Materials used in high optical power projection devices such as laser-based displays and optical switches are prone to light-induced light scattering and low threshold damage. Field-driven liquid crystal reorientation is commonly coupled to the optical response that affects contrast, switching speed, lifetime and laser power handling. In this presentation, we address challenges of using photoaligned and polymer-protected liquid crystal liquid crystal special light modulator (SLM) exposed continuously to high power kW-MW lasers. We will compare liquid crystals and photoalignment materials in laser-initiated damage and rationalize the results regarding their thermal properties and light stress tests for area printing applications and augmented reality displays.

New generation of adaptive liquid crystal devices, such as smart eyewear, AR/VR optical elements, flexible displays or modulators, typically incorporate one or more active layers imposing alignment or enable the application of electric field. While these functional layers are critical for achieving the desired performance, their integration can introduce significant fabrication complexity and modify interface effects. Such interface effects, particularly anchoring strength and pretilt, need to be carefully characterised and monitored over time. This is especially relevant for active alignment layers or structured substrates, whose electrical, alignment or spectroscopic properties can vary as a function of the incident light or frequency. Furthermore, the reliance on external AC driving electronics imposes further design constraints and presents a significant limitation for miniaturisation and portability. Consequently, the overall performance of the device performance is governed by the complex interplay between material properties and structural design parameters. In this presentation, we present a technique designed to tailor and optimise the performance of integrated, liquid crystal devices. Our approach enables comprehensive two-dimensional mapping of key parameters, while also facilitating monitoring of optical quality and long-term device stability, the factors that are essential for ensuring reliable functionality and scalable implementation. We will show how using selected combinations of passive and photoactive alignment layers and nematics can lead to different anchoring strengths (weak/strong), varying pretilt angles (low/high) [1] as well as detect small variations in cell thickness (figure 1). Furthermore, to address the challenges associated with developing energy-efficient and self-sustained photonic components capable of all-optical control, we present a class of optically addressable, photovoltaic-driven optical modulators, characterised with our instrument.

A ferroelectric nematic liquid crystal is formed by achiral molecules with large dipole moments. Its orientational order is universally described as unidirectionally polar, which raises the question of how the structure avoids a strong depolarization field and splay deformations that bring about a bound charge. We demonstrate a rich plethora of polarization patterns in ferroelectric nematics not constrained by crystallographic axes. Domain walls take on the shapes of conic sections, separating domains with uniform and circular polarization [1]. When a flat ferroelectric nematic slab is anchored only at one bounding plate, its ground state becomes optically active, with left- and right-hand twists of polarization [2]. Despite the increase in elastic energy due to helicoidal deformations and domain walls, the twists reduce the electrostatic energy and weaken when the material is doped with ions. An external electric field applied to create a splay produces structures in which the splay of one polarity is compensated by a splay of opposite polarity, thus solving the electrostatic problem by geometrical means [3]. Our study shows that the polar orientational order of molecules triggers complex spatially nonuniform patterns, including chirality that does not require chemically induced chiral centers, paving the way for practical applications. Acknowledgments: This work was funded by NSF grant DMR-2341830. References: [1] P. Kumari, B. Basnet, H. Wang, O. D. Lavrentovich. Nature Communications 14, 748 (2023). [2] P. Kumari, B. Basnet, M. O. Lavrentovich, O. D. Lavrentovich. Science 383, 1364 (2024). [3] B. Basnet, S. Paladugu, O. Kurochkin, O. Buluy, N. Aryasova, V. G. Nazarenko, S. V. Shiyanovskii, O. D. Lavrentovich. Nature Communications 16, 1444 (2025).

The structural characteristics of cholesteric liquid crystals give rise to wavelength- and polarization-selective properties of reflected and transmitted light beams. The tuning of helix pitch, sense of twist, and in-volume orientation of the helical axis allows for the modulation of the pattern, color, and polarization of optical films. This phenomenon has been observed in beetles, fish, and plants with iridescent structural colors [1]. It is relevant to optical signaling in functional facades, camouflage skins, photonic actuators, anti-counterfeiting labels, and cryptography [2, 3]. We contribute to the topic through the physical design of time-temperature loggers that combine twisted and untwisted structures [4] (Fig. 1), bicolor tags resulting from variable surface tensions [5] (Fig. 2), and polychromatic tags generated by different bulky pitch profiles [6] (Fig. 3). Acknowledgements: Support by the French government through the France 2030 investment plan managed by the National Research Agency (ANR), as part of the Initiative of Excellence Université Côte d’Azur (ANR-15-IDEX-01). References: [1] M. Mitov, Soft Matter, 13, 4176 (2017). [2] P. Wu, J. Wang, Mater. Horiz., 7, 338 (2020). [3] J. Zhang, Y. Zhang, J. Yiang, X. Wang, Micromachines, 15, 808 (2024). [4] C. Boyon, V. Soldan, M. Mitov, ACS Appl. Mater. Interfaces, 13, 30118-3016 (2021). [5] M. Mitov, C. Boyon, V. Soldan, ACS Appl. Nano Mater., 5, 10560-10571 (2022). [6] S. Dhingra, M. Mitov, submitted (2025).

