between the two coupler’s two channels, an effect visible in other studies. A low differential birefringence allows to operate the component in unpolarized light without having to split the two orthogonal polarizations [40].
Fig. 5 Figure 5(a) shows the experimental L band interferogram after photometric correction of the two chip outputs with a contrast of 93.0%. The inset magnifies the central region and demonstrates the near-π phase shift. Figure 5(b) shows the corresponding bandwidth of the measurement and the phase variation of the interferogram across the band. The right phase is set to zero at 3.4 µm and the left phase is lowered by π to visualize the near-π phase shift between the two outputs. The phase of the bench is lowered by 0.25 for better visualization.
A typical limitation of IO combiners for broadband interferometry is differential dispersion which stems from different propagation constants and/or different lengths between the two waveguides that form the coupler. This results in different OPDs for different wavelengths and a smeared out interferogram with an attenuated contrast. This is detrimental to astronomical interferometry where the instrumental visibility should be as close as possible to one. In Fig. 5(a), we can clearly identify the first and second lobe of the interferogram, which is an excellent indicator for a low differential dispersion. Yet, the effect of the differential dispersion can be further investigated qualitatively by analyzing the phase curvature of the interferogram [41]. A flat phase – i.e. with a zero first derivative against wavelength – corresponds to a perfectly dispersion-free interferogram. The phase is estimated through the real and imaginary part of the Fourier transform of the interferogram. Figure 5(b) depicts the variation of the phase of the left and right output across the spectrum, quantifying the dispersion present in the interferogram. The phases of the right and left outputs exhibit almost the same curvature across the band, pointing at identical behaviours in terms of dispersion. We also measured the phase without component – i.e. of the experimental setup – for which we would expect a flat phase. We find that its phase curvature is very similar to the component’s one, which indicates that the experimental phase curvature is dominated by our setup, possibly because of the pellicle beamsplitter which has a very small but non-zero thickness. After subtracting the dispersion due to our bench, we find a residual phase variation of σL = 0.02 rad (measured as the standard deviation across the band) intrinsic to the component. This variation is within the error bars of the measurement. Note that the absolute offset of the bench’s phase is not relevant here, only its curvature is. In Fig. 5(b) the left output phase was artificially lowered by an offset of π for visualization purposes. The left and right phases should then have overlapped with each other, which is not the case here with a residual offset of about 0.2 rad. The two interferograms not being in perfect phase opposition points to additional losses.
We conducted the same test by inserting the L’ band filter (λc=3.8 µm, FWHM=0.4 µm) into the setup (see Fig. 6(b) for the measured bandwidth). The same coupler that was used for the L band shows interferometric outputs with a high broadband contrast of CL′ =93.5% ± 0.2% over the L’ band as seen in Fig. 6(a). As for the L band, we find that the phase curvature mainly results from the experimental setup (see Fig. 6(b)). The residual phase variation after removing the bench is again on the order of σL′ = 0.02 rad. Similarly, we find that the phase shift between the two outputs is not exactly π but about 0.3 rad off.
Fig. 6 Figure 6(a) shows the experimental L’ band interferogram after photometric correction of the two chip outputs with a contrast of 93.5% along with an inset of the central region. Figure 6(b) shows the corresponding bandwidth of the measurement and the phase variation of the interferogram. The right phase is set to zero at 3.8 µm and the left phase is lowered by π to visualize the near-π phase shift between the two outputs. The phase of the bench is lowered by 0.25 for better visualization.
5. Discussion and conclusion
We have demonstrated that ULI in ZBLAN is a suitable platform to manufacture good quality 2×2 directional couplers as the basic brick for single-mode integrated optics mid-infrared beam combiners.
We measure high broadband interferometric contrasts of 93.0% and 93.5% in unpolarized light over the L and L’ band, respectively, with spectral bandwidths of ∼0.4 µm. The origins of fringe contrast loss are typically an unbalanced spectral splitting ratio, differential dispersion, differential birefringence, multimode behaviour, or improper photometric correction.
At first we assessed the splitting ratio of the coupler and found a variation of less than 0.3/µm. These are promising results as the spectral splitting ratio is flatter than the recently reported directional evanescent coupler inscribed in GLS glass [34] for which a slope of 0.8/µm was measured. For this ZBLAN coupler, the measured spectral unbalance of the splitting ratio would result in a contrast loss of about 1%. The crossing point lies at 3.3 µm. In order to obtain a high raw contrast (i.e. before photometric correction), it is important that the crossing point of the splitting ratio lies in the center of the bandwidth. The position of the crossing point can be fine-tuned by altering the separation of the waveguides in the interaction area.
