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Recent experimental work has demonstrated the potential of combining the merits of diffractive and on-chip photonic information processing devices in a single chip by making use of planar (or slab) waveguides. Here, arguments are developed to show that diffraction formulas familiar from 3D Fourier optics can be adapted to 2D under certain mild conditions on the operating speeds of the devices in question. In addition to serving those working in on-chip photonics, this Letter provides analytical tools for the study of surface plasmon polaritons, surface waves, and the optical, acoustic, and crystallographic properties of 2D materials.
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We implement a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization of phase-only computer-generated hologram for a multi-depth three-dimensional (3D) target. Instead of computing the full 3D reconstruction of the hologram, we use a novel method using L-BFGS with sequential slicing (SS) for partial evaluation of the hologram during optimization that only computes loss for a single slice of the reconstruction at every iteration. We demonstrate that its ability to record curvature information enables L-BFGS to have good quality imbalance suppression under the SS technique.
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We present dynamic time-resolved measurements of a multi-pixel analog liquid crystal phase modulator driven at a 1 kHz frame rate. A heterodyne interferometer is used to interrogate two pixels independently and simultaneously, to deconvolve phase modulation with a wide bandwidth. The root mean squared optical phase error within a 30 Hz to 25 kHz bandwidth is <0.5° and the crosstalk rejection is 50 dB. Measurements are shown for a custom-built device with a flexoelectro-optic chiral nematic liquid crystal. However, the technique is applicable to many different types of optical phase modulators and spatial light modulators.
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Iterative Fourier transform algorithms are widely used for hologram generation for phase-modulating spatial light modulators. In this paper, we introduce a new technique called the "intermediate domain," which decomposes the Fourier transforms used into multiple subtransforms, the combination of which can offer major performance benefits over traditional approaches. To demonstrate this, we introduce ID-GS, an implementation of the intermediate domain technique for possibly the best known hologram generation algorithm, Gerchberg-Saxton. We discuss the performance of this across a wide range of configurations with a focus on computational performance.
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The effects of time-varying measurement noise on transmission matrix acquisition processes are considered for the first time, to our knowledge. Dominant noise sources are discussed, and the noise properties of a typical interferometer system used for characterizing a multimode fiber transmission matrix are quantified. It is demonstrated that an appropriate choice of measurement basis allows a more accurate transmission matrix to be more quickly obtained in the presence of measurement noise. Finally, it is shown that characterizing the noise figure of the experimental system allows the inverse transmission matrix to be constructed with an ideal amount of regularization, which can in turn be used for optimal image acquisition.
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A complex-valued transmission matrix describing a scattering medium can be constructed from a sequence of many interferometric measurements. A major challenge in such experiments is to correct for rapid phase drift of the optical system during the data acquisition process, especially when the phase drifts significantly between consecutive measurements. Therefore, a new method is presented where the exact phase drift between two measurements is characterized and corrected using a single additional measurement. This approach removes the need to continuously track the phase and significantly relaxes the phase stability requirements of the interferometer, allowing transmission matrices to be constructed in the presence of fast and erratic phase drift.
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A holographic automotive head-up display was developed to project 2D and 3D ultra-high definition (UHD) images using LiDAR data in the driver's field of view. The LiDAR data was collected with a 3D terrestrial laser scanner and was converted to computer-generated holograms (CGHs). The reconstructions were obtained with a HeNe laser and a UHD spatial light modulator with a panel resolution of 3840×2160 px for replay field projections. By decreasing the focal distance of the CGHs, the zero-order spot was diffused into the holographic replay field image. 3D holograms were observed floating as a ghost image at a variable focal distance with a digital Fresnel lens into the CGH and a concave lens.
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Spatial light modulators (SLMs) are key research tools in several contemporary applied optics research domains. In this paper, we present the argument that an open platform for interacting with SLMs would dramatically increase their accessibility to researchers. We introduce HoloBlade, an open-hardware implementation of an SLM driver-stack, and provide a detailed exposition of HoloBlade's architecture, key components, and detailed design. An optical verification rig is constructed to demonstrate that HoloBlade can provide Fourier imaging capability in a 4f system. Finally, we discuss HoloBlade's future development roadmap and the opportunities that it presents as a research tool for applied optics.
