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Abstract
Research into planets beyond our own star system has until recently relied on indirect imaging methods. Direct imaging methods are now establishing a foothold in the hunt for alien planets and habitable worlds. Nulling interferometry is a promising approach for suppressing the host star brightness and resolving surrounding planets. A key requirement in this method is the interference of light from multiple telescopes/baselines and free space optical devices have already rendered images of other worlds. Photonic chip based systems are also becoming accepted as means of accomplishing this but require, in particular, wide bandwidth, high precision on chip beam splitters. In this paper a design improvement is outlined to one of the most fabrication tolerant integrated beam splitter components that significantly increases its coupling bandwidth and therefore its bandwidth at high extinction. Preliminary experimental results from a fabricated device are also shown. The predicted bandwidth spans 3.8 – 4.1 μm at an extinction of ∼50 dB but at the expense of increasing the loss to 0.6 dB in transmission.
© 2017 Optical Society of America
Corrections
7 August 2017: A typographical correction was made to the author listing.
1. Astronomy background
The hunt for exoplanets began in the mid-1900s with the first discovery in 1989 [1]. The predominant exoplanet discovery methods use indirect techniques from either transit detection (exemplified by the Kepler space telescope), or the radial velocity methods. More recently, direct observational methods have started to be employed, with the first directly imaged multi-planet exoplanetary system observed in 2008 [2].
The major issue in direct imaging methods is the need to attenuate the host star’s intensity by typically > 106 times in order to render the weak exoplanetary emissions visible. The standard method for star suppression in direct imaging uses coronagraphs [3]. These physically block the starlight and allow for large exoplanets at multiple earth orbits from the host star to be imaged [4]. However, small, Earth-like exoplanets 1 au away from the host star are not easily imaged this way. Direct imaging interferometry, first used in astronomy by Michelson [5], provides the Fourier components of the angular brightness distribution of the stellar object that can be transformed into an image. With interferometry; the light from many telescopes (or a single telescope split into multiple baselines) are combined to form interference fringes. A null can be arranged over the host star by appropriate manipulation of the baseline phases to create destructive interference of the star light. Bracewell [6] first proposed the idea of using interference to null the star itself. He noted that due to the phase difference between the star and any surrounding object, a null on the star still allows for constructive interference (and so visibility) of the surrounding objects.
The first nulling interferometer implementations, based on Bracewell’s idea, were proposed in free space optics form [7,8]. This was realised on the Keck telescopes [9,10]. However, as more baselines are used, the alignment and stability requirements become very challenging leading to the desire to replace free space optics with photonic chips. The first generation is currently undergoing testing on sky in the 1550 nm band and longer wavelength versions are under development [11–15].
In the search for exoplanets, the mid-infrared (MIR) wavelengths are most intriguing as this is where chemical indications of extraterrestrial life are available: Ozone (at 9.7 μm) for example [16]. The astronomical L band (3.7 – 4.2 μm) is especially interesting for a number of reasons: Earth has an atmospheric transmission window in this region [2] with adaptive optics (AO) systems [17,18] used to compensate the remaining atmospheric disturbances; the star to exoplanet light ratio is much more favourable in this regime than for the visible spectrum; and the use of longer wavelengths enables vision through low temperature dust clouds. Young star systems, with forming exoplanets, can have an optical depth of unity temperature 700 K or more which provides a blackbody peak in the L band. The host star is still too bright for direct imaging of exoplanets close into the star system [2] and thus nulling interferometry is required to see into the star’s glare.
The MIR regime cannot utilise widely available and proven silica photonic chips as silica is not transparent in the desired 3.7–4.2 μm band. Materials such as Silicon on Sapphire [19], Silicon Germanium [20], Indium Phosphide [21], Aluminium Gallium Arsenide [22], Lithium Niobate [23] and Chalcogenide glass (ChG) [24]; have all been used substantially in MIR photonics. ChG appears a very promising route for astronomy applications due to its lower refractive index and easy extension to the 10 μm band for follow up experiments focusing on the atmospheric detection of Ozone.
