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Abstract
Ring resonators provide a means of filtering specific wavelengths from a waveguide, and optionally dropping the filtered wavelengths into a second waveguide. Both of these features are potentially useful for astronomical instruments. In this paper we focus on their use as notch filters to remove the signal from atmospheric OH emission lines from astronomical spectra. We derive the design requirements for ring resonators for OH suppression from theory and finite difference time domain simulations. We find that rings with small radii (< 10 μm) are required to provide an adequate free spectral range, leading to high index contrast materials such as Si and Si3N4. Critically coupled rings with high self-coupling coefficients should provide the necessary Q factors, suppression depth, and throughput for efficient OH suppression, but will require post-inscription tuning of the coupling and the resonant wavelengths. The overall prospects for the use of ring resonators in astronomical instruments is promising, provided efficient fibre-chip coupling can be achieved.
© 2017 Optical Society of America
1. Introduction
Observations at near-infrared (NIR) wavelengths (0.9 – 2.5 μm) are crucial for many areas of astronomy. For example, the lowest mass stars and highest mass planets emit most of their light at near-infrared wavelengths, and NIR spectroscopy is essential for classifying such objects. Dusty regions within our own and other galaxies are highly opaque to visible wavelengths, but transparent at long wavelengths due to the λ−4 dependence of Rayleigh scattering. Thus, studying the inner regions of the Milky Way, or star-forming regions within other galaxies, often requires NIR spectroscopy. Deep NIR spectroscopy is also necessary to study the high redshift Universe, when the diagnostic visible features are redshifted into the NIR. Measuring star-formation rates during the epoch of peak star-formation, measuring Lyman-α emission during the epoch of reionisation, and identifying high redshift supernovæ would all benefit significantly from NIR spectroscopy.
Unfortunately, deep observations at near infrared wavelengths are currently very challenging due to the bright atmospheric background. The surface brightness of the night sky at a good site is thousands of times brighter in the NIR than in the visible. Between 0.9 – 1.8 μm almost all of this background results from the de-excitation of atmospheric OH molecules [1, 2] at an altitude of ≈ 90 km giving rise to an extremely bright emission line spectrum, shown in Fig. 1 (see Ellis & Bland-Hawthorn [3] and references therein for a review of the NIR background). Not only is this OH line spectrum extremely bright, it is also variable on a time scale of minutes. Subtracting this background from astronomical observations is very inaccurate due to the large Poissonian and systematic noise [4]. Solving the difficulty of the NIR night sky background is a long standing problem in astronomy.
Fig. 1 A model spectrum of the near-infrared night sky. The background is dominated by OH emission lines (top plot). The OH lines are intrinsically very narrow, with dark sky in between.
Several solutions to this problem have been proposed. One obvious, but expensive, solution is to launch a telescope into orbit above the atmosphere. Indeed, this is one of the primary motivations for the James Webb Space Telescope (JWST) [5], which is planned for launch in 2018 at a cost of ≈ US$ 8.8 billion. While NIR space telescopes completely avoid the problem of atmospheric emission, ground-based solutions are also desirable: space telescopes have a finite lifetime and are expensive to replace; ground-based facilities can take advantage of developments in technology and scientific understanding and allow for the optimisation of instruments for specific requirements as the need arises. Furthermore, in the case of JWST the field-of-view of the NIRSPEC instrument is 3.6 ×3.4 arcmin [6], significantly limiting its ability to perform large surveys. Additionally, space-based observatories are often significantly more over-subscribed than ground-based facilities, leading to significant restrictions in the proportion of researchers able to take advantage of such resources.
Ground-based solutions exploit the fact that the OH lines are intrinsically very narrow (FWHM ≈ 0.3 pm), with a fixed wavelength, and the sky between the lines is very dark, as shown in the bottom panels of Fig. 1. If the lines can be filtered at high resolution and high suppression, then the remaining background spectrum will be orders of magnitude darker.
It is not possible simply to observe at high resolution to see between the lines, since the OH lines will be smeared by the spectrograph scattering point spread function, contaminating the inter-line region. To realise efficient OH suppression this scattering problem must be avoided; the OH light must be removed prior to dispersion. Furthermore, it is often desirous to observe at lower spectral resolution to obtain better signal-to-noise and larger wavelength coverage.
Several ground-based solutions have been proposed. These include high-dispersion masking [7–11], ultra-narrow band filters [12], Rugate filters [13] and holographic filters [14]. All of these have met with limited success, either due to the spectrograph scattering problem, difficulties in fabrication or difficulties in implementation (see Ellis & Bland-Hawthorn. [3] for a full discussion).