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The generation of computer-generated holograms (CGHs) requires a significant amount of computational power. To accelerate the process, highly parallel field-programmable gate arrays (FPGAs) are deemed to be a promising computing platform to implement non-iterative hologram generation algorithms. In this paper, we present a cost-optimized heterogeneous FPGA architecture based on a one-step phase retrieval algorithm for CGH generation. The results indicate that our hardware implementation is 2.5× faster than the equivalent software implementation on a personal computer with a high-end multi-core CPU. Trade-offs between cost and performance are demonstrated, and we show that the proposed heterogeneous architecture can be used in a compact display system that is cost and size optimized.
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We have solved the long-standing problems of stability and hysteresis, and we are able to obtain the homogeneous uniform lying helix structure in polymer-free cholesteric liquid crystals. This is instrumental for the present work to demonstrate the analog modulation at high speed and high precision. The device is configured for the transverse field switching wherein the substrate surface is flat. In addition to the response time of 10 ms at room temperature, we have obtained the R-squared and the adjusted R-squared as a measure of true sine wave for the sinusoidal responding transmissions from 1 Hz to 100 kHz that are all greater than 0.9993. In a Michelson interferometer, the phase shift at wavelength 633 nm after two passes has been measured to be equal to about $\pi /{9}$π/9 at 4.6 V/µm for the chiral-doped nematic mixtures E7.
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Flexible optical fibres, used in conventional medical endoscopy and industrial inspection, scramble phase and polarisation information, restricting users to amplitude-only imaging. Here, we exploit the near-diagonality of the multi-core fibre (MCF) transmission matrix in a parallelised fibre characterisation architecture, enabling accurate imaging of quantitative phase (error <0.3 rad) and polarisation-resolved (errors <10%) properties. We first demonstrate accurate recovery of optical amplitude and phase in two polarisations through the MCF by measuring and inverting the transmission matrix, and then present a robust Bayesian inference approach to resolving 5 polarimetric properties of samples. Our method produces high-resolution (9.0±2.6µm amplitude, phase; 36.0±10.4µm polarimetric) full-field images at working distances up to 1mm over a field-of-view up to 750×750µm 2 using an MCF with potential for flexible operation. We demonstrate the potential of using quantitative phase for computational image focusing and polarisation-resolved properties in imaging birefringence.
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We present here the first time-resolved tilt-angle and retardance measurements for large-tilt (>45°) flexoelectro-optic liquid crystal modulators. These devices have potential for next generation fast switching (>1 kHz), 0-2π analog phase spatial light modulators (SLMs), with applications in optical beamsteering, microscopy and micromachining. The chiral nematic device used consisted of a mixture of CBC7CB and the chiral dopant R5011 in a nominally 5 µm-thick cell, aligned in the uniform lying helix mode. As the device is dynamically switched over angles of ± 54°, retardance changes of up to 0.17λ are observed. Furthermore, the time-resolved measurements reveal an asymmetry in the tilt in the optic-axis depending on the polarity of the applied electric field. The change in the optic-axis exhibits a pattern dependence, whereby it is determined by both the pulse history and the applied field. This pattern dependence results in tilt-angle errors of up to 8.8°, which could manifest as phase errors as large as 35.2° in potential SLMs. These time domain measurements may allow correction of these deterministic errors, to realize practical devices.
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We present an algorithm for generating high-quality holograms for computer generated holography: holographic predictive search. This approach is presented as an alternative to traditional holographic search algorithms such as direct search (DS) and simulated annealing (SA). We first introduce the current search-based methods and then introduce an analytical model of the underlying Fourier elements. This is used to make prescient judgments regarding the next iteration of the algorithm. This approach is developed for the case of phase-modulating devices with phase-sensitive reconstructions. When compared to conventional iterative approaches such as DS and SA on a multiphase device, holographic predictive search offered a fivefold improvement in quality as well as up to a 10-fold improvement in convergence time. This comes at the cost of an increased iteration overhead.
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Traditional search algorithms for computer hologram generation such as Direct Search and Simulated Annealing offer some of the best hologram qualities at convergence when compared to rival approaches. Their slow generation times and high processing power requirements mean, however, that they see little use in performance critical applications. This paper presents the novel sorted pixel selection (SPS) modification for holographic search algorithms that offers mean square error reductions in the range of 14.7-19.2% for the test images used. SPS operates by substituting a weighted search selection procedure for traditional random pixel selection processes. While small, the improvements seen are observed consistently across a wide range of test cases and require limited overhead for implementation.