MIR ChG waveguides fabricated by the deposit and etch method have already been shown to have low loss [24] down to ≈ 0.2 dB/cm when appropriate glass purification and material processing methods are employed. Another method of creating ChG structures is using three-dimensional laser writing [25,26] where evanescent coupling has been used to split light between two waveguides. The advantage of this method is the ease of coupling into the photonic chips due to the large mode field sizes resulting from the low index contrast provided. Ultra-fast laser inscription has direct application to astronomical MIR interferometry [27] for both remapping the incident light from the three dimensional array of baselines to a two dimensional line array for coupling into planar chips [28] and in the beam combination itself [15]. However the low index contrast severely compromises the integration density limiting its utility for more complex nulling circuits. It was recently theoretically proven [29] that MIR nulling interferometers constructed from multimode interference couplers (MMIs) in intermediate index contrast buried ChG waveguides, provide good performance with high fabrication tolerances. In a double nulling architecture, an MMI analogue to the nulling system proposed in [8], provided an extinction bandwidth of 400 nm at 60 dB over the range of realistic fabrication tolerances, and in a single nulling arrangement, 13.5 nm at 60 dB extinction. In that work, the impact of the input/output taper width was touched upon with the only conclusion on the topic being that any taper width > 6 μm had an acceptable loss with the optimum width being three tenths the width of the MMI cavity, as expected [30].
In this paper, the impact of taper is studied further with emphasis on the interaction between the taper width and the MMI main cavity. It will be shown that a much wider bandwidth at high extinction is achieved in a single nulling device by optimizing the taper width away from the optimum for transmission at the expense of a small amount of insertion loss.
2. Theory MMI
A multimode interference coupler (MMI) is a device that is commonly used to split light evenly - a 50:50 beamsplitter. The device uses a single mode waveguide as an input and excites a number of higher order modes in a much larger waveguide, the MMI cavity, that at various points interfere to form localized intensity maxima..
The example in Fig. 1 has a single input through a 13.5 μm wide taper, that is launched into the multimode cavity and evolves to two localized intensity maxima at the output. The equation defining the approximate position of the localized outputs for this example, is
for the length of the cavity (L), width of the cavity (W), refractive index (n) and wavelength of the input light (λ). Note that Eq. (1) is for a specific case of a restricted interference MMI as described in [31] for the first iteration of two self-images. The restricted case is used as it reduces the length of the MMI by a factor of three. The requirement for the restricted case is that the input waveguides are positioned at W/3 and 2W/3 along the width (or ±W/6 from the centre of the MMI).
Fig. 1 BPM simulation of the optimised MMI, from [29], were the width is 45 μm the length is 875 μm, the taper width and length is is 13.5 μm and 200 μm respectively and light is directed from the left to right. Note that this is the reduced case MMI as described in [31].
3. Taper dependence
3.1. Numerical simulation
The taper input/output to the MMI cavity was first investigated by Hill [30] where the optimum MMI transmission (and imbalance at the design wavelength) was achieved at a taper width of 0.3 × MMI width. However the impact of taper width on the coupling bandwidth was not studied, and to the author’s best knowledge has not been subsequently investigated. The simulated MMIs in Fig. 11 of [29] confirmed that, at the design wavelength, the 0.3 × MMI width was optimum for a ChG MMI of width 45 μm and showed that below a taper width of 8 μm the insertion loss started to increase significantly. Following from [29] the full vector Beam Propagation Method (BPM) using R-Soft BeamPROP was used to determine the wavelength dependence of the imbalance and transmission for a range of taper widths in an MMI nominally optimised at 4 μm wavelength and of width 45 μm, this being previously shown to be a highly fabrication tolerant base design. From this, the optical bandwidth for an extinction of 40 dB, 50 dB and 60 dB between two equal, but 90° phased inputs, was calculated. Figures 2(a) and 2(b) show the resulting taper width dependence of transmission and bandwidth.
Fig. 2 (a) loss vs taper width over operational bandwidth, data points joined by standard fitting (b) bandwidth around 4 μm for specified extinction vs taper width.
Figure 2(b) is particularly important here as it indicates that there are in fact preferred widths for the tapers that offer improved interferometric bandwidth. This is particularly clear for the 50 dB extinction level where 8 and 12 μm are clearly the superior options offering coverage of almost the whole operating window from 3.7 – 4.2 μm. At 60 dB extinction, the trend is less obvious but it is clear that the “optimum” 0.3 × MMI width design is the worst performing. In terms of insertion loss, the 12 μm design is very close to the “optimum” design with an additional loss of 0.6 dB at the edges of the operating window, whilst the 8 μm design has an additional 2 dB insertion loss at the short wavelength edge of the operational window. Despite its inferior insertion loss performance, the 8 μm taper width is however perhaps the preferable design due to the increased gap (7 versus 3 μm) between the closest points of the tapers. The larger gap makes the top cladding fill and the lithography considerably easier when real fabrication challenges are considered. Another interesting feature is the nature of the extinction response.