A more recent solution uses fibre Bragg gratings (FBGs) [15, 16], wherein up to 150 individual notches may be written into a single fibre [17], which are perfectly matched in wavelength to the OH lines, have up to 40 dB of suppression, and a width of ≈ 1.5 Å. Such devices have been proven on-sky with the GNOSIS prototype instrument [18–20]. The chief limitation of FBGs is that they must be written into individual single mode fibres, and therefore require a photonic lantern [21, 22] to couple efficiently to a spectrograph. Even so, FBGs are currently only suitable for single object spectroscopy, since the cost of scaling GNOSIS-type instruments to larger field of view is currently prohibitive. More efficient methods of manufacture are currently being investigated, for example multicore FBGs [23, 24] would simplify the production and integration of large numbers of fibres.
In this paper we examine another class of notch filter, viz. ring resonators. Ring resonators consist of one or more waveguides coupled to a looped waveguide. Figure 2 shows a schematic diagram of a ring resonator and an SEM image of one of our prototype devices. Light from the input waveguide evanescently couples into the ring, whereupon it constructively and destructively interferes with itself until only light at the resonant wavelengths of the cavity remains. The condition for resonance is therefore
where m is an integer, λ is the wavelength, ne is the effective index and L is the circumference of the ring. The resonant light couples back into the input waveguide and destructively interferes with the input light. Thus, a series of ring resonators, each tuned to the wavelength of a different OH night sky line, could provide a means of OH suppression [25].Fig. 2 Top panel: schematic diagram of a simple ring resonator showing the input, through and drop ports and a sketch of the spectrum at each port. Bottom panel: SEM image of one of our prototype silicon-based ring resonators with a through port and drop port, manufactured at the Center for Nanoscale Materials at Argonne National Laboratory.
Ring resonators have been developed for applications in telecommunications, industry, and photonics research as filters, add/drop multiplexers, delay lines, modulators, sensors, laser generation, tuneable dispersion compensators, all-optical wavelength converters, frequency combs, and tuneable cross-connects [26–28]. The motivation to explore the use of ring resonators for OH suppression is primarily due to their method of manufacture. Ring resonators can be lithographically printed in a photonic integrated circuit (PIC), and are therefore very versatile and repeatable. Ring resonators are inherently small devices (1 – 100μm), providing an excellent means of miniaturising parts of instruments. Lithography enables many rings to be coupled to the same waveguide, therefore the insertion losses are limited to a single coupling loss at input and output, even for an arbitrarily high number of rings. Finally, since they are printed in a PIC, they may be easily combined with other photonic components, e.g. array-waveguide gratings [29–32] to form fully photonic systems. Although both ring resonators and FBGs require photonic lanterns to feed an array of single mode fibres, ring resonators are potentially more modular and scalable. Many devices can fit onto a small chip, and fabrication is highly repeatable, simplifying their production. Additionally, their small size should make them more compact than a similar FBG instrument, with the size limited by the input array of SMF, whereas FBGs are both much longer (tens of cm) and are more widely separated due to the necessary athermal packaging around the fibres.
Note that these potential benefits of ring resonators have not previously been properly assessed; the detailed requirements for ring resonator based OH suppression have not been calculated, and moreover, these requirements have not been compared to the published performance of ring resonators. It is the purpose of this paper to provide this assessment through a detailed requirement study, and a comparison with measured performance of ring resonators in the literature.
In section 2 we give an overview of the applicability of ring resonators for OH suppression. Following this we develop the requirements for ring resonators in section 2.2, based on their theoretical properties, and a comparison with state-of-the-art devices from the literature. In section 3 we summarise the feasibility of using ring resonators in astronomical instruments, and discuss the future development and testing necessary.
2. Ring resonators for OH suppression
The theoretical properties of ring resonators are well understood [27]. Using these properties we now quantify the astronomical requirements and the consequent design requirements on the use of ring resonators for OH suppression. In this section we give a brief depiction of how ring resonators can be incorporated into an near-infrared spectrograph to provide OH suppression (§ 2.1). We then examine the astronomical requirements and the consequent technical requirements in section 2.2.
2.1. An outline of OH suppression with ring resonators
The general problem of OH suppression was introduced in section 1. We require a filter with a deep and narrow notch at the wavelength of each bright OH line. (Actually the OH lines are doublets, most of which are very closely spaced such that a pair of lines can be suppressed with a single notch). Figure 3 shows an example of the theoretical transmission of a simple ring resonator with no drop port, which is critically coupled such that the throughput of one passage around the ring, α, is equal to the self-coupling along the input waveguide t. The total phase change for a single passage around the ring may be expressed in terms of wavelength as, θ = 2πneL/λ.
Fig. 3 The transmission for a simple ring resonator with no drop port as a function of phase with α = t = 0.99 (black), α = t = 0.9 (red), α = t = 0.8 (blue), and α = t = 0.7 (green).
Thus, light from the telescope can be fed into a PIC within which ring resonators provide this filtering function. The filtered light from the through port of the ring resonators can then be fed into a spectrograph.
The OH lines are not periodic with frequency, whereas the multiple notches of a single ring resonator are. Therefore each wavelength to be suppressed must be suppressed by an individual ring; if there are N lines to be suppressed, there must be N rings. In the most optimistic case, it may be possible to suppress two lines with an individual ring, if the FSR can be matched to the spacing between the lines without compromising the Q factor and suppression factor.
