Throughout optics and photonics, phase is normally controlled via an optical path difference. Although much less common, an alternative means for phase control exists: a geometric phase (GP) shift occurring when a light wave is transformed through one parameter space, e.g., polarization, in such a way as to create a change in a second parameter, e.g., phase. In thin films and surfaces where only the GP varies spatially-which may be called GP holograms (GPHs)-the phase profile of nearly any (physical or virtual) object can in principle be embodied as an inhomogeneous anisotropy manifesting exceptional diffraction and polarization behavior. Pure GP elements have had poor efficiency and utility up to now, except in isolated cases, due to the lack of fabrication techniques producing elements with an arbitrary spatially varying GP shift at visible and near-infrared wavelengths. Here, we describe two methods to create high-fidelity GPHs, one interferometric and another direct-write, capable of recording the wavefront of nearly any physical or virtual object. We employ photoaligned liquid crystals to record the patterns as an inhomogeneous optical axis profile in thin films with a few μm thickness. We report on eight representative examples, including a GP lens with F/2.3 (at 633 nm) and 99% diffraction efficiency across visible wavelengths, and several GP vortex phase plates with excellent modal purity and remarkably small central defect size (e.g., 0.7 and 7 μm for topological charges of 1 and 8, respectively). We also report on a GP Fourier hologram, a fan-out grid with dozens of far-field spots, and an elaborate phase profile, which showed excellent fidelity and very low leakage wave transmittance and haze. Together, these techniques are the first practical bases for arbitrary GPHs with essentially no loss, high phase gradients (∼rad∕μm), novel polarization functionality, and broadband behavior.

We report on a direct-write system for patterning of arbitrary, high-quality, continuous liquid crystal (LC) alignment patterns. The system uses a focused UV laser and XY scanning stages to expose a photoalignment layer, which then aligns a subsequent LC layer. We intentionally arrange for multiple overlapping exposures of the photoalignment material by a scanned Gaussian beam, often with a plurality of polarizations and intensities, in order to promote continuous and precise LC alignment. This type of exposure protocol has not been well investigated, and sometimes results in unexpected LC responses. Ultimately, this enables us to create continuous alignment patterns with feature sizes smaller than the recording beam. We describe the system design along with a thorough mathematical system description, starting from the direct-write system inputs and ending with the estimated alignment of the LC. We fabricate a number of test patterns to validate our system model, then design and fabricate a number of interesting well-known elements, including a q-plate and polarization grating.

Patterned light from a laser can induce rapid self-folding of pre-strained polymer sheets. Black ink coated on the sheet absorbs the light, which converts the photon energy into thermal energy that heats the sheet locally; the temperature of the sheet is highest at the surface where the light impinges on the sheet and decreases through the sheet thickness. The gradient of temperature induces a gradient of strain relaxation through the depth of the sheet, which causes folding within seconds of irradiation. The pattern of laser light that irradiates the compositionally homogeneous two-dimensional (2D) substrate dictates the resulting three-dimensional (3D) shape. Unlike most approaches to self-folding, the methodology described here requires no patterning of pre-defined hinges. It opens up the possibility of using a patterning technique that is inherently 2D to form 3D shapes. The use of lasers also enables systematic control of key process parameters such as power, intensity, and the pattern of light (i.e., beam width and shape). The rate of folding and folding angle measured with respect to these parameters provide an indirect quantification of heat loss in the sample and thereby identify the threshold power and power intensity that must be delivered to the hinge for folding to occur. V

One of the main challenges for the direct imaging of planets around nearby stars is the suppression of the diffracted halo from the primary star. Coronagraphs are angular filters that suppress this diffracted halo. The Apodizing Phase Plate coronagraph modifies the pupil-plane phase with an anti-symmetric pattern to suppress diffraction over a 180 degree region from 2 to 7 λ/D and achieves a mean raw contrast of 10(-4) in this area, independent of the tip-tilt stability of the system. Current APP coronagraphs implemented using classical phase techniques are limited in bandwidth and suppression region geometry (i.e. only on one side of the star). In this paper, we introduce the vector-APP (vAPP) whose phase pattern is implemented through the vector phase imposed by the orientation of patterned liquid crystals. Beam-splitting according to circular polarization states produces two, complementary PSFs with dark holes on either side. We have developed a prototype vAPP that consists of a stack of three twisting liquid crystal layers to yield a bandwidth of 500 to 900 nm. We characterize the properties of this device using reconstructions of the pupil-plane pattern, and of the ensuing PSF structures. By imaging the pupil between crossed and parallel polarizers we reconstruct the fast axis pattern, transmission, and retardance of the vAPP, and use this as input for a PSF model. This model includes aberrations of the laboratory set-up, and matches the measured PSF, which shows a raw contrast of 10(-3.8) between 2 and 7 λ/D in a 135 degree wedge. The vAPP coronagraph is relatively easy to manufacture and can be implemented together with a broadband quarter-wave plate and Wollaston prism in a pupil wheel in high-contrast imaging instruments. The liquid crystal patterning technique permits the application of extreme phase patterns with deeper contrasts inside the dark holes, and the multilayer liquid crystal achromatization technique enables unprecedented spectral bandwidths for phase-manipulation coronagraphy.

The apodizing phase plate (APP) is a solid-state pupil optic that clears out a D-shaped area next to the core of the ensuing PSF. To make the APP more efficient for high-contrast imaging, its bandwidth should be as large as possible, and the location of the D-shaped area should be easily swapped to the other side of the PSF. We present the design of a broadband APP that yields two PSFs that have the opposite sides cleared out. Both properties are enabled by a half-wave liquid crystal layer, for which the local fast axis orientation over the pupil is forced to follow the required phase structure. For each of the two circular polarization states, the required phase apodization is thus obtained, and, moreover, the PSFs after a quarter-wave plate and a polarizing beam-splitter are complementary due to the antisymmetric nature of the phase apodization. The device can be achromatized in the same way as half-wave plates of the Pancharatnam type or by layering self-aligning twisted liquid crystals to form a monolithic film called a multi-twist retarder. As the VAPP introduces a known phase diversity between the two PSFs, they may be used directly for wavefront sensing. By applying an additional quarter-wave plate in front, the device also acts as a regular polarizing beam-splitter, which therefore furnishes high-contrast polarimetric imaging. If the PSF core is not saturated, the polarimetric dual-beam correction can also be applied to polarized circumstellar structure. The prototype results show the viability of the vector-APP concept.Keywords: coronagraphy, apodization, polarimetry CORONAGRAPHY WITH APODIZING PHASE PLATESThe direct detection of extrasolar planets enables insight into the configuration and architecture of planetary systems around nearby stars in our galaxy, testing current theories and mechanisms of formation. Analysis of the light of an exoplanet enables the unambiguous characterization of the planetary atmosphere and surface, and ultimately allows for the detection of biomarkers (e.g. the presence of oxygen and liquid water) at rocky planets. Direct imaging is primarily limited by the proximity of the parent star, where the light from the planet can be several decades fainter than the extended halo of light diffracted by the telescope and science camera optics. In order to minimize the contrast between star and planet, several methods are used together. Adaptive optics (AO) systems increase the encircled energy of the planets signal whilst reducing the diffracted host star light. Using models of the telescope point spread function (PSF) are limited by the presence of time varying optical aberration errors that are unsensed by the telescope's AO system, adding an additional component of noise that does not decrease as √ t with the total observation time. Observing at longer wavelengths towards the black body peak emission of the planet at infrared and thermal wavelengths reduces the contrast by a factor of a hundred to a thousand. Polarimetric observations allows one to reduce the contrast bet...