Taking the worst case fabricational tolerances and using a Monte Carlo simulation as [29], then the worst case extinction for a device with real world fabrication can be calculated as a function of wavelength. This is presented in Fig. 3. It is clear that the 13 μm taper width exhibits a single null corresponding to the single point at which the imbalance is zero. It is this monotonic behaviour in the imbalance response that causes the narrow extinction bandwidth at 60 dB previously illustrated in [29]. The 8 and 12 μm taper widths however show multiple nulls as the imbalance oscillates around zero in the operating window and the oscillation enables a wider operating extinction bandwidth of 350 nm and 300 nm respectively. This is similar to what is presented as the double null scenario in [29] and is hence attractive as an initial device. There is a mismatch between the bandwidths in Fig. 2 and 3, the 50 dB bandwidth being 0.08 μm, 0.36 μm and 0.24 μm for the 13.5 μm, 12 μm and 8 μm respectively compared to 0.08 μm, 0.46 μm, 0.36 μm from Fig. 2. This arises due to the difference between simulations of a single device design with variable tapers and a full Monte Carlo simulation with outline and MMI width as variables. However, the key details of which taper width is better are not contradicted. The intriguing question is why do these particular taper widths produce a better extinction and is there a general relationship present?
Fig. 3 Worst case extinction over full range of random fabricational variations for a taper width of 8 μm, 12 μm and 13.5 μm. The simulation is calculated similarly to that of Fig. 14(a) of [29] but taking the lowest extinction case at each wavelength.
3.2. Theory
Why the taper width has such a dramatic effect on the extinction bandwidth of the MMI is, to the best of the author’s knowledge, unknown. BPM simulations offer little insight, so to gain some physical understanding, the sine wave based mode field approximation of Soldano [31] and Hill [30] was employed. Under these conditions, the light propagation through the MMI has an analytical solution and is described by the sum of the mode fields weighted by their excitation strength and phase:
where ν is the mode number, ψν is the modal field distribution, Lπ is the beat length of the two lowest order modes, and cν is the field excitation coefficient (or Fourier component) as described byEach mode is represented as a sine-wave [30] and thus:
where taper width (Wa) and position of the taper (xc) are now included in Eq. (2). Note that the coordinates define the base of the MMI as (0,0) and the top as (0,W).Substituting the numbers for the optimum MMI from section 2 then establishes all but two variables: taper width (Wa) and mode number (ν) in Eq. (4). Thus the output field at the end of the multimode section can be calculated as a function of wavelength for different taper widths.
To obtain the coupling ratios requires further approximation. Looking at the right hand side tapers in Fig. 1, it is clear that these do not function as adiabatic mode transformers as the intensity in them has rapidly evolving maxima and minima as the light first encounters the taper. This is the hallmark of mode conversion, here converting higher order modes in the taper into the fundamental mode of the output waveguide as the loss of the device is close to zero. This is however not the case for narrower tapers substantiated by the fact that such MMIs have more loss (sometimes substantially so) and so the mode conversion is incomplete. This poses a problem for the simple model as there is no simple analytical way to represent this process, and it is therefore assumed that the coupling ratios can instead be approximated by means of an overlap integral with the taper fundamental mode and that this all converts to the output waveguide mode without loss. Given the different phase constants of the modes in the taper, the mode coupling effects may well contribute to the imbalance wavelength dependence, and such effects are then lost in the approximate model. For a waveguide of 45 μm width, 29 modes are supported in the multimode slab region as per the V value:
However, modes ν = 2, 5, 8, . . . are not excited in the restricted case of the MMI [31]. Setting the taper width to 13.5, 12 and 8 μm and calculating the modal excitation coefficients in the slab from the input taper yields the result of Fig. 4.As expected; Cν=2,5,8,... = 0 but there is a very clear difference in the behavior for modes 9 and 10. Cν=9 = 0 for a taper width of 13.5 μm but not for 8 or 12 μm and Cν=10 is very much larger for a taper width of 8 μm and of reversed sign for both 8 and 12 μm. Beyond mode 10, the sign of the Fourier component is reversed until mode 24 for 8 μm. The contribution of each Fourier term, however, past mode 14 is significantly diminished due to the low excitation, thus the behavior at mode 9 is the dominant feature. How this effects extinction bandwidth is explored by utilising the Eq. (2) and subsequently introducing a wavelength dependence. Figure 5(a) shows the resulting calculated imbalance wavelength dependence for a 12 μm taper with and without mode 9 included, and Fig. 5(b) for an 8 μm taper.
