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Abstract
In astronomy and related fields there is a pressing need to efficiently inject light, transmitted through the atmosphere, into a single-mode fibre. However this is extremely difficult due to the large, rapidly changing aberrations imprinted on the light by the turbulent atmosphere. An adaptive optics system must be used, but its effectiveness is limited by non-common-path aberrations and insensitivity to certain crucial modes. Here we introduce a new concept device - the hybrid mode-selective photonic lantern - which incorporates both focal plane wavefront sensing and broadband single-mode fibre injection into a single photonic package. The fundamental mode of an input multimode fibre is directly mapped over a broad (1.5 to 1.8μm) bandwidth to a single-mode output fibre with minimal (<0.1%) crosstalk, while all higher order modes are sent to a fast detector or spectrograph for wavefront sensing. This will enable an AO system optimised for maximum single-mode injection, sensitive to otherwise ‘blind’ modes and avoiding non-common-path wavefront-sensor aberrations.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In astronomy, it is often desired to efficiently inject starlight into a single-mode (SM) fibre, for subsequent analysis by a single-mode spectrograph [1–7], photonic interferometer [8–10], or other instrument. The same challenge is faced in free-space optical communications [11], remote sensing [12], LIDAR [13], and other fields [14]. But doing this efficiently is extremely difficult, since the light has been subject to strong, rapidly varying aberrations by the turbulent atmosphere. The resulting point-spread-function (PSF) of the focused light has complex, high-frequency spatial structure, having minimal overlap with an SM fibre’s mode field.
Usually some sort of adaptive optics (AO) system [15,16] is used to address this [17], but the effectiveness of this technique is limited by the fact that the AO system’s wavefront sensor (WFS) is located at a different physical location and optical plane in the instrument and is performed at a different wavelength. The different optical elements traversed introduce non-common aberrations between wavefront sensor and fibre, which change over time due to thermal and mechanical drift in the instrument (which is especially pronounced when the fibre core to be injected into is a few microns in diameter). Additionally, the standard pupil-plane wavefront sensors used in AO systems are unable to detect certain aberration modes, such as low-wind effect (LWE) [18,19], which are severely detrimental to focal-plane fibre-injection for large aperture telescopes.
These issues can be addressed by the use of a photonic-lantern focal-plane wavefront sensor (PL-WFS) [20]. Such a wavefront sensor sits at the focal plane at or near the final science PSF, minimising non-common aberrations, is sensitive to blind modes such as LWE, and (since it has a fibre-based output) is trivial to spectrally disperse for multi-wavelength measurements. It is also compact (fitting in a standard fibre connector) and well suited to multi-object applications, and efficient in its detector requirements. If the goal of the AO system fed by such a WFS is optimal injection into a SM fibre, non-common-path aberrations could be completely eliminated by using one of the PL-WFS’s output fibres as the science fibre (routed to a spectrograph or other instrument), and the AO’s zero-point chosen such that it maximises light output to that output alone [21,22]. The remaining (wavefront-sensing) output fibres would then be used to drive the AO system to maintain this injection. But the transfer function of a standard photonic lantern is strongly chromatic, so such a solution only works for monochromatic applications, while in astronomy broad bandwidths are required.
Here we present a device to tackle all these problems - the ‘hybrid’ mode-selective photonic lantern (HMS-PL). This incorporates a focal-plane wavefront sensor and SM fibre injection over a broad bandwidth into a single monolithic package. When placed at the focal plane of a telescope’s AO system, the device measures the residual wavefront aberrations and sends feedback to the AO system to correct the wavefront to the optimum injection solution. Then, a mode-selective output ensures maximum light is sent to the science fibre over a broad bandwidth (the entire astronomical H band, 1.5$\mu$m to 1.8$\mu$m). We present a design for a HMS-PL optimised using numerical models, and explore its performance over wide bandwidths using numerical simulations.