These considerations lead to a design such as that sketched in Fig. 4, which is very similar to the GNOSIS [19] and PRAXIS [33] OH suppression FBG instruments. Light from the telescope is focussed onto a microlens array, each element of which feeds a multimode fibre. This stage is necessary to reduce the number of modes in each fibre, whilst enabling an adequate field of view, but may be superfluous if very highly multimode photonic lanterns are developed. Each multimode fibre is converted into an array of single mode fibres via a photonic lantern. Each single mode fibre is then coupled to an individual waveguide on a photonic circuit. There can be multiple copies of each circuit, e.g. one for each multimode fibre. If necessary there could be several different circuits for each multimode fibre, each covering a different wavelength range, the light being directed to the appropriate circuit by means of dichroic beam splitters.
Each waveguide on the photonic circuit will couple to N rings in series, where N is the number of OH lines to be suppressed. It may be necessary to split each waveguide into two, one for each of the TE/TM modes (see § 2.2.7 below).
At the output of the waveguides the reverse processes will take place, with the single-mode fibres (SMFs) feeding individual multi-mode fibres (MMFs) via a photonic lantern, as well as recoupling any separate wavelength or polarisation tracks. All the MMFs can then be aligned at the entrance to a spectrograph, allowing the spectrum of each microlens element to be measured, free of OH line emission.
2.2. Requirements of ring resonators for OH suppression
2.2.1. Number of rings, bandwidth and suppression factors
Every notch in an OH suppression filter suppresses both the background and the signal from the object of interest. Therefore, although more notches, deeper notches and wider notches will decrease the background they will also decrease the signal. It is therefore desired to choose a combination of number, depth and width of notches to maximise the signal to noise. We have calculated the increase in signal to noise as a function of number, depth and width of notches, assuming that the observations are sky background limited (N.B. if the sky background is strongly suppressed, and the interline continuum is very dark, then observations may be detector noise limited). Thus the signal to noise is simply,
where S is the integrated signal, and B is the integrated background, over the passband of interest. For the purposes of these calculations we assume idealised notches with a perfectly rectangular profile, and that all notches have the same depth and width (except where notches overlap). Lines are selected to be suppressed in order of their average brightness. Further we assume that the signal spectrum is flat; for many science cases there may be a particular feature which is important, rather than the whole spectrum. Neverthless, these calculations give an idea of the general requirements for OH suppression. We assume the sky-background to be as given in Ellis & Bland-Hawthorn [3], except with the interline continuum as measured by Maihara et al. [34].Figure 5 shows the improvement in signal to noise as a function of the number of notches, for notch widths of 100, 150 and 200 pm and for notch depths of 10, 20, 30 and 40 dB over the J and H bands. The signal-to-noise improves with increasing notch depth, but the difference between 30 dB and 40 dB notches is very slight. In the J band, the notch width is relatively unimportant between 100 and 200 pm. In the H band, 200 pm notches are better than narrower notches in all cases, except for the 10 dB notches. The optimal number of notches for each combination of notch width and depth are given in Table 1. In both the J and H band these correspond to approximately 1 notch for every 2 nm of passband, which is a useful approximation when considering shorter passbands.
Fig. 5 The improvement in signal to noise due to OH suppression as a function of the number of notches, for notch widths of 100, 150 and 200 pm and for notch depths of 10, 20, 30 and 40 dB over the J (left) and H (right) bands. The signal to noise is improved with deeper notches, up to ≈ 30 dB, and with more notches up to ≈ 90 notches in J and ≈ 150 notches in H. In the J band the notch width is not significant since the doublets are very closely spaced. In the H band 200 pm wide notches are significantly better than narrower notches.
Table 1. The optimal number of notches for maximum signal-to-noise for various notch widths and depths.
The improvement in signal to noise will be compromised by the total throughput of the system. However, because , where η is the throughput, the total end-to-end throughput of the system need only be > 4 % if the OH suppression increases the S/N by a factor 5. To be competitive with FBG OH suppression the total throughput of the OH suppression system itself should be > 50 %.
Figure 5 suggests that the suppression factors should be ∼ 30 dB, but after this there are diminishing returns. The notch depth, D, is given by
with the throughput of one passage around the ring given by α, and the self-coupling along the input waveguide by t. Note that if α = t then the transmission is always zero on resonance for a ring resonator with no drop port. Therefore to increase the notch depth α and t should be made as equal as possible. Other considerations, such as high Q factor and high inter-notch transmission require α and t to be close to 1. Figure 6 shows contours of the suppression factors of a simple notch as a function of α and t according to Eq. 3. In the limit of α = t ≈ 1 the tolerances on α ≈ t are rather tight, since a slight inequality reduces the notch depth.Fig. 6 Contours of the notch depth in dB for a simple ring with no drop port as a function of α and t (Eq. 3). To improve the notch depth for our device t and α should be matched, and kept close to 1.