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The efficacy with which solvent vapor annealing (SVA) can control block copolymer self-assembly has so far been demonstrated primarily for the simplest class of copolymer, the linear diblock copolymer. Adding a third distinct block-thereby creating a triblock terpolymer-not only provides convenient access to complex continuous network morphologies, particularly the gyroid phases, but also opens up a route toward the fabrication of novel nanoscale devices such as optical metamaterials. Such applications, however, require the generation of well-ordered 3D continuous networks, which in turn requires a detailed understanding of the SVA process in terpolymer network morphologies. Here, in situ grazing-incidence small-angle X-ray scattering (GISAXS) is employed to study the self-assembly of a gyroid-forming triblock terpolymer during SVA, revealing the effects of several key SVA parameters on the morphology, lateral order, and, in particular, its preservation in the dried film. The robustness of the terpolymer gyroid morphology is a key requirement for successful SVA, allowing the exploration of annealing parameters which may enable the generation of films with long-range order, e.g., for optical metamaterial applications.
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We present a design of graded-index ring-core fiber (GI-RCF) supporting 3 linearly polarized (LP) mode-groups (i.e. LP01, LP11 and LP21) with a single radial index of one for mode-division multiplexed (MDM) transmission. Reconfigurable spatial light modulator (SLM) based spatial (mode) (de)multiplexers are used to systematically characterize spatial/temporal modal properties of the GI-RCF. We also demonstrate all-optical mode-group multiplexed transmissions over a 360m fabricated GI-RCF without using multiple-input multiple-output digital signal processing (MIMO DSP).
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A method of generating an aberration- and distortion-free wide-angle holographically projected image in real time is presented. The target projector is first calibrated using an automated adaptive-optical mechanism. The calibration parameters are then fed into the hologram generation program, which applies a novel piece-wise aberration correction algorithm. The method is found to offer hologram generation times up to three orders of magnitude faster than the standard method. A projection of an aberration- and distortion-free image with a field of view of 90x45 degrees is demonstrated. The implementation on a mid-range GPU achieves high resolution at a frame rate up to 12fps. The presented methods are automated and can be performed on any holographic projector.
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High-energy electron beam lithography for patterning nanostructures on insulating substrates can be challenging. For high resolution, conventional resists require large exposure doses and for reasonable throughput, using typical beam currents leads to charge dissipation problems. Here, we use UV1116 photoresist (Dow Chemical Company), designed for photolithographic technologies, with a relatively low area dose at a standard operating current (80 kV, 40-50 µC cm-2, 1 nAs-1) to pattern over large areas on commercially coated ITO-glass cover slips. The minimum linewidth fabricated was â¼33 nm with 80 nm spacing; for isolated structures, â¼45 nm structural width with 50 nm separation. Due to the low beam dose, and nA current, throughput is high. This work highlights the use of UV1116 photoresist as an alternative to conventional e-beam resists on insulating substrates. To evaluate suitability, we fabricate a range of transmissive optical devices, that could find application for customized wire-grid polarisers and spectral filters for imaging, which operate based on the excitation of surface plasmon polaritons in nanosized geometries, with arrays encompassing areas â¼0.25 cm2.
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A single-step fabrication method is presented for ultra-thin, linearly variable optical bandpass filters (LVBFs) based on a metal-insulator-metal arrangement using modified evaporation deposition techniques. This alternate process methodology offers reduced complexity and cost in comparison to conventional techniques for fabricating LVBFs. We are able to achieve linear variation of insulator thickness across a sample, by adjusting the geometrical parameters of a typical physical vapor deposition process. We demonstrate LVBFs with spectral selectivity from 400 to 850 nm based on Ag (25 nm) and MgF2 (75-250 nm). Maximum spectral transmittance is measured at â¼70% with a Q-factor of â¼20.
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We propose a synchronous implementation of compressive imaging. This method is mathematically equivalent to prevailing sequential methods, but uses a static holographic optical element to create a spatially distributed spot array from which the image can be reconstructed with an instantaneous measurement. We present the holographic design requirements and demonstrate experimentally that the linear algebra of compressed imaging can be implemented with this technique. We believe this technique can be integrated with optical metasurfaces, which will allow the development of new compressive sensing methods.