2. Principle of operation
When light is injected into a multi-mode fibre (MMF), the amplitude of the excited modes are determined by the spatially-dependent, complex amplitude of the incident light. Thus when placed at the telescope focal plane, the amplitude of modes in such a fibre encode the complex electric field of the telescope point-spread function (unlike a standard focal plane imaging detector, which measures only intensity). If the amplitude of the excited modes were known, in principle the incident wavefront could be reconstructed. To efficiently measure the mode amplitudes, a photonic mode-converter, a.k.a a photonic lantern (PL) is used [23,24]. This device acts as an interface between a multimode fibre and multiple, single-mode fibres. Via an adiabatic taper transition, light in the MMF is efficiently transferred into a set of single-mode output fibres (SMFs), as long as the number of output SMFs is equal to or greater than the number of input modes [24]. The maximum achievable efficiency is then limited by material absorption and by deviation of the structure from that supporting idealised step-index fibre modes as described in Fontaine et al [25]. Spatial information is preserved, and so given the transfer function of the PL, the incident wavefront can be reconstructed from the measured intensities of the output fibres [20,21,26]. This transfer function is difficult to precisely define at fabrication and is highly nonlinear, so a neural network is used to learn this transfer function. This is the principle of the photonic-lantern wavefront sensor (PL-WFS), detailed in Ref. [20].
As described in Section 1, the PL-WFS offers several advantages over a standard pupil-plane wavefront sensor, and could also be used to optimally inject light into one of its output fibres. However - the PL’s transfer function is highly wavelength-dependant, so this method only works monochromatically (whereas astronomy and sensing applications require very broad bandwidths).
On the other hand, mode-selective photonic lanterns exist [27–30], which do directly map an input mode to an output fibre over a broad bandwidth [31], and have been investigated for efficient injection of starlight [32]. However, these are limited to very few-mode devices [33], making them less suitable for wavefront sensing. The hybrid mode-selective photonic lantern presented here is the best of both worlds. It maintains strong, broad-band mode-selectivity for the fundamental (LP$_{01}$) input mode of the photonic lantern to the central output SM fibre, where it is needed for science-light injection, and then features a non-mode-selective transfer matrix for higher order modes used for wavefront sensing, where mode-selectivity is not required, and could indeed be detrimental. The wavefront sensing fibres would be spectrally dispersed onto the detector, with the measurement of the chromatic-dependence of atmospheric seeing being extremely useful for AO (e.g. to measure scintillation). The device designed here has 19 modes, while the design principle is expected to scale to an arbitrary number of modes.
In the envisioned deployment, the HMS-PL would be placed at the focal plane of a telescope’s AO system. The wavefront sensing output fibres would be imaged via a v-groove onto to a fast detector (such as is used for standard wavefront sensing), with optional spectral dispersion implemented by incorporating a diffraction grating or prism. This would drive the AO system as described in [20]. Meanwhile, the mode-selective output would be routed to an instrument such as a high-dispersion single-mode spectrograph, interferometer, or other SMF-fed instrument. During setup, the target position for the AO system would be determined so that it maximally excited the LP$_{01}$ mode of the device (using standard non-realtime injection scanning or optimisation methods). During observations, the AO system continually adjusts the wavefront to this desired target position, driven by the wavefront sensing fibres. When injection is optimal, there will be very little light in these fibres; any departure from ideal injection will introduce light into these fibres, which is sensed by the AO system and used to drive the system back to the optimal injection state. Even a relatively small number of corrected modes dramatically increases coupling to a fibre, with the vast majority of power being present in the lowest modes [31]. It is envisioned that a PIAA apodiser [34] would be used in the optical system, to allow the PSF to most closely match the LP$_{01}$ mode field.