In practice, fabrication tolerances lead to variations of a few percent in coupling coefficients, which are enough to significantly decrease the suppression since α ≠ t [35]. Thus for chips containing multiple rings the coupling must be actively tuned, e.g. using thermal resistive heaters incorporated into the couplers [35,36]. Further, the coupling coefficients are wavelength-dependent [28], and so each ring must be tuned independently.
2.2.2. Free spectral range
Because the OH lines are not periodic with frequency or wavelength, each individual line must be suppressed with an individual ring. It could be possible to suppress two lines with the same ring if the FSR can be matched to the spacing between them without compromising the other requirements such as notch depth, notch profile and interline continuum.
In general then, the FSR must be larger than the passband of interest. The J and H band filters in the Mauna Kea filter set [37] are 160 and 290 nm wide respectively. The free spectral range of a simple ring resonator, Δλ is given by,
where ng is the group refractive index.Because the passbands and FSR are large, there will be a significant change in the group refractive index of the waveguides over the wavelength range of interest, and consequently there will be significant group velocity dispersion [38] which must be taken into account when designing the rings.
Figure 10 shows the free spectral range as a function of radius for a circular ring for the measured group indices of our prototype Si and Si3N4 devices. Comparing with these FSRs full coverage of J and H bands would require radii of 0.66 and 0.37 μm for Si3N4, and Si respectively (the radii are approximately the same for each band). These radii are too small to be made without significant bending losses. To cover the entire J and H bands will therefore require several wavelength sub-windows of 30 − 70 nm each.
Preliminary laboratory tests of simple ring resonators show that FSRs of this order are not difficult to achieve with small radii Si or Si3N4 waveguides, see Fig. 7. However, to achieve high Q and large FSR simultaneously will require active tuning of the coupling coefficients (see § 2.2.1) or advanced designs and fabrication techniques [39].
Fig. 7 The measured FSRs (red points) of several devices compared to the theoretical curves for Si3N4 and Si, with ng = 2.15 and ng = 3.85, respectively.
It is possible to increase the FSR by using Vernier coupled ring resonators. In this case, the two rings have a resonant wavelength in common, but have different radii, such that the neighbouring resonances from each ring do not overlap, see Fig. 8. For example if the circumferences of the two rings are chosen to be L1 = Mλ/ne and L2 = Pλ/ne, then every Mth notch of ring 1 will overlap with every Pth notch of ring 2, with no overlapping in between, in which case the rings can be said to be Veriner coupled. Figure 9 shows an example transmission function with λ0 = 1.6, M = 9 and P = 10, compared to the transmission function of devices made from the individual rings, in this example the FSR is increased tenfold. Note however, that Vernier rings are difficult to achieve in practice, since they require very tight tolerances on the inter-ring coupling.
Fig. 8 Schematic diagram of the electric fields and coupling coefficients in a Vernier coupled resonator with no drop port.
Fig. 9 The transmission function of a Vernier coupled double ring resonator (black) with R1 = 9/10R2, and α = 0.998, β = 0.98 and t = 0.9, compared to devices made from the individual rings (red and blue) with α = t = 0.9.
Fig. 10 The free spectral range at λ = 1.55 μm of a circular ring resonator as a function of ring radius for Si3N4 and Si with ng = 2.15 and ng = 3.85 respectively, where the values come from our measured FSR.
2.2.3. Inter-notch throughput
The inter-notch transmission, T, is given by,
and is always higher for the same values of α and t. The difference for optimally coupled Vernier ring resonators with and without a drop port is insignificant.The total interline throughput will be given by TN where T is the interline transmission of a single ring. For example if using simple notch filters (Eq. 5), then we have,
which is plotted for the case α = t for various α in Fig. 11.If it is required to have an inter-notch transmission of ≥ τ, then
For example, an inter-notch transmission of τ = 0.9 is possible even for 100 rings in series if α = t > 0.96.Fig. 11 The total transmission for multiple simple ring-resonators in series with α = t (or identically, simple Vernier coupled notch filters with α = β = t) as a function of the number of rings.
N.B. the requirements on high Q for OH suppression, usually require higher α and t than the requirements on internotch throughput. That is, if the rings have high Q, they will also have high inter-notch throughput.
2.2.4. Coupling to astronomical instruments
One of the major challenges in using ring resonators in astronomical instrumentation is feeding light from the telescope into the waveguides at high efficiency. Indeed this is a problem for all astrophotonic instruments that use single mode waveguides.
This problem has two parts: (i) feeding the light from a telescope beam which has an AΩ etendue equivalent to a highly multimode waveguide into single mode fibres, (ii) feeding the light from a single mode fibre into the waveguides.
The first part of the problem can be solved either through the use of photonic lanterns [21,40], which split a multimode fibre into an array of SMFs at high efficiency, or through the use of extreme adaptive optics [41,42].