Fig. 5 Analytical MMI model imbalance vs wavelength for (a) 13.5 and 12 μm taper widths and 12 μm without mode 9 included, (b) 13.5 and 8 μm taper widths and 8 μm without mode 9. The horizontal green lines correspond to imbalances providing 60 dB extinction.
Figure 5 shows that the ninth mode serves to significantly flatten the wavelength response at the level required to significantly enhance the 60 dB extinction bandwidth. Examining the intercepts with the 60 dB extinction contour, the analytical model suggests that the 12 μm taper offers a 60 dB extinction bandwidth of 0.13 μm vs 0.085 μm for the 13.5 μm “optimum” design, and the 8 μm taper a 60 dB extinction bandwidth of 0.15 μm. The BPM model produces nearly double the bandwidth for the 8 and 12 μm tapers (0.34 and 0.30 μm respectively), but almost a quarter (0.02 μm bandwidth) for the 13.5 μm “optimum” likely indicating the impacts of the mode coupling in the tapers at the output. The approximate model also reproduces the multiple zero crossings in the imbalance leading to multiple deep nulls seen in Fig. 3(a). The electric field of mode nine over the wavelength range of Fig. 5 is plotted across the taper positions in Fig. 6.
Fig. 6 Wavelength dependence of the real part of the electric field distribution of ν = 9 in for 8 μm taper width plotted across taper mouth.
The mode, as shown in Fig. 6, is asymmetric having opposing signs at the entrance to each taper and a close match to the taper fundamental mode. It therefore serves to increase the field on one taper and reduce it on the other at any given wavelength thereby modifying the imbalance. As the wavelength scans, at the shortest wavelength in that range, mode nine compensates the negative imbalance but imperfectly; and as the wavelength increases, the field addition of the other modes increases faster than the reduction around the peak of the sinusoid response of mode nine, thus pushing the imbalance positive. As the wavelength increases further, the reduction in mode nine accelerates across the sinusoidal phase response leading to a further zero crossing into negative imbalance again. At the nominal design wavelength, mode nine has no contribution but the whole design is perfectly balanced by default and so the imbalance is zero again. Increasing the wavelength further beyond the design wavelength, the whole process reverses to compensate the now positive imbalance of the device response with mode nine omitted. Whilst the effects are clearly beneficial in the design shown here, further research is required to deduce the general design rules, if any, that apply here, but it is evident that significant improvements are possible in performance in at least some classes of design. Following the modelling, efforts were put into trying to experimentally verify the findings.
4. Experimental results
For an experimental ChG chip the combination of Germanium, Arsenic, Sulphur (Ge11.5 As24 S64.5) as the cladding material and Germanium, Arsenic, Selenium (Ge11.5 As24 Se64.5) as the core material was used as this combination has low loss [24]. The ChG films were deposited using thermal evaporation, onto an oxidised 100 mm silicon wafer, in a single deposition: first an undercladding layer of GeAsS, the core layer of GeAsSe, and a thin protective top cladding of GeAsS, all deposited without breaking vacuum to reduce contamination and improve inter-film adhesion. The GeAsS undercladding was deposited 3 μm thick, the GeAsSe core layer 2 μm, and the GeAsS top clad 1 μm thick which was used to protect the core layer from any top surface roughness induced by the etch process and mask removal. Standard I-Line projection positive photolithography and inductively coupled plasma (ICP) etching were then used to pattern the core. A CHF3 plasma used to etch the ChG and the resist was dry stripped after etching in O2. After plasma processing was completed, standard wet resist stripping was applied to ensure no trace quantities of resist remained on the top surface. An additional layer of GeAsS (3 μm) was then deposited at a ∼ 60° angle of incidence to uniformly clad the core. After cleaving, the chip was measured using a tunable optical parametric amplifier as a source [32] and a pair of 0.5 NA reflective Schwarzschild objectives for in and out coupling. The cross and bar ports of the MMI were imaged onto a Xenics Onca InSb camera with its imaging lens in place and using its inbuilt non-uniformity correction with the lens. Frame integration of 100 to 256 frames was then applied, and circular regions of interest corresponding to the second null of the Airy disc used to cut off any background light before pixel integration to obtain the relative port powers. Integration usually produced convergence to the fourth significant digit and then the wavelength was stepped to the next measurement point. Wavelength scans of measured imbalance across the available tuning range (3.3 – 4.95 μm with a gap due to parasitic second harmonic processes) for a 45 μm wide MMI with an 8 μm wide taper are presented in Fig. 7 along with the theoretical response computed with R-Soft BeamPROP and presented in [29] for the 13.5 μm taper only.
