Abstract We present the design, fabrication, and characterization of continuous phase Fresnel zone plates (FZPs) using two-photon polymerization direct laser writing in a polymerizable nematic liquid crystal (LC) confined between glass substrates. Unlike conventional binary LC diffractive elements, our devices exhibit a smooth, continuous three-dimensional phase profile. Two devices were demonstrated with wrapped phase profiles of 2π and 4π radians, respectively. Polarized optical microscopy and digital holographic microscopy confirm that the polymerized regions follow the intended spatially varying phase distribution. Far field measurements show that the 2π rad FZP generates a strong focal spot at 0 Vpp and switches off at higher voltages. In contrast, the 4π rad FZP exhibits varifocal behavior, switching between two focal lengths: 24 mm at 0 Vpp and 48 mm at an intermediate voltage of 2.1 Vpp. At higher voltages, the focus disappears entirely. Compared to a binary FZP of equal size and focal length, the continuous phase design nearly doubles the focusing efficiency and enables switchable, compact, vari-focal, and energy-efficient optical components. This approach offers new opportunities for advanced applications such as augmented and virtual reality, adaptive optics, and other next-generation photonic systems.

Programmable patterning of nematic liquid crystals (LCs) enables spatially encoded optical functionality, but existing approaches often face trade-offs between patterned area, feature fidelity, dimensionality, and device integration. Many methods rely on surface alignment, electrode patterning, or global illumination, limiting local addressability, depth control, or scalability. Field-assisted polymerization of reactive mesogens offers a means to capture designed LC director configurations as permanent, structurally encoded profiles. Here, we report a hybrid strategy combining wide-field one-photon polymerization (1PP) for rapid, large-area templating with two-photon polymerization direct laser writing (2PP-DLW) for localized, maskless microstructuring with depth control. This decoupling of patterned area from feature fidelity allows multiple, spatially co-located director profiles to be encoded within a single glass cell, enabling voltage-selective visibility and reconfigurable optical responses. Local 2PP-DLW features define confinement boundaries and deterministic defect nucleation and guidance, while 1PP establishes the global architecture with high throughput. Because patterning is encoded in the polymer rather than electrode geometry, complex profiles can be realized using uniform electrodes. In a nematic Pi-cell, this approach enables controlled defect channeling, programmable topological transitions, and multistate optical patterns, offering a scalable route to high-fidelity reconfigurable LC micro-optics.

Determining the amplitude, phase, and polarization profile of light is essential for both fundamental scientific discovery and applications spanning optical metrology, microscopy, astronomy, and optical communication/computing technologies. However, most modern measurement approaches are unable to retrieve such parameters readily, often relying on bulky and expensive hardware, or lacking the capability for single-shot sensing. Here, we introduce a low cost, compact, full vectorial field sensor based on an inkjet-printed nematic liquid crystal droplet array that enables simultaneous measurement of these important characteristics of light. Polarization and intensity are measured via division-of-wavefront polarimetry, exploiting the droplets' spatially varying birefringence, while the phase is reconstructed by treating each droplet as a separate microlens in a Shack-Hartmann-like wavefront sensor configuration. To demonstrate the system's performance, we characterize aberrated dual-wavelength beams carrying distinct intensity, phase, and polarization information, confirming accurate retrieval of the optical field profiles for both spectral components.

The rapid growth of artificial intelligence, coupled with the slowing of Moore's law, is straining computing infrastructure, as CMOS electronics face inherent limits in bandwidth, energy efficiency, and parallelism. Integrated photonic computing encodes and processes information using the phase, amplitude, spatial modes, wavelength channels, and polarisation of guided optical fields, offering a scalable and energy-efficient route beyond charge-based signalling. Here, we review on-chip photonic computing, emphasising the progression from low-dimensional to high-dimensional architectures. At the foundational level, low-dimensional approaches manipulate the phase and amplitude of guided light through Mach-Zehnder interferometers, diffractive structures, microring resonators, and absorptive elements, forming a programmable basis for optical matrix-vector multiplication. Crucially, high-dimensional architectures exploit spatial modes and wavelength channels to carry multiple independent data streams through a single waveguide, achieving higher throughput with moderate hardware overhead. Practical deployment, however, demands more than device innovation. We examine how system-level techniques, from time-wavelength interleaving to hardware-aware training, address energy efficiency, precision, and algorithm-hardware co-design. Five challenges nevertheless remain: electro-optic conversion efficiency, computing parallelism, spatial integration, reconfigurability, and robustness. We highlight emerging topological structures, such as optical skyrmions, as a promising route to fault-tolerant, topologically protected encoding that exploits the largely untapped polarisation degree of freedom. We argue that, by embracing the higher dimensionality of light, photonic computing can offer not merely an incremental improvement but a new paradigm for high-performance, energy-efficient information processing.

