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Abstract Photonic lanterns (PLs) are tapered waveguides that gradually transition from a multimode fiber geometry to a bundle of single-mode fibers (SMFs). They can efficiently couple multimode telescope light into a multimode fiber entrance at the focal plane and convert it into multiple single-mode beams. Thus, each SMF samples its unique mode (lantern principal mode) of the telescope light in the pupil, analogous to subapertures in aperture masking interferometry (AMI). Coherent imaging with PLs can be enabled by the interference of SMF outputs and applying phase modulation, which can be achieved using a photonic chip beam combiner at the backend (e.g., the ABCD beam combiner). In this study, we investigate the potential of coherent imaging by the interference of SMF outputs of a PL with a single telescope. We demonstrate that the visibilities that can be measured from a PL are mutual intensities incident on the pupil weighted by the cross correlation of a pair of lantern modes. From numerically simulated lantern principal modes of a 6-port PL, we find that interferometric observables using a PL behave similarly to separated-aperture visibilities for simple models on small angular scales (<λ/D) but with greater sensitivity to symmetries and capability to break phase angle degeneracies. Furthermore, we present simulated observations with wave front errors (WFEs) and compare them to AMI. Despite the redundancy caused by extended lantern principal modes, spatial filtering offers stability to WFEs. Our simulated observations suggest that PLs may offer significant benefits in the photon-noise-limited regime and in resolving small angular scales at the low-contrast regime. 

Abstract The direct imaging of an Earth-like exoplanet will require sub-nanometric wave-front control across large light-collecting apertures to reject host starlight and detect the faint planetary signal. Current adaptive optics systems, which use wave-front sensors that reimage the telescope pupil, face two challenges that prevent this level of control: non-common-path aberrations, caused by differences between the sensing and science arms of the instrument; and petaling modes: discontinuous phase aberrations caused by pupil fragmentation, especially relevant for the upcoming 30 m class telescopes. Such aberrations drastically impact the capabilities of high-contrast instruments. To address these issues, we can add a second-stage wave-front sensor to the science focal plane. One promising architecture uses the photonic lantern (PL): a waveguide that efficiently couples aberrated light into single-mode fibers (SMFs). In turn, SMF-confined light can be stably injected into high-resolution spectrographs, enabling direct exoplanet characterization and precision radial velocity measurements; simultaneously, the PL can be used for focal-plane wave-front sensing. We present a real-time experimental demonstration of the PL wave-front sensor on the Subaru/SCExAO testbed. Our system is stable out to around ±400 nm of low-order Zernike wave-front error and can correct petaling modes. When injecting ∼30 nm rms of low-order time-varying error, we achieve ∼10× rejection at 1 s timescales; further refinements to the control law and lantern fabrication process should make sub-nanometric wave-front control possible. In the future, novel sensors like the PL wave-front sensor may prove to be critical in resolving the wave-front control challenges posed by exoplanet direct imaging. 

Adaptive optics (AO) systems are critical in any application where highly resolved imaging or beam control must be performed through a dynamic medium. Such applications include astronomy and free-space optical communications, where light propagates through the atmosphere, as well as medical microscopy and vision science, where light propagates through biological tissues. Recent works have demonstrated common-path wavefront sensors (WFSs) for adaptive optics using the photonic lantern (PL), a slowly varying waveguide that can efficiently couple multi-moded light into single-mode fibers (SMFs). We use the SCExAO astrophotonics platform at the 8 m Subaru Telescope to show that spectral dispersion of lantern outputs can improve correction fidelity, culminating with an on-sky demonstration of real-time wavefront control. This is the first, to the best of our knowledge, result for either a spectrally dispersed or a photonic lantern wavefront sensor. Combined with the benefits offered by lanterns in precision spectroscopy, our results suggest the future possibility of a unified wavefront sensing spectrograph using compact photonic devices. 