Fig. 7 Wavelength dependence of imbalance vs the theoretical prediction. The difference in polerization is small, as expectecd from [29].
The experimental data in Fig. 7 suggests a good match with the 8 μm taper width theoretical prediction, rather than the 13.5 μm simulation, excepting the rather high “noise” present on the experimental traces which renders impossible evaluation of the imbalance at the level required to verify the 60 dB extinction bandwidth predictions. Scanning the devices at high wavelength resolution showed that the excursions were actual changes in the coupling ratio and not measurement noise (estimated at 0.1% imbalance). The imbalance noise is believed to arise from scattering off particulate contamination within the MMI slab region and from scattered/uncoupled light trapped in the in the core layer vertically by the high index cladding and horizontally by effective cladding rib waveguide formed by the “bump” in the cladding as the core is overcoated [13]. BeamPROP simulations that place a 1 μm diameter column of undercladding material into the core indeed showed that random wavelength dependent variation of the imbalance results from such defects at levels consistent with the noise measured here, but at a periodicity longer than that typically observed. What it did not show was the increase in noise the further away from zero imabalance, as shown in Fig. 7. This observation will need further investigation.
Figure 8 shows a light field micrograph of a typical measured MMI, the defects visible as dots in the image. The reasons for the particle growth are yet to be elucidated and are the subject of ongoing research. Interestingly it is clear that this does not occur with the Selenide core material, so one option would be to move to an all Selenide combination of glasses to eliminate it. BeamPROP simulations with the cladding bump included rather than with an infinite cladding also resulted in imbalance ripple, this time with a shorter periodicity. In order to verify the precise imbalance behavior, the defects need to be eliminated by improvement of the deposition processes, and adding an additional top cladding layer with an index intermediate to the core and cladding may prevent light from being trapped in the top layer. This is discussed somewhat in [13] to rectify a different problem that is not seen in these waveguides. Furthermore, “side stepping” the device inputs and outputs can also be employed to reduce the influence of scattered light.
Fig. 8 Micrograph of the measured MMI (875 μm length, 45 μm width) of taper width 13.5 μm and taper length 200 μm.
5. Conclusion
It was shown theoretically that the coupling ratio uniformity and so extinction bandwidth of MMI devices is dependent on the taper width into the MMI slab region. Indeed for extinction ratios of 40 dB and above, the effects can be very strong. The design often considered as optimal (in terms of insertion loss bandwidth) was actually the worst performing design when the device is used as a high extinction ratio interferometer. Considerably wider bandwidths at the high extinction ratios required for use in astronomical interferometric nullers were shown to be possible by optimizing the taper width. Two design options exist: the 12 μm taper width that has minimal additional insertion loss across the 3.7 – 4.2 μm band, and the 8 μm taper width with ∼2 dB additional loss at the short wavelength edge, but with significantly eased fabrication tolerances and bandwidth of 350 nmat > 60 dB extinction. The reason behind the increase in bandwidth appeared to be due a single slab mode not excited in the loss optimized case, this mode flattening the coupling ratio imbalance in the high extinction zone. This theoretically provides up to 4 times the bandwidth at the 60 dB extinction level required for nulling interferometry to directly observe distant exoplanets that could be considered Earth-like. In the astronomy L band this resulted in a predicted 50 dB extinction bandwidth sufficient to cover almost the whole 3.7 – 4.2 μm band. An experimentally fabricated device showed characteristics that appear to support the theory, but with significant “noise” on the coupling imbalance that resulted from defects within the film stack leaking light into cladding modes, and guidance of uncoupled and scattered light by the structured cladding to the output. It is expected that these will be eliminated and that full experimental verification will be achieved in the near future.
Funding
Australian Research Council (ARC) Centre of Excellence for Ultrahigh bandwidth Devices for Optic Systems (CUDOS) project CE110001018.
Acknowledgments
Thank you to the Australian National Fabrication Facilities for their financial support for the RSoft design tools.
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