Using speckle correlations for single-shot 3D imaging.

Recovery of a 3D object behind a scattering medium is an important problem in many fields, including biomedical and defense applications. Speckle correlation imaging can recover objects in a single shot but contains no depth information. To date, its extension to 3D recovery has relied on multiple measurements, multi-spectral light, or pre-calibration of the speckle with a reference object. Here, we show that the presence of a point source behind the scatterer enables single-shot reconstruction of multiple objects at multiple depths. The method relies on speckle scaling from the axial memory effect, in addition to the transverse one, and recovers objects directly, without the need for phase retrieval. We provide simulation and experimental results to show object reconstructions at different depths with a single-shot measurement. We also provide theoretical principles describing the region where speckle scales with axial distance and its effects on the depth of field. Our technique will be useful where a natural point source exists, such as fluorescence imaging or car headlights in fog.

Ultrahigh-Resolution, Label-Free Hyperlens Imaging in the Mid-IR.

The hyperbolic phonon polaritons supported in hexagonal boron nitride (hBN) with long scattering lifetimes are advantageous for applications such as super-resolution imaging via hyperlensing. Yet, hyperlens imaging is challenging for distinguishing individual and closely spaced objects and for correlating the complicated hyperlens fields with the structure of an unknown object underneath. Here, we make significant strides to overcome each of these challenges. First, we demonstrate that monoisotopic h11BN provides significant improvements in spatial resolution, experimentally resolving structures as small as 44 nm and those with sub 25 nm spacings at 6.76 µm free-space wavelength. We also present an image reconstruction algorithm that provides a structurally accurate, visual representation of the embedded objects from the complex hyperlens field. Further, we offer additional insights into optimizing hyperlens performance on the basis of material properties, with an eye toward realizing far-field imaging modalities. Thus, our results significantly advance label-free, high-resolution, spectrally selective hyperlens imaging and image reconstruction methodologies.

High-resolution light-field imaging via phase space retrieval.

By combining a high-resolution image from a standard camera with a low-resolution light-field image from a lenslet array, we numerically reconstruct a high-resolution light-field image. We experimentally demonstrate the method by creating a high-definition 3D image of a human cheek cell with a commercially available microscope.

General Model of Photon-Pair Detection with an Image Sensor.

We develop an analytic model that relates intensity correlation measurements performed by an image sensor to the properties of photon pairs illuminating it. Experiments using an effective single-photon counting camera, a linear electron-multiplying charge-coupled device camera, and a standard CCD camera confirm the model. The results open the field of quantum optical sensing using conventional detectors.

Adaptive Quantum Optics with Spatially Entangled Photon Pairs.

Light shaping facilitates the preparation and detection of optical states and underlies many applications in communications, computing, and imaging. In this Letter, we generalize light shaping to the quantum domain. We show that patterns of phase modulation for classical laser light can also shape higher orders of spatial coherence, allowing deterministic tailoring of high-dimensional quantum entanglement. By modulating spatially entangled photon pairs, we create periodic, topological, and random patterns of quantum illumination, without effect on intensity. We then structure the quantum illumination to simultaneously compensate for entanglement that has been randomized by a scattering medium and to characterize the medium's properties via a quantum measurement of the optical memory effect. The results demonstrate fundamental aspects of spatial coherence and open the field of adaptive quantum optics.

Enhanced phase retrieval using nonlinear dynamics.

Historically, phase retrieval algorithms have relied on linear propagation between two different amplitude (intensity) measurements. While generally successful, these algorithms have many issues, including susceptibility to noise, local minima, and indeterminate initial and final conditions. Here, we show that nonlinear propagation overcomes these issues, as intensity-induced changes to the index of refraction create additional constraints on the phase. More specifically, phase-matching conditions (conservation of wave energy and momentum) induce an object-dependent resonance between the measured amplitudes and the unknown phase. The result is a non-classical convergence profile in the reconstruction algorithm that contains a zero crossing, where the observable minimum in amplitude error and the unobservable minimum in phase error align at the same iteration number. We demonstrate this convergence experimentally in a photorefractive crystal, showing that there is a clear rule for stopping iterations. We find that the optimum phase retrieval occurs for a nonlinear strength that gives minimal correlation between the linear and nonlinear output amplitudes, i.e. a condition that maximizes the information diversity between linear and nonlinear propagation. The corresponding algorithm greatly improves the conventional Gerchberg-Saxton result and holds much potential for enhancing other methods of diffractive imaging.