The dispersion in the interferogram, measured as the phase variation across the band, is dominated by our experimental setup. The intrinsic differential dispersion of the component itself introduces a phase curvature of less than 0.02 rad over both L and L’ band. These are similar results as for the GLS sample measured in Tepper et al 2017 [34]. Therefore, we can conclude that laser inscription is capable of repeatedly inscribing waveguides with precisely equalized lengths and propagation constants (cf. [41], Eq.15). Our simulations indicate that the phase curvature of the setup results into a contrast loss not larger than 0.8%.
The core size of 50 µm and the Δn of ~6×10−4 point in the first order to a single-mode behavior at these mid-IR wavelengths with a normalized frequency V well below 2.405. This can be confirmed on a later stage through classical near-field imaging.
A detailed study of the differential birefringence is not reported in this paper. Although we do not expect high differential birefringence in light of the high broadband contrast, this is still an effect that, if not controlled, may introduce additional contrast loss of few percents. This will be assessed later by investigating the evolution of the monochromatic interferometric contrast at 3.39 µm for different angular directions of the input linear polarization by using a λ/2 plate.
Finally, since the photometric channels are not recorded simultaneously to the interferometric signal, the photometric correction may add additional systematic biases given the randomness of the delay-line mirror tip-tilt when coupling in the component’s channel. This may lead in some cases to an underestimated instrumental calibrated contrast. This will be assessed in the future through the acquisition of a large number of repeated contrast measurements.
Concerning the sample transmission, we measured a very high throughput of 58% over the L band including coupling losses and Fresnel reflections. We find that the spectral transmission is relatively flat over the 3 to 4 µm range of interest. Evanescent couplers in GLS have shown a lower total throughput of 25% [34], partly hampered by the higher Fresnel losses. The larger throughput could be a significant advantage, although the GLS platform provides a wider transparency range up to ∼10 µm compared to the cutoff of ZBLAN at about 5 µm. Gross et al 2015 [25] reported propagation losses of 0.29 dB/cm in ZBLAN channel waveguides. By comparing this value to the measured 0.33 dB/cm for the coupler, we can derive the important result that additional bendings do not introduce significant losses.
From the analysis of the phase we could determine that the phase shift between the two outputs is not exactly π but by about 0.2–0.3 rad off this value. As the π phase shift is a consequence of energy conservation in the coupler, this result points to additional, albeit small, flux losses in the cladding that are not seen in the GLS couplers. This could result from small bending or scattering losses in the interaction area during the process of energy transfer from one waveguide to the other. More importantly, this possible deviation from the expected π phase shift needs to be understood and controlled if the ZBLAN platform would be used to manufacture ABCD integrated optics combiners [42] for which the phase opposition and quadratures have to be accurately guaranteed.
So far, laser inscription in ZBLAN has not capitalized on the 3D potential of ULI. While functioning 3D ABCD couplers have been inscribed into GLS [43], it is not yet clear whether the negative writing in ZBLAN allows for more complex functions due to its smaller refractive index contrast and consequently limited mode confinement; a critical aspect that needs to be targeted in the next phase. Gross et al 2012 [44] has demonstrated the feasibility of higher refractive index contrast in ZBLAN (up to 4 · 10−3) at the expense of slower manufacturing.
It should be noted that the performance of both the ZBLAN and the GLS couplers critically depend on the chosen laser writing parameters as well as the design of the coupler (cf. McMillen et al 2012 [45]). In this work, as well as in Tepper et al 2017 [34], the best performing coupler was picked from a number of couplers (6 and 20, respectively) without a detailed previous parameter scan over all possible inscription configurations. Thus, there may still be room for potential improvement in the waveguide properties for both technological platforms.
With this work, we have presented a comprehensive quantitative comparison of the performances of two promising ULI platforms, namely ZBLAN and GLS glasses. We confirm the strong potential of the ZBLAN platform to produce the basic bricks for mid-IR integrated optics with this first interferometric characterization.
Funding
Bundesministerium für Bildung und Forschung (BMBF) (05A14PK2, 05A14SJA); Australian Research Council Centre of Excellence for Ultrahigh bandwidth Devices for Optical Systems (CUDOS) (CE110001018).
Acknowledgments
JT, LL, SM and RD acknowledge the financial support of the German Ministry of Research and Education (BMBF) through the ALSI project.
This research was supported by the Australian Research Council Centre of Excellence for Ultrahigh bandwidth Devices for Optical Systems (project number CE110001018) and an ARC Discovery Project, and was performed in part at the Optofab node of the Australian National Fabrication Facility using Commonwealth and NSW and SA State Government funding. S. Gross acknowledges funding by an Australian Research Council DECRA Fellowship.
The authors thank the anonymous referees for the constructive remarks.
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