3. Design
Achieving maximal mode selectivity (minimum cross-talk) is the key to obtaining broad-bandwidth operation. This is because any mixing of modes, each of which have different propagation constants, will result in interference between modes, causing beating. This leads to a strong, non-linear variation of the amount of flux in all the cores as a function of wavelength. Given the requirements for high mode-selectivity of the LP$_{01}$ mode to be maintained across the astronomical H band (1.5 to 1.8 $\mu$m), high throughput, and sufficient outputs to enable wavefront sensing, a design was developed and optimised using numerical simulations. RSoft’s Beamprop and Femsim tools were used for beam propagation and mode-finding respectively, with custom tools to perform testing, optimisation and simulations. A schematic of the resulting hybrid mode-selective PL is shown in Fig. 1. The underlying component is a 19-core hexagonal-pattern fibre array (or multicore fibre) with core index of 1.4468, cladding index of 1.44, single-mode core diameter of 4 $\mu$m and core-to-core separation of 60 $\mu$m. The central core is larger than the other cores, with a diameter of 15$\mu$m, but with the same index. The fibre array (or multicore fibre) is placed into a low-index capillary tube (fluorine-doped fused silica) with refractive index of 1.43451, with inner diameter 328 $\mu$m and outer diameter 763 $\mu$m. This is then tapered, reducing the fibre diameters by a factor of 10 over a taper-length of 40 mm.
Fig. 1. Schematics of the hybrid mode-selective PL including the design parameters, showing the constituent cores, cladding and capillary. At the un-tapered, single-mode multicore output end, the central, larger core is the mode-selective output. The device is tapered down to the narrower multi-mode input end, where the original cores disappear, the cores’ original cladding becomes the new core and the low-index capillary becomes the new cladding.
The result is that the tapered end now becomes a multi-mode fibre, with the low-index capillary becoming the cladding of this new fibre, the original SM fibre’s cladding becoming the new core, and the original SM fibre’s cores becoming too narrow to effectively guide any light. Parameters have been tuned such that resulting multimode fibre, with core diameter 32.8 $\mu$m, supports 19 spatial modes (at the shortest design wavelength of 1.5 $\mu$m), matching the number of output modes. This, along with the optimised geometric parameters, enables an adiabatic transition with very high throughput of 99.5% at 1.6 $\mu$m (not including material absorption). For the sake of simplicity, this simulations assume a custom multicore fibre is used to build the PL model. Operationally, there is no difference between a multicore and a fibre bundle (the ’traditional’ method of building a PL) photonic lantern with same parameters.
The larger, central output fibre is the mode-selective (MS) output. This is achieved by increasing its fundamental mode effective refractive index $n_\mathrm {eff}$ (by increasing its diameter) with respect to the other fibres. While the $n_\mathrm {eff}$s of all cores vary throughout the taper transition, the central waveguide remains the highest. As the PL tapers from the narrow (multimode) input end to the wider output end, the input LP$_{01}$ mode (having the highest $n_\mathrm {eff}$) preferentially couples to the high $n_\mathrm {eff}$ central output core. All other input modes couple to the set of degenerate single-modes comprising the remaining output fibres. This is shown graphically in Fig. 2, where the modal evolution of the hybrid MS PL is shown.
Fig. 2. Plot of waveguide effective index $n_\mathrm {eff}$ as a function of inner diameter, equivalent to position along the length taper. At the multimode input (right of plot) up to 19 modes are excited. The $n_\mathrm {eff}$ of the LP$_{01}$ smoothly transitions to the $n_\mathrm {eff}$ of the mode selective output’s LP$_{01}$ mode. This results in the input LP$_{01}$ mode coupling exclusively to the mode selective output (orange). All other input mode $n_\mathrm {eff}$s transition to the $n_\mathrm {eff}$ of the 18 single-mode outputs (purple). Additionally, LP$_{11}$ modes can be supported in the MS output (brown). A small amount of non-science light couples into this, which is subsequently filtered out. LP$_{21}$ modes can also be supported (cyan), but negligible power couples into these.