Linear and nonlinear light localization through scattering media.

We extend the principles of time-resolved super-resolution source localization from diffractive microscopy to the imaging of objects through scattering media. We show that isolation and localization of the scattering (versus diffractive) point-spread function can be done by individually illuminating or individually darkening image segments. We experimentally demonstrate reconstruction of both bright and dark sources. Further, we show that self-focusing nonlinearity improves the localization accuracy for bright sources.

Phase-space measurement for depth-resolved memory-effect imaging.

Random scattering of light by a turbid layer prevents conventional imaging of objects hidden behind it. Angular correlations in the scattered light, created by the so-called optical memory effect, have been shown to enable computational image retrieval of hidden sources. However, basic memory-effect imaging contains no spatial (x) information, as only angular (k-space) measurements are made. Here, we use windowed Fourier transforms to record scattered-light images in the full {x,k} phase space. The result is the ability to discriminate size and depth of individual sources that are hidden behind a thin scattering layer.

Quantitative amplification of weak images by nonlinear propagation.

We demonstrate quantitative nonlinear recovery of images that have been hidden by the addition of partially coherent light. The method assumes a simple model for spatial nonlinearity that allows direct Laplacian inversion based on intensity transport.

Enhancing layered 3D displays with a lens.

We augment layered three-dimensional (3D) displays using a lens placed in front of or between attenuation layers. The lens, or similar optical element, improves the angular resolution of the system and enables translation of the displayed scene from a near-field image to a far-field projection. We analyze the relation between angular resolution (scene depth) and the number of layers and characterize the phase-space trade-offs between spatial and angular frequency components. We also introduce an algorithm for determining the layers of the display, which significantly reduces the computational requirements. The method is demonstrated on a standard 4D light field scene.

Phase retrieval using nonlinear diversity.

We extend the Gerchberg-Saxton algorithm to phase retrieval in a nonlinear system. Using a tunable photorefractive crystal, we experimentally demonstrate the noninterferometric technique by reconstructing an unknown phase object from optical intensity measurements taken at different nonlinear strengths.

Spectral dynamics of spatially incoherent modulation instability.

To date, all experiments in nonlinear statistical optics have relied on beams whose transverse spatial statistics were Gaussian. Here, we present a new technique to generalize these studies by using a spatial light modulator to create spatially incoherent beams with arbitrary spectral distributions. As a specific example of the new dynamics possible, we consider the spatial modulation instability of a partially coherent beam. We show that, for statistical beams of uniform intensity and equal correlation length, the underlying spectral shape determines the threshold and visibility of intensity modulations as well as the spectral profile of the growing sidebands. We demonstrate the behavior using statistical light, but the results will hold for any wave-kinetic system, such as plasma, ultracold gases, and turbulent acoustic waves.

Wave and defect dynamics in nonlinear photonic quasicrystals.

Quasicrystals are unique structures with long-range order but no periodicity. Their properties have intrigued scientists ever since their discovery and initial theoretical analysis. The lack of periodicity excludes the possibility of describing quasicrystal structures with well-established analytical tools, including common notions like Brillouin zones and Bloch's theorem. New and unique features such as fractal-like band structures and 'phason' degrees of freedom are introduced. In general, it is very difficult to directly observe the evolution of electronic waves in solid-state atomic quasicrystals, or the dynamics of the structure itself. Here we use optical induction to create two-dimensional photonic quasicrystals, whose macroscopic nature allows us to explore wave transport phenomena. We demonstrate that light launched at different quasicrystal sites travels through the lattice in a way equivalent to quantum tunnelling of electrons in a quasiperiodic potential. At high intensity, lattice solitons are formed. Finally, we directly observe dislocation dynamics when crystal sites are allowed to interact with each other. Our experimental results apply not only to photonics, but also to other quasiperiodic systems such as matter waves in quasiperiodic traps, generic pattern-forming systems as in parametrically excited surface waves, liquid quasicrystals, and the more familiar atomic quasicrystals.

