Angularly resolved polarization microscopy for birefringent materials with Fourier ptychography.

Polarization light microscopy is a very popular approach for structural imaging in optics. So far these methods mainly probe the sample at a fixed angle of illumination. They are consequently only sensitive to the polarization properties along the microscope optical axis. This paper presents a novel method to resolve angularly the polarization properties of birefringent materials, by retrieving quantitatively the spatial variation of their index ellipsoids. Since this method is based on Fourier ptychography microscopy the latter properties are retrieved with a spatial super-resolution factor. An adequate formalism for the Fourier ptychography forward model is introduced to cope with angularly resolved polarization properties. The inverse problem is solved using an unsupervised deep neural network approach that is proven efficient thanks to its performing regularization properties together with its automatic differentiation. Simulated results are reported showing the feasibility of the methods.

Amorphous-to-crystal transition in the layer-by-layer growth of bivalve shell prisms.

Biomineralization integrates complex physical and chemical processes bio-controlled by the living organisms through ionic concentration regulation and organic molecules production. It allows tuning the structural, optical and mechanical properties of hard tissues during ambient-condition crystallisation, motivating a deeper understanding of the underlying processes. By combining state-of-the-art optical and X-ray microscopy methods, we investigated early-mineralized calcareous units from two bivalve species, Pinctada margaritifera and Pinna nobilis, revealing chemical and crystallographic structural insights. In these calcite units, we observed ring-like structural features correlated with a lack of calcite and an increase of amorphous calcium carbonate and proteins contents. The rings also correspond to a larger crystalline disorder and a larger strain level. Based on these observations, we propose a temporal biomineralization cycle, initiated by the production of an amorphous precursor layer, which further crystallizes with a transition front progressing radially from the unit centre, while the organics are expelled towards the prism edge. Simultaneously, along the shell thickness, the growth occurs following a layer-by-layer mode. These findings open biomimetic perspectives for the design of refined crystalline materials. STATEMENT OF SIGNIFICANCE: Calcareous biominerals are amongst the most present forms of biominerals. They exhibit astonishing structural, optical and mechanical properties while being formed at ambient synthesis conditions from ubiquitous ions, motivating the deep understanding of biomineralization. Here, we unveil the first formation steps involved in the biomineralization cycle of prismatic units of two bivalve species by applying a new multi-modal non-destructive characterization approach, sensitive to chemical and crystalline properties. The observations of structural features in mineralized units of different ages allowed the derivation of a temporal sequence for prism biomineralization, involving an amorphous precursor, a radial crystallisation front and a layer-by-layer sequence. Beyond these chemical and physical findings, the herein introduced multi-modal approach is highly relevant to other biominerals and bio-inspired studies.

Broadband decoupling of intensity and polarization with vectorial Fourier metasurfaces.

Intensity and polarization are two fundamental components of light. Independent control of them is of tremendous interest in many applications. In this paper, we propose a general vectorial encryption method, which enables arbitrary far-field light distribution with the local polarization, including orientations and ellipticities, decoupling intensity from polarization across a broad bandwidth using geometric phase metasurfaces. By revamping the well-known iterative Fourier transform algorithm, we propose "à la carte" design of far-field intensity and polarization distribution with vectorial Fourier metasurfaces. A series of non-conventional vectorial field distribution, mimicking cylindrical vector beams in the sense that they share the same intensity profile but with different polarization distribution and a speckled phase distribution, is demonstrated. Vectorial Fourier optical metasurfaces may enable important applications in the area of complex light beam generation, secure optical data storage, steganography and optical communications.

Reference-free quantitative microscopic imaging of coherent arbitrary vectorial light beams.

Precise spatial characterization of vectorial beams is crucial for many advanced optical experiments, but challenging when wavefront and polarization features are involved together. Here we propose a reference-free method aimed at extracting the map of the complex-amplitude components of any coherent beam at an optical-microscopy resolution. Our method exploits recent advances in ptychographic imaging approaches. We emphasize its versatility by reconstructing successfully various experimental vectorial beams including polarization and phase vortices, the exit field of a multicore fiber and a speckle pattern.

Ptychography retrieval of fully polarized holograms from geometric-phase metasurfaces.

Controlling light properties with diffractive planar elements requires full-polarization channels and accurate reconstruction of optical signal for real applications. Here, we present a general method that enables wavefront shaping with arbitrary output polarization by encoding both phase and polarization information into pixelated metasurfaces. We apply this concept to convert an input plane wave with linear polarization to a holographic image with arbitrary spatial output polarization. A vectorial ptychography technique is introduced for mapping the Jones matrix to monitor the reconstructed metasurface output field and to compute the full polarization properties of the vectorial far field patterns, confirming that pixelated interfaces can deflect vectorial images to desired directions for accurate targeting and wavefront shaping. Multiplexing pixelated deflectors that address different polarizations have been integrated into a shared aperture to display several arbitrary polarized images, leading to promising new applications in vector beam generation, full color display and augmented/virtual reality imaging.

Joint estimation of object and probes in vectorial ptychography.

Vectorial ptychography has been recently introduced to reconstruct the Jones matrix of an anisotropic object by means of series of ptychographic measurements performed using a set of polarized illumination probes in conjugation with various analyzers. So far, the probes were assumed to be completely known (amplitude, wavefront, state of polarization), which is rarely the case in practice. Here we address the issue of the joint estimating of the set of polarized illumination probes together with the Jones matrix of an anisotropic object in vectorial ptychography. We propose an algorithm based on a conjugate gradient strategy. Experimental results are reported, showing an improvement on the object estimate, in addition to a precise reconstruction of the probes.

Quantitative imaging of anisotropic material properties with vectorial ptychography.

Following the recent establishment of the formalism of vectorial ptychography [Opt. Lett.40, 5144 (2015)OPLEDP0146-959210.1364/OL.40.005144], first measurements, to the best of our knowledge, are reported in the optical range, demonstrating the capability of the proposed method to map the four parameters of the Jones matrix of an anisotropic specimen, and therefore to quantify a wide range of optical material properties, including power transmittance, optical path difference, diattenuation, retardance, and fast-axis orientation.