Abstract Skyrmions are important topologically non-trivial fields characteristic of models spanning scales from the microscopic to the cosmological. However, the skyrmion number can only be defined for fields with specific boundary conditions, limiting its use in broader contexts. Here, we address this issue through a generalized notion of the skyrmion derived from the de Rham cohomology of compactly supported forms. This allows for the definition of an entirely new $${\coprod }_{i=1}^{\infty }{{\mathbb{Z}}}^{i}$$ ∐ i = 1 ∞ Z i -valued topological number that assigns a tuple of integers $$({a}_{1},\ldots,{a}_{k})\in {{\mathbb{Z}}}^{k}$$ ( a 1 , … , a k ) ∈ Z k to a field instead of a single number, with no restrictions to its boundary. To demonstrate the power of our new formalism, we focus on the propagation of optical polarization fields and show, both theoretically and experimentally, that our newly defined generalized skyrmion number significantly increases the dimension of data that can be stored within the field while also demonstrating strong robustness. This novel topological number supports the idea that optical skyrmions are topologically protected states when interpreted in this more general context, and addresses some of the core issues in the application of optical skyrmions to communications and computing.

This paper presents a holographic display architecture that integrates polarization gratings with fast-response nematic liquid crystal (LC) pi-cells to achieve fast switching and the simultaneous visual perception of multiple high-quality discrete beam-steering positions, enabling visual enlargement of holographic projected images through spatiotemporal tiling, thereby overcoming the limited projection coverage achieved using a single spatial light modulator (SLM). The system integrates voltage-controlled nematic LC pi-cell phase shifters that dynamically modulate the polarization state to achieve precise beam steering in a selected diffraction order with 80% optical transmittance and a rapid response (<3 ms). By synchronizing the voltage driving waveforms applied to the nematic LC pi-cells with the refresh rate of the SLM, the reconstructed holographic images in the replay field can be steered among multiple spatial locations in real time. Under low-frequency driving, individual holographic subframes are sequentially displayed at distinct spatial positions. At higher driving frequencies, multiple holographic projected images are visually perceived as being displayed at the same time, creating the impression of an enlarged holographic projection display area, corresponding to a 4-fold increase in the effective display area compared with a conventional holographic projection display using a single SLM at the same far-field distance. Experimental results demonstrate beam steering among four discrete positions with millisecond-scale response time, forming either a linear array (1D) or a two-by-two spatial configuration (2D). Overall, this approach provides a scalable route toward high-speed, wide-angle, and visually large-area holographic displays through the integration of polarization gratings with fast-response nematic LC devices.

This work reports the design, simulation, and fabrication of an optically-transparent microstrip line resonator that is employed to characterize the dielectric properties of a nematic liquid crystal (LC) at a frequency of 5 GHz, to understand the behaviour of LC-based optically-transparent radio frequency devices, and to allow direct observations of the LC through a polarising optical microscope while operating the device. The microstrip line is constructed by etching indium tin oxide (ITO) coated glass and exploiting the first-order resonance to infer the anisotropic dielectric properties of the nematic LC. Results are compared with a microstrip line device featuring the same geometry but constructed from FR-4 and copper, and full-wave electromagnetic simulations that suggest an accuracy of 95% in the LC dielectric properties.

We demonstrate speckle noise reduction in an in-line holographic imaging system using a zwitterion-doped liquid crystal dynamic scatterer (LCDS) cell diffuser. Integrated into a minimally modified bright-field microscope, the LCDS actively modulates the system's spatial coherence. The proposed solution suppresses coherent artifacts without introducing bulky moving parts while enhancing image resolution and preserving overall system simplicity. Quantitative performance tested on a phase and amplitude test targets, as well as a phase-amplitude biological sample, shows significant noise reduction and the method's versatility. Although validated in a holographic in-line setup, the approach is applicable to other imaging techniques requiring compact, vibration-free speckle suppression.

With the growing use of optical polarization in applications ranging from communications to medical diagnoses, adaptive correction of complex vectorial aberrations in optical systems has become an increasingly important area of research. However, research to date has focused primarily on phase and retardance aberrations, whereas another major source of aberration-diattenuation-remains largely unexplored. Unlike the others, diattenuation affects intensity in addition to phase and polarization, limiting the intrinsic correction capability of adaptive systems. In this work, we propose the use of optical skyrmions to probe diattenuation-aberrated systems and provide metrics that characterize the performance of vectorial adaptive optics (V-AO), with theoretical and experimental validations. Based on the probed results, we demonstrate V-AO correction under real-world aberrations for complex media imaging and analyze correction strategies to optimize measurements in aberrated polarimetric systems. This work paves the way for high-dimensional aberration correction, introduces a previously unidentified use of optical skyrmions, and provides insights that will aid the development of vectorial measurement systems.

In this paper, we investigate the potential of achieving polarization independent phase modulation using supertwisted nematic (STN) liquid crystal (LC) devices. Here, we describe the use of a burst driving voltage applied to a 180° STN LC device to obtain a twist symmetric H (T-Hs) state, which enables simultaneous modulation of light for all polarizations, demonstrating a polarization independent characteristic in the time domain. Additionally, we consider a 90° twisted nematic (TN) LC device for comparison, as this can also exhibit polarization independent characteristics. Simulations were carried out using a numerical model based on the Ericksen-Leslie continuum equations, which was employed in conjunction with the Jones calculus to simulate the optical properties of the device. The time-dependent optical phase modulation of the device was subsequently measured by using a phase-shifting Mach-Zehnder interferometer. The experimental results demonstrate that an STN device with an 8.9 μm thick LC layer operating in the T-Hs state exhibited a π/2 optical phase modulation in 1 ms for a burst voltage of 30 Vrms that was found to be independent of the incident polarization. These measurements were obtained at room temperature in a single optical path configuration and were found to be in good agreement with the results from the simulations.