The second part of the problem arises because ring resonators require high index contrast waveguides in order to achieve the small bending radii necessary for the large FSR without introducing unacceptable bending losses. High index contrast waveguides are necessarily narrow to maintain single mode operation. Therefore there is a large mismatch between the mode field diameter of the SMFs and the waveguides. RSOFT BeamPROP simulations show that straight butt-coupling of a SMF-28 fibre to a ≈ 400 × 300 nm Si waveguide would lead to an insertion loss of ≈ −13 dB, with an identical loss at the output coupling.
High efficiency fibre to chip coupling is an active area of research within the photonics community [43]. As such there are several promising solutions to this problem [44].
One solution is to use grating couplers, in which a diffraction grating is written into the surface of the waveguide, which thus diffracts light of a specific wavelength at specific angles. A fibre can therefore be placed at the corresponding angle to the waveguide and thereby collect the diffracted light from the waveguide, or in reverse, feed light into the waveguide.
Following such strategies grating couplers can reach peak efficiencies of > −1 dB. However, these efficiencies peak in a narrow range of wavelengths. Typical 3 dB bandwidths are ≈ 40 – 70 nm. Compared to the required astronomical passbands of ∼ 160 – 290 nm (§ 2.2), grating couplers are very narrow band. They could find applications if the passband is subdivided into a number of smaller wavelength windows, or for particular niche science cases in which only specific wavelengths are to be targeted.
A more promising solution for astronomical requirements is to use an inverted taper on the waveguide, whereby the waveguide decreases in width at the edges of the chip – see Fig. 12a. As the width of the waveguide narrows, more of the light is squeezed out of the core into the evanescent field, increasing the mode field diameter. Note that the waveguide need only be tapered in one dimension, viz. the width, in order to increase the mode field diameter in this way. Insertion losses of less than 10% have been demonstrated in multiple publications [45–48]. Figure 13 shows the results from RSOFT BeamPROP simulations of the coupled power between an 8 μm core fibre, and a Si3N4 waveguide in SiO2 cladding, of height 650 nm and width 900 nm, which tapers over a distance 400 μm to a final tip width as plotted. The maximum coupled power of ≈ −1.6 dB occurs when the waveguide is tapered down to ≈ 50 nm.
Fig. 12 (a.) Sketch of an inverted taper butt-coupled to a fibre. The dimensions are not drawn to scale, in order to make all components visible. (b.) An SEM image of one of our tested cantilever devices based on the work of Galan [49].
Fig. 13 The power coupled between a perfectly aligned 8 μm core fibre, and a Si3N4 waveguide in SiO2 cladding, of height 650 nm and width 900 nm, which tapers over a distance 400 μm to a final tip width as plotted.
Coupling between a fibre and an inverted waveguide taper may be further improved in several ways [44]. For example, the tapered waveguide may be covered in a polymer cladding which acts as a new waveguide better matched to the fibre, and eases the alignment tolerances [45]; the fibre itself may also be lensed or of a high NA in order to match the fibre mode to that of the waveguide.
An interesting refinement of inverted tapers was suggested by Galan [49]. In this method the inverted taper sits on top of a ‘cantilever’ type structure, which is etched from the SiO2 substrate, as in Fig. 12b. Thus, as the light is squeezed out of the waveguide during the taper, it is guided by the SiO2 cantilever, which now acts as a waveguide surrounded by air. This cantilever waveguide has an MFD much better matched to a SMF, increasing the coupling, and easing the alignment tolerances. Furthermore, a V-groove can be etched under the cantilever to facilitate alignment. However, the V-grooves/cantilever system, with silicon waveguides, proved challenging to fabricate and assemble without damaging the waveguides and cantilevers. As a result, we decided to focus our current fabrication efforts on the study of the ring resonators with more conventional butt-coupling schemes.
Even with these refinements fibre-chip coupling remains a challenge to achieving an efficient instrument. Although inverted tapers are generally more broadband than grating couplers, the coupling efficiency is still a function of wavelength, which depends on the waveguide geometry, since the mode profile is wavelength-dependent. Nevertheless, inverted taper couplers with 1 dB bandwidth > 100 nm have been demonstrated [50].
The difficulty of fibre-chip couping is intensified for arrays of fibres, such as will be necessary in a multimode astronomical instrument. In this case the alignment tolerances proliferate as any misalignment can add up across the array, e.g. Doany et al. [51] report on an 8 channel coupler with 10.3 dB insertion loss for the best channel, compared to 9.3 dB for a single channel. These difficulties can be mitigated through more intensive fabrication processes [52], but at the cost of decreased yields, and increased expense. In addition to the coupling losses are the material absorption losses, which can be as high as 1 dB cm−1 for Si waveguides, which are already close to the requirement of 50 % total efficiency.
2.2.5. Quality factor
The quality of a ring resonator is equal to its resolving power, λ/Δλ. For OH suppression notch widths of Δλ ≈ 100 – 200 pm are necessary, which are equivalent to Q factors of 7750 – 15500 at λ = 1.55 μm.