Ideally, this central waveguide would itself be strictly single-moded. However it was found that the the maximum $n_\mathrm {eff}$ difference possible while maintaining single-mode behaviour in both sized waveguides did not provide strong mode-selectivity, with approximately 7% of power in the input LP$_{02}$ mode also coupling into the central output waveguide, as expected by the geometry overlap between both LP$_{0m}$ modes. Instead, a solution was found wherein the MS output core was also allowed to support LP$_{11}$ modes, which are slightly excited by higher order (LP$_{11}$ and LP$_{12}$) input modes at the PL multimode end, while the coupling between input LP$_{01}$ mode and the MS output’s LP$_{01}$ mode remains strongly selective. At short wavelengths LP$_{21}$ modes are also weakly guided by the MS output fibre, but negligible power couples into these. These higher modes are then filtered out with a standard mode filter (e.g. via a fibre taper) at the MS PL output. As a result extremely high mode selectivity is achieved, with an intensity coupling from the input LP$_{01}$ mode to the MS output of >99.9 % and, most importantly, less than 0.1% total cross talk from other modes into the MS output (at 1.6 $\mu$m). This high mode selectivity sets the upper-limit on the proportion of total light which can be sent out the mode-selective output. In practice this efficiency will be limited by the limitations of the AO system being driven by this device (e.g. loop latency, number of deformable mirror actuators, and higher-order aberrations). The rejection of the higher modes in the MS output via modal filtering results in the loss of approximately 5% of the wavefront-sensing light, which in most applications would be negligible. Note that the modal filtering does not attenuate any of the ‘science’ (LP$_{01}$ input) light.
A complex transfer matrix for the device at 1.6 $\mu$m is shown in Fig. 3. The strongly selective mapping between the LP$_{01}$ input and MS output fibre (waveguide 9) is clearly seen in the form of there being just a single matrix component, of value $\sim$1, mapping the LP$_{01}$ input mode to output waveguide 9.
Fig. 3. Complex transfer matrix for mode selective lantern ($\lambda =1575$ nm), showing the mapping between mode excited in the MM end and output from each SM waveguide. Waveguide 9 is the mode selective output (LP$_{01}$ mode) to be sent to the science instrument. Virtually all power in this output arises from the multi-mode fibre’s LP$_{01}$ mode, with all higher modes extincted by $\sim$27 dB. Outputs 9a and 9b represent the higher modes (LP$_{11\mathrm {a}}$ and LP$_{11\mathrm {b}}$) excited in the mode selective output, which are subsequently filtered out by the modal filter (not shown here). All other modes/outputs are used for wavefront sensing, to ensure maximum excitation of the input LP$_{01}$ mode.
4. Broadband injection performance
Key to the device’s utility is its ability to provide strong mode selectivity over a broad bandwidth. In Fig. 4 a plot of extinction as a function of wavelength across the entire band is shown. It can be seen that over the entire astronomical H band, the extinction (that is the degree by which power from all modes other than the input LP$_{01}$ mode is suppressed from coupling into the mode-selective output) is always better than 20 dB, reaching $\sim$30dB at $\sim$1.6 $\mu$m.
Fig. 4. Plot of the mode selectivity of the device as a function of wavelength. Here, extinction refers to the degree by which power from all modes other than the input LP$_{01}$ mode is suppressed from coupling into the mode-selective output.
To demonstrate this performance of the device across a broad bandwidth, a basic simulation was performed where the PL’s input modes were randomly excited, and their coefficients then randomly perturbed via a random walk (a phase error drawn from a Gaussian distribution of $\sigma$=0.1 radians per mode added for each time step) to produce a time-series. This is analogous to the smoothly, randomly varying PSF aberrations (which subsequently randomly excite fibre modes when injected) arising from imaging a star through a turbulent atmosphere.
In Fig. 5 all modes in the MM input region were excited using a uniform random set of amplitudes and phases, with amplitudes between 0 and 1 and phases between 0 and $\pi$ radians. It can be seen that the output amplitude of the mode selective waveguide is achromatic, whilst all other waveguides are a strongly non-linear function of wavelength (and used for spectrally-resolved wavefront sensing). With this random set of mode amplitudes and phases, the mode-selective output intensity varies by less than 2% across the band.
Fig. 5. Output amplitudes for all waveguides when all input modes are excited with a random set of amplitudes ($0< A <1$) and phases ($0<\phi <\pi$), as a function of wavelength. The mode selective waveguide (no. 9) is unique in that its output amplitude is not dependent on wavelength, unlike the standard photonic lantern outputs. In the bottom plot, the mode selective output is plotted in green. This plot is a 2D representation of the data set used in the top panel.