Pixel super-resolution with spatially entangled photons.

Pixelation occurs in many imaging systems and limits the spatial resolution of the acquired images. This effect is notably present in quantum imaging experiments with correlated photons in which the number of pixels used to detect coincidences is often limited by the sensor technology or the acquisition speed. Here, we introduce a pixel super-resolution technique based on measuring the full spatially-resolved joint probability distribution (JPD) of spatially-entangled photons. Without shifting optical elements or using prior information, our technique increases the pixel resolution of the imaging system by a factor two and enables retrieval of spatial information lost due to undersampling. We demonstrate its use in various quantum imaging protocols using photon pairs, including quantum illumination, entanglement-enabled quantum holography, and in a full-field version of N00N-state quantum holography. The JPD pixel super-resolution technique can benefit any full-field imaging system limited by the sensor spatial resolution, including all already established and future photon-correlation-based quantum imaging schemes, bringing these techniques closer to real-world applications.

Instability-driven recovery of diffused images.

We demonstrate the nonlinear recovery of diffused images in a self-focusing photorefractive medium. The method is based on the convolution property of nonlinearity, in which related modes reinforce each other as they propagate. The resulting mode coupling enables energy transfer from the scattered light to the underlying signal. The dynamics is well described by a model in which the signal seeds a modulation instability in the diffused background.

Optimizing holographic data storage using a fractional Fourier transform.

We demonstrate a method to optimize the reconstruction of a hologram when the storage device has a limited dynamic range and a minimum grain size. The optimal solution at the recording plane occurs when the object wave has propagated an intermediate distance between the near and far fields. This distance corresponds to an optimal order and magnification of the fractional Fourier transform of the object.

Observation of random-phase lattice solitons.

The coherence of waves in periodic systems (lattices) is crucial to their dynamics, as interference effects, such as Bragg reflections, largely determine their propagation. Whereas linear systems allow superposition, nonlinearity introduces a non-trivial interplay between localization effects, coupling between lattice sites, and incoherence. Until recently, all research on solitary waves (solitons) in nonlinear lattices has involved only coherent waves. In such cases, linear dispersion or diffraction of wave packets can be balanced by nonlinear effects, resulting in coherent lattice (or 'discrete') solitons; these have been studied in many branches of science. However, in most natural systems, waves with only partial coherence are more common, because fluctuations (thermal, quantum or some other) can reduce the correlation length to a distance comparable to the lattice spacing. Such systems should support random-phase lattice solitons displaying distinct features. Here we report the experimental observation of random-phase lattice solitons, demonstrating their self-trapping and local periodicity in real space, in addition to their multi-peaked power spectrum in momentum space. We discuss the relevance of such solitons to other nonlinear periodic systems in which fluctuating waves propagate, such as atomic systems, plasmas and molecular chains.

Nonlinear light propagation in fractal waveguide arrays.

We experimentally and numerically study nonlinear light propagation in a fractal waveguide array. We consider a nested set of periodic arrays and examine energy transport as a function of band structure, nonlinearity, and probe beam geometry. Experimentally, we observe the behavior directly by recording intensity in position space and power spectra in momentum space. The results are fundamental to nonlinear wave dynamics in self-similar structures and hold potential to improve the efficiency and sensitivity of fractal photonic devices.

Modulation instability of a coherent-incoherent mixture.

We examine the nonlinear coupling and modulation instability of a coherent beam with one that is partially spatially incoherent. Using a mutual coherence approach, we derive the growth rate for perturbations and show that the presence of any amount of coherent component eliminates the nonlinear threshold for instability. The fraction of coherent light is shown to determine the gain and characteristic period of the resulting patterns. Theoretical considerations are confirmed by numerical simulation and by experimental observations in a self-focusing photorefractive crystal.

Diffraction from an edge in a self-focusing medium.

We experimentally demonstrate diffraction from a straight edge in a medium with self-focusing nonlinearity. Diffraction into the shadow region is suppressed with increasing nonlinearity, but mode coupling leads to excitations and traveling waves on the high-intensity side. Theoretically, we interpret these modulations as spatially dispersive shock waves with negative pressure.