The Q factor can be increased by increasing the self-coupling factor t through careful control of the gap size, and the throughput values α through minimising leaking into the substrate with a thicker SiO2 cladding above and below the waveguides. Note that high Q devices are certainly feasible [53,54].
2.2.6. Notch wavelengths, shape and stability
The wavelengths of the notches need to be aligned to the OH lines. The accuracy of this alignment needs to be better than half of the notch width, such that the notch will always cover the OH lines. Figure 5 shows the best improvement in signal to noise is achieved with notches 200 pm wide. The H band signal to noise is more sensitive to the notch width than the J band, because the average OH doublet spacing is larger in the H band than in J. In either case the notch wavelengths must be tuned to within ≈ 100 pm of the OH line wavelengths.
These tolerances are difficult to achieve during fabrication, e.g. due to variations in the width of the waveguide. This is especially true for devices containing multiple rings. Therefore, postfabrication tuning of the resonance wavelengths will be required, either via thermal resistive heaters, similar to the tuning of the coupling [55], or via heavy-ion doping [56]. Devices of coupled resonator optical waveguides (CROWs) have been demonstrated in which all the resonances are precisely aligned, either via thermal tuning of up to 64 rings [57], or by precise control of waveguide surface roughness during fabrication for up to 235 rings [58]. These same techniques could be used to tune individual rings to specific wavelengths.
Such post-tuning can also be used to stabilise the ring-resonators against temperature dependent changes of the resonance wavelengths. Both the refractive index of the materials used and the dimensions of the waveguide, are temperature dependent, and therefore changes in temperature will affect the effective index of the waveguides, and also the ring radii, which will directly affect the resonant wavelength. These effects need to be minimised via temperature control in order to use ring-resonators for astronomy, when it is imperative that the resonant wavelengths stay aligned with the OH lines. Fortunately, since ring resonators are very small the temperature control is not restrictive.
Rouger, Chrostowski, & Vafaei (2010) [59] have determined the magnitude of these temperature effects for SOI waveguides. The changes in dimensions due to thermal expansion are negligible, with only 0.038% increase in the dimensions for a temperature change of 107 K. We have used their changes in effective index to calculate the shift in resonant wavelength as a function of temperature and wavelength for a SOI waveguide with width 620 nm and height 250 nm, see Fig. 14. Controlling the temperature to within 0.3 deg will stabilise the resonant wavelength to within 50 pm, such that even a 100 pm wide notch will remain aligned to the OH lines.
Fig. 14 The change in resonant wavelength as a function of temperature for a SOI waveguide with R = 5 μm, at λ = 1.1, 1.55 and 1.8 μm (black, dashed, dotted lines respectively).
Temperature stabilised ring resonators have been demonstrated [60] using a resistive thermal device to provide temperature feedback to a thermo-electric cooler. A wavelength stability of 1 pm was achieved over a 24hr period for a single peak.
Ideally, the notches should be as rectangular as possible. This ensures that the maximum suppression occurs across the full width of the notch, allows for slight misalignments in wavelength, and avoids suppressing the interline regions.
In practice the notch shape is determined by the layout of the device, i.e., the number of rings and the presence or absence of a drop port. Figure 15 shows that Vernier coupled rings are squarer than single rings, and indeed more rings would make the notch even squarer [61]. However, for cascaded rings such as Vernier coupled filters, the inter-ring coupling coefficients must be carefully controlled to achieve a flat Butterworth filter profile; mode splitting, such as seen in Chebyshev filters can result in a rippled profile with reduced suppression in the centre of the band [62].
Fig. 15 Comparison of the notches of optimised ring-resonators consisting of a single ring with no drop port (α = t = 0.9), a single ring with a drop port (α = 1, t = 0.9), a double ring with no drop port (α = 0.998, β = 0.98, t = 0.9), and a double ring with a drop port (α = 0.998, β = 0.98, t = 0.9).
2.2.7. Polarisation
In general rectangular waveguides have two modes of polarisation which are approximately transverse electric (TE) or transverse magnetic (TM). Each polarisation mode will have a different effective index, and therefore a different set of resonant wavelengths.
Therefore, we may require double sets of ring resonator circuits, one for each polarisation, or polarisation independent waveguides. In this case the light must be split into orthogonal polarisations, either on or off chip, and in a wavelength independent manner over the wavelength range of interest.
Even when fed by a single polarisation, there will be significant on-chip polarisation due to surface roughness in the waveguides themselves. This results in polarisation dependent backscattering which can limit the suppression of Si ring-resonators to ≈ 20 dB [63]. These effects will be lessened for materials with lower refractive index contrast, and for TM polarisations. It is possible in theory to design rings to mitigate the effects of back-scattering, whilst achieving high FSR and high Q [39], though for this particular solution to avoid back-scattering practical devices are currently limited to very small FSR [64].