We present several nonlinear wavefront sensing techniques for few-mode sensors, all of which are empirically calibrated and agnostic to the choice of wavefront sensor. The first class of techniques involves a straightforward extension of the linear phase retrieval scheme to higher order; the resulting Taylor polynomial can then be solved using the method of successive approximations, though we discuss alternate methods such as homotopy continuation. In the second class of techniques, a model of the WFS intensity response is created using radial basis function interpolation. We consider both forward models, which map phase to intensity and can be solved with nonlinear least-squares methods such as the Levenberg-Marquardt algorithm, as well as backwards models, which directly map intensity to phase and do not require a solver. We provide demonstrations for both types of techniques in simulation using a quad-cell sensor and a photonic lantern wavefront sensor as examples. Next, we demonstrate how the nonlinearity of an arbitrary sensor may be studied using the method of numerical continuation, and apply this technique both to the quad-cell sensor and a photonic lantern sensor. Finally, we briefly consider the extension of nonlinear techniques to polychromatic sensors. 

We present numerical characterizations of the wavefront sensing performance for few-mode photonic lantern wavefront sensors (PLWFSs). These characterizations include calculations of the throughput, control space, sensor linearity, and an estimate of the maximum linear reconstruction range for standard and hybrid lanterns with between 3 and 19 ports, atλ=1550nm. We additionally consider the impact of beam-shaping optics and a charge-1 vortex mask placed in the pupil plane. The former is motivated by the application of PLs to high-resolution spectroscopy, which could enable efficient injection into the spectrometer along with simultaneous focal-plane wavefront sensing; similarly, the latter is motivated by the application of PLs to vortex fiber nulling (VFN), which can simultaneously enable wavefront sensing and the nulling of on-axis starlight. Overall, we find that the PLWFS setups tested in this work exhibit good linearity out to ∼0.25−0.5 radians of RMS wavefront error (WFE). Meanwhile, we estimate the maximum amount of WFE that can be handled by these sensors to be around ∼1−2 radians RMS before the sensor response becomes degenerate. In the future, we expect these limits can be pushed further by increasing the number of degrees of freedom, either by adopting higher mode-count lanterns, dispersing lantern outputs, or separating polarizations. Finally, we consider optimization strategies for the design of the PLWFS, which involve both modification of the lantern itself and the use of pre- and post-lantern optics like phase masks and interferometric beam recombiners. 

Abstract Coronagraphs allow for faint off-axis exoplanets to be observed, but are limited to angular separations greater than a few beam widths. Accessing closer-in separations would greatly increase the expected number of detectable planets, which scales inversely with the inner working angle. The vortex fiber nuller (VFN) is an instrument concept designed to characterize exoplanets within a single beam width. It requires few optical elements and is compatible with many coronagraph designs as a complementary characterization tool. However, the peak throughput for planet light is limited to about 20%, and the measurement places poor constraints on the planet location and flux ratio. We propose to augment the VFN design by replacing its single-mode fiber with a six-port mode-selective photonic lantern, retaining the original functionality while providing several additional ports that reject starlight but couple planet light. We show that the photonic lantern can also be used as a nuller without a vortex. We present monochromatic simulations characterizing the response of the photonic lantern nuller (PLN) to astrophysical signals and wavefront errors, and show that combining exoplanet flux from the nulled ports significantly increases the overall throughput of the instrument. We show using synthetically generated data that the PLN detects exoplanets more effectively than the VFN. Furthermore, with the PLN, the exoplanet can be partially localized, and its flux ratio constrained. The PLN has the potential to be a powerful characterization tool complementary to traditional coronagraphs in future high-contrast instruments. 

The photonic lantern (PL) is a tapered waveguide that can efficiently couple light into multiple single-mode optical fibers. Such devices are currently being considered for a number of tasks, including the coupling of telescopes and high-resolution, fiber-fed spectrometers, coherent detection, nulling interferometry, and vortex-fiber nulling. In conjunction with these use cases, PLs can simultaneously perform low-order focal-plane wavefront sensing. In this work, we provide a mathematical framework for the analysis of a PL wavefront sensor (PLWFS), deriving linear and higher-order reconstruction models as well as metrics through which sensing performance—in both the linear and nonlinear regimes—can be quantified. This framework can be extended to account for additional optics such as beam-shaping optics and vortex masks, and can be generalized for other wavefront sensing architectures. Finally, we provide initial numerical verification of our mathematical models by simulating a six-port PLWFS. In a forthcoming companion paper (Lin and Fitzgerald), we provide a more comprehensive numerical characterization of few-port PLWFSs, and consider how the sensing properties of these devices can be controlled and optimized.