The Mueller matrix polar decomposition method decomposes a Mueller matrix into a diattenuator, a retarder, and a depolarizer. Among these elements, the retarder, which plays a key role in medical and material characterization, is usually modelled as a circular retarder followed by a linear retarder. However, this model may not accurately reflect the actual structure of the retarder in certain cases as many practical retarders do not have a layered structure or consist of multiple (unknown) layers. Misinterpretation, therefore, may occur when the actual structure differs from the model. Here, we circumvent this limitation by proposing to use an elliptical retarder parameter set that includes the axis orientation angle phi, the degree of ellipticity chi, and the elliptical retardance rho. By working with this set of parameters, an overall characterization of any retarder is provided, encompassing its full optical response without making any assumptions about the structure of the material. In this study, experiments were carried out on liquid crystalline samples to validate the feasibility of our approach, demonstrating that the elliptical retarder parameter set adopted provides a useful tool for a broader range of applications in optical material analysis.

This paper presents a switchable and rotatable chiral nematic liquid crystal (LC) diffraction grating that can be operated using low applied voltages at room temperature. A chiral nematic LC mixture is prepared such that the thickness ( d ) to pitch ( p ) ratio is set to 1.85, enabling the formation of a uniform lying helix configuration when combined with homeotropic alignment layers and the appropriate electric field conditions, resulting in the formation of a diffraction grating. The addition of a small concentration by weight of the LC dimer, CB7CB, is found to lead to an asymmetry in the flexoelectro‐optic tilt angle, generating torque on the helix axis, which in turn enables a uniform 360° in‐plane rotation of the diffraction grating and the corresponding far‐field diffraction pattern. Results are presented to demonstrate that this rotation of the diffraction grating and subsequent rotation in the diffraction pattern requires the application of tailored voltage waveforms with adjustable temporal parameters. Furthermore, analysis of the normalized intensity of the zero‐order reveals systematic correlations with the temporal parameters of the waveform, while exhibiting dependence on the incident light polarization. These findings offer promising insights into the potential development of advanced beam‐steering devices.

This study demonstrates a novel liquid crystal-based active screen for effective speckle reduction in laser-projection displays. By optimising the device architecture, the proposed approach achieves an 88 % reduction in laser speckle while maintaining optical throughput. Comparative analysis highlights the advantages of reflective active screens over transmissive designs. Practical demonstrations confirm the device's ability to suppress speckle across the visible spectrum without degrading image quality. Unlike previously adopted methods, these novel devices are simultaneously compatible with high-power projection systems, maintain wide colour gamuts and possess no mechanically-moving components. These findings position liquid crystal active screens as a promising solution for improving laser-projection technology, offering a pathway toward clearer, high-quality projection displays with minimal speckle noise.

Fibre Bragg gratings (FBGs) are ubiquitous as sensors for a range of parameters and also as optical components in telecommunications systems. However, their temperature dependence of around + 10 pm/°C is a limiting factor, making it challenging for sensors to discriminate strain from temperature, while telecommunications components require additional thermal stabilization. We microfabricate low loss FBGs in standard single-mode fibre, with wide control over their temperature coefficient between + 10 pm/°C and − 55 pm/°C. We also show a temperature insensitive FBG which is stable to ± 12.5 pm over a 17 to 45°C range, which is an order of magnitude reduction in sensitivity. It has only ± 3.5% reflectivity variation over this range and only 1.29 dB transmission loss. The large negative coefficient FBGs would find application in separating strain and temperature effects, as well as for thermally tunable components. Separately, the temperature insensitive FBG would have applications for strain sensing with low temperature cross-sensitivity as well as for low-cost temperature stable optical components. Moreover, the microfabrication process developed has significant potential for new classes of sensor and tunable optical devices.

Inkjet-printed liquid crystal (LC) droplets exhibit an intricate spatially-varying birefringence due to their complex internal director configuration. While such anisotropy is often viewed as a drawback when LC droplets are used as microlenses, here, this remarkable birefringence property is leveraged to generate complex structured light. Through a selection of the alignment layer, and by varying the chiral pitch, three distinct droplet types are created with tailored intrinsic director configurations, each exhibiting a unique birefringence distribution for structured light beam generation. It is shown that these printed LC droplets can generate beams that exhibit skyrmionic structures carrying two units of orbital angular momentum, beams that contain azimuthal/radial polarized fields, and beams with polarization singularities. The method enables new possibilities for using LC droplet technology to engineer sophisticated optical beam patterns.

Fiber Bragg gratings (FBGs) are ubiquitous as sensors for a range of parameters and as optical components in telecommunications systems. However, their temperature dependence is a limiting factor [1], making it challenging for sensors to discriminate strain from temperature. In this work, we demonstrate how temperature insensitivity in FBGs can be achieved.