It has been shown that it is possible to tune the waveguide geometry precisely to enable approximately polarisation-independent behaviour, even for small waveguide structure and ring resonators as small as R = 3 μm [65]. Further work is necessary to see if this is practicable whilst meeting the other requirements for OH suppression, especially maintaining polarisation independence of wavelength ranges of 30 nm or more. However, even if polarisation-dependent effects do limit notch depth, Fig. 5 shows that significant signal to noise improvement can nevertheless be realised, thus making even such sub-optimal devices worthwhile.
2.2.8. Summary of requirements
In the next section we will discuss the practical aspects of implementing devices satisfying these requirements, but already there are some theoretical limitations to realistic devices.
In summary, for efficient OH suppression we require a total of ≈ 90 notches with a width of ≈ 150 pm and a depth of ≈ 30 dB for optimal suppression of the J band, and ≈ 150 notches with a width of ≈ 200 pm and a depth of ≈ 30 dB for optimal suppression of the H band; Table 1. The total throughput of the OH suppression system should be > 50 % to be competitive with other schemes.
However, the total passbands of the J and H bands would require FSRs corresponding to radii < 1 μm, which are would be extremely lossy. Thus the J and H passbands must be broken up into a series of smaller bands, each of which is suppressed separately (Fig. 4). For example, a ring with radius 6.5 μm would have α ≈ 0.9 and a FSR of ≈ 31 nm at λ = 1.6 μm. A 31 nm bandpass would require ∼ 15 notches (Table 1). Fifteen notches with α = t = 0.9 would have a total interline throughput of ≈ 0.85 (Eq. 6).
However, to obtain a sufficiently high Q factor would require even higher α and t. FDTD simulations made with Lumerical show that to meet the requirements of high Q and large FSR simultaneously with a single ring will require using Si waveguides, see Fig. 16. Nine such ‘circuits’ could cover the entire H band, noting that each would have to be reproduced for every spatial and polarisation mode (but given the extremely small dimensions of such devices, several circuits could fit on one wafer). If Vernier coupled rings can be implemented then wider passbands and fewer individual circuits can be used.
Fig. 16 (Left.) The simulated response of a 5 μm Si3N4 ring, with the parameters from a fit to a Lorentzian distribution. This device has a FSR of 38nm. (Right.) The simulated response of a 1.5 μm Si ring has a higher Q and a larger FSR of 73 nm.
3. Discussion
We have examined the application of ring resonators to astronomical instrumentation, with a focus on their use as notch filters for OH suppression. Ring resonators are an attractive solution to the problem of OH suppression because their size and method of fabrication is ideally suited to incorporating hundreds of rings in a single monolithic device [25]. Thus they are very scalable to the demands of a scientific instrument, and can be incorporated into an instrument in a modular fashion.
This modularity will become increasingly important in the era of extremely large telescopes. The beam size of a telescope scales with its diameter, and so as telescopes get larger so must astronomical instruments. However, this scaling can be broken by working at the diffraction limit [32], when the beam size is independent of telescope aperture. Thus by splitting the multimode beam of a seeing limited telescope into many single mode fibres via a photonic lantern, the problem changes from one of increasing the size of the instruments to one of replicating many miniature modular devices. The lithographic manufacture of ring resonators makes them ideally suited for this task.
We reviewed the astronomical requirements for OH suppression in section 2, and thereafter discussed the consequent requirements for ring resonators in section 2.2. From a theoretical perspective ring resonators are very well suited for OH suppression provided that certain conditions can be met. In particular they must have low loss, and optimally matched coupling coefficients, i.e. α = t > 0.9. If this can be achieved, which will require post-fabrication tuning of the coupling [28, 35, 36] and the resonances [55–58] then the requirements of deep notch depth (< −30 dB), narrow notch width (< 200 pm) and high interline throughput (> 0.8) can all be met.
Another requirement is to achieve a large FSR (> 30 nm), such that within the wavelength range of interest there is only one notch from each ring. Larger wavelength ranges can be builtup from several such ∼ 30 nm windows. A large FSR requires a small radius ring. Therefore care must be taken to avoid large bend losses. This leads us to waveguides with large refractive indices, such as Si or Si3N4; although note that a large index reduces the FSR, so a balance must be found. Note that high Q tunable rings have been designed with FSR > 150 nm, by using a tunable Mach-Zender Interferometer coupled to the ring [39].
The next stages of development for ring resonator based OH suppression requires the fabrication and testing of prototype devices. This work has already begun, and we we have fabricated more than 23 Si and Si3N4 waveguides in order to test their performance and to determine the design and fabrication specifications. Although this work is yet at an early stage we have several promising preliminary results. First, we have measured FSRs for several devices (Fig. 7), and find results fully consistent with the theoretical performance of our devices. Moreover, we have already fabricated devices with FSR > 30 nm, meeting the goal developed in section 2.2 for simple ring resonator devices. Second, we have fabricated devices with double rings, with different resonant wavelengths. Again, the measured resonant wavelengths are fully consistent with the theoretical predictions. Third, we have measured the quality, throughput (α), and self-coupling coefficients of several rings. We find that the α/t parameters are > 0.9, which is high enough to ensure good interline throughput over the 30 nm wavelength range. However, these α/t values are not yet high enough to ensure adequate Q, and indeed the measured Qs of ≈ 4000 do not yet have high enough resolution for OH suppression.