Figure 6 shows the output amplitudes from this simulation as a function of wavelength and time, for three representative non mode-selective outputs (waveguides 1, 11 and 15) used for wavefront sensing, and the mode-selective output (waveguide 9) used for the science instrument. The output amplitude of the standard waveguide is strongly wavelength dependent, while the mode-selective output is largely achromatic. In this example the initial excitation for all input modes were chosen randomly. A discontinuity in the pattern can be seen at $\sim 1.76\mu$m, where the multimode region stops guiding the highest-order modes. When deployed in an adaptive optics application the AO system’s reference wavefront would be set to maximally optimise output to the mode selective output (i.e. maximising excitation of the input LP$_{01}$ mode), using feedback from the other outputs to maintain it.
Fig. 6. Wavelength-dependent output for three standard (top-left, top-right, and bottom-left) and mode-selective (bottom-right) waveguides, for a simulated observation with randomly varying phase errors (such as through an atmosphere) - see text for details. The output of the standard waveguides (used for wavefront sensing) varies strongly as a function of the lantern’s input mode excitation, while the mode-selective output remains very stable.
5. Conclusion
Injecting light corrupted by atmospheric turbulence into a single-mode fibre is greatly desirable not only in astronomy but also in technologically related fields such as free-space optical communication, LIDAR, and remote sensing. But it is extremely difficult to do so efficiently due to the large wavefront aberrations of the focused light and rapidly changing PSF. Adaptive optics are required, but standard pupil-plane wavefront sensors are limited in their ability to achieve efficient injection, due to non-common optical aberrations between wavefront sensor and fibre, and their inability to sense certain extremely damaging modes (such as low wind effect). A photonic lantern wavefront sensor is one potential solution to this measurement problem. This injects the telescope PSF at the pupil plane into a multimode fibre and uses a photonic lantern as a fibre mode converter to transfer its modal content to set a set of multiple, single-mode output fibres. The intensity of these outputs encode the complex electric field of the incident PSF, and can hence be used to reconstruct the wavefront, while avoiding most non-common-path aberrations and maintaining sensitivity to ’blind’ modes, among other advantages. However this would still require a separate optical path leading to the single-mode ’science’ fibre, leading to residual non-common path errors.
In this paper we present a novel device – a hybrid mode-selective photonic lantern – which aims to provide a solution to this problem. Instead of attempting to inject light directly into a single-mode fibre at all, we propose that light only be injected into a larger multimode fibre, a much easier task. The hybrid photonic lantern performs the same wavefront sensing task as the conventional photonic lantern wavefront sensor, but additionally it directly maps the fundamental (LP$_{01}$) mode of the input multimode fibre to a specific output single-mode fibre. This mapping works over a broad bandwidth (1.5 to 1.8 $\mu$m, the astronomical H band) and with very high selectivity (less than 0.1% cross-talk at 1.6 $\mu$m).
In this application, the non-mode-selective output fibres are sent to a fast detector for wavefront sensing, while the mode-selective ‘science’ output is fed to an instrument such as high-dispersion spectrograph, interferometer, or another science device. By setting the AO system’s zero point to the wavefront which maximally excites the multimode fibre’s LP$_{01}$ mode (previously determined offline), it uses the intensity in the wavefront-sensing fibres to continuously drive the AO correction to maximum-injection. This integrated wavefront sensor and fibre injection device, which has zero non-common-path aberration, will help enable high precision astrophotonic science on fainter targets, and with higher signal to noise ratio, than has been previously possible. Applications include single-mode spectroscopy for astronomical research such as exoplanet detection and exoplanet atmosphere characterisation, astronomical interferometry, as well as areas such as free-space optical communication.
Funding
Australian Research Council (DE210100953); National Aeronautics and Space Administration (80NSSC21K0624).
Acknowledgements
B.Norris is the recipient of an Australian Research Council Discovery Early Career Award (DE210100953) funded by the Australian Government. R.Amezcua-Correa and S.Leon-Saval would like to acknowledge that part of this material is based upon work supported by the National Aeronautics and Space Administration under Grant No. 80NSSC21K0624.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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