The next stages will be to optimise the behaviour of the rings themselves. That is, we need to identify and tune the design parameters to increase α/t and Q, as discussed in sections 2.2.1 and 2.2.6. Devices to test these parameters are already being made, and these tests are ongoing. Full testing will require a large number of devices in order to assess the accuracy of resonant wavelengths, coupling ratios and typical yields.
Second, we need to demonstrate the tuning of multi-ring devices to the specific OH wavelengths. Since we can already predict the accurate spacings of double ring devices, the printing of multi-ring devices with correct spacings should not be a fundamental barrier. However, there is a second part of this step, which requires the absolute tuning of the ring frequencies to the OH lines, and thereafter maintaining this tuning. This may be accomplished using temperature control of all the rings simultaneously, or may require tuning of the rings independently. We have not yet tested the temperature control of the rings, but the requirements on the stability are not expected to be severe (§ 2.2.6).
Third, we need to demonstrate efficient fibre-chip coupling. This is currently the biggest challenge for incorporating ring resonators into astronomical instruments. The fundamental mismatch between the MFD of the waveguides and that of a SMF adds an extra level of difficulty in accepting light from the focus of a telescope, since not only must there be a multimode to single mode conversion, but also a fibre to chip conversion. We are currently investigating the use of inverted tapers butt-coupled to lensed fibres, and have previously fabricated V-groove aligned cantilevers (§ 2.2.4). We note that this same problem presents a challenge to the use of silicon photonics in general [43], and hence it has received considerable attention, since solving it would enable the CMOS manufacture of many photonic components. However, the challenges for commercial packaging are somewhat different, with high-volume and low-cost automated packaging a priority. For astronomical instruments we do not need high volume, since instruments are built on a case-by-base basis, and for the same reason we do not necessarily require automated fibre-chip packaging. However, we do require very high efficiency, since the astronomical targets of interest are by their nature intrinsically faint, and ring resonators will be one part of a long chain of optical components from the telescope to the detector.
In summary, the overall prospects for ring-resonator-based astronomical instruments are good. The internal properties of the devices present no fundamental barriers to their use, and it should be possible to meet all the requirements for OH suppression, with the caveats that the large wavelength range will need to be split over several sub-windows, and there will need to be multiple copies of each window for every spatial and polarisation mode. However, the lithographic fabrication of ring resonators makes such replication trivial. There is also reason to be optimistic about the integration of ring resonators to astronomical instruments despite the current challenges in coupling to fibres. Coupling techniques are an active area of research, and moreover we can afford to spend the time fine tuning the most promising techniques, since we do not require mass production.
Of course, all these issues will take considerable development before a ring resonator based instrument is realised. However, this development is well worth the investment. The challenge of building affordable instruments in the current era with extremely large telescopes is not trivial. Astrophotonic instruments based on optical devices embedded within single mode waveguides offer a new solution to the process of building instruments for large telescopes. Already there are astrophotonic components of traditional instruments, providing new and better functionality, e.g. interferometric beam combination [66], pupil re-mapping aperture masking [67], and FBG OH suppression [16, 18, 19]. However, the true potential of astrophotonics lies in fully photonic instruments. Once the light from the telescope is fed into single mode fibres, all subsequent processing of light can take place on photonic chips. For example, following ring resonator based OH suppression spectroscopy could be carried out on the same chip using array waveguide gratings [31, 32, 68, 69], since the same fabrication methods can be used for both. This would lead to truly modular and miniature instruments.
Funding
U.S. Department of Energy, Office of Science, and Office of Basic Sciences contract DE-AC02-06CH11357 and Award DE-SC0012130. Alfred P. Sloan Foundation.
Acknowledgments
Many thanks to Martin Ams, Ben Johnston, Alex Stokes, and Graham Smith for their invaluable help in the laboratory testing of our devices. We are also very grateful for the help of our AAO vacation students: R. Nash, J. St. Antoine, J. Lorenzo Redondo, J. Kepple, and A. Crouzier. Many thanks to Jon Lawrence and Sergio León-Saval for useful discussions.
We wish to thank the staff at the Argonne Center for Nanoscale Materials, whose contributions made the ring resonator fabrication possible. This includes co-author Leo Ocola, Dave Czaplewski, Ralu Divan, Suzanne Miller, and Valentina Kutepova. Argonne students have been crucial for our device testing program: Danny Davies, James DerKacy, Ariel Matalon, Alexis Miranda, Kasia Pomian, and Joe Pastore. We wish to thank Tom Kasprzyk for his technical help with the Argonne test-stand.
This work was performed in-part at the OptoFab node of the Australian National Fabrication Facility, utilising NCRIS and NSW state government funding.
We thank two anonymous referees whose comments helped improve this paper.
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