Lyotropic chromonic liquid crystals (LCLCs) are mixtures of charged, organic, plate-like molecules and water. In the presence of a polar solvent, such as water, the molecules tend to aggregate face-to-face, forming columns with varying aggregation numbers. Aqueous suspensions of the molecule of the azo dye Sunset Yellow (SSY) show liquid crystalline mesofases. The present study is devoted to the investigation of the nonlinear optical (NLO) response of thermal origin of SSY, particularly in the nematic mesophase. Using the time-resolved Z-Scan (ZS) technique, it is investigated how the concentration of this azo-dye affects the nonlinear properties of samples in the isotropic and nematic phases. In systems with supramolecular structures in a liquid carrier (in our case, water), the heating of the sample to stablish the thermal lens can be done in two different ways: a) heating the supramolecular aggregates, that will transfer the energy to the water, or, b) heat the water, that will transfer the energy to the system as a whole. This depends on the wavelength of the light used in the heating process and the linear absorption spectra of the components of the mixture. We will explore this aspect working with two laser wavelengths, visible (532 nm) and infra-red (979 nm) light, independently. Interestingly, the signals of the NLO responses in both parallel and perpendicular orientations of the optical field with respect to the director are different, with almost the same magnitude: θ_∥=-0.056(9) and θ_⊥=0.041(3). Our results (Fig. 1) show that the amplitude of the NLO effect in the nematic sample, regardless the orientation of the optical field with respect to n ⃗, is greater than the amplitude in the isotropic phase: |θ_cor^nem |~2.5 |θ_cor^iso |. Since the main light absorber in these experiments at 979 nm is water, this result seems to indicate that the oriented stacks affect the structural organization of water molecules in the stacks surfaces/vicinity. At the borders of the SSY molecules there are SO_3^- groups attached to the structure and 〖Na〗^+ counterions. The presence of these charged structure in the surface of the stacks may organize the water molecules around them (i.e., a solvation-like layer), as observed in amphiphilic-based lyotropics. Fig. 1 Normalized transmittance (ZS experiment) of the SSY sample in the nematic phase with planar alignment, measured in two regimes: n ⃗ parallel to the optical field (blue triangles), and n ⃗ perpendicular to the optical field (gray triangles). The dashed lines correspond to the best fits of parabolic thermal-lens model to the experimental data. Acknowledgments: This work was funded by FAPESP, CNPq, CAPES, INCT-FCx

The availability of micro- and nano-scale photoalignment patterning has created a whole range of new opportunities for liquid crystal (LC) photonic devices. Gratings and lenses based on the Pancharatnam-Berry or geometric phase with slowly varying director have been known for some time. By reducing the photoalignment period, an increase in the diffraction angle can be achieved, but for nematic LC it is difficult to decrease the period below the layer thickness. Chiral LC (CLC) with reflection band in the visible range has an intrinsic 1D nano-scale periodicity which is well suited for photoalignment patterns with a sub-micrometer period. This has resulted in the development of linear reflective diffraction gratings with short pitch and high efficiency to couple light into and out of a planar waveguide. CLCs can be used to create reflective lenses or single component spectrometers that combine diffraction with focusing. In combination with total internal reflection transmissive CLCs with negative refraction can be realized. Blue phase LC with their intrinsic 3D nanoscale structure has also successfully aligned over large domains by photoalignment, to achieve strong reflections in particular directions. Nematic LC between substrates with patterned photoalignment can exhibit interesting 3D configurations, such as q-plates (when the photoalignment pattern contains a defect), optical waveguides (when a line of perpendicular directors is created), or grids of disclination lines.

During the last decade, topological photonics [1] and microphotonics [2] have become rapidly developing fields of research, exploited to control various parameters of light. Placing the emitter in a planar optical microcavity (MC) can lead to strong light–matter coupling regime, exhibits exciton-polariton lasing and Bose–Einstein condensation (BEC) even at room temperature. A MC with a tunable mesogenic layer (LC) serves as a flexible photonic platform, enabling novel functionalities: spatial and angular (momentum) control over lasing and BEC, spin (polarization) textures, and tunable topological states of light. Spin–orbit coupling (SOC) of bosonic states can be easily controlled and observed in this system. LC-based microcavities (LC-MCs) provide tunability of photonic modes, paving the way for unconventional microlasers (see Fig. 1). We created and studied a series of LC-MCs and demonstrated photonic devices that can be described by a synthetic Hamiltonians of “massive photons” with Rashba–Dresselhaus SOC and Zeeman terms known from solid state physics [3]. Additionally, we proposed an active photonic polarization converter, leveraging the extremely wide tunable splitting of cavity modes – far beyond what is possible in conventional semiconductor microcavities [4]. We also demonstrated the optical spin Hall effect (OSHE) in a photonic cavity, highlighting its potential for polarization-based applications. In further experiments, we created a monocrystalline CsPbBr₃ perovskite-filled microcavity, where LC control allows us to tune the BEC energy states and induce SOC – shaping the emission into either a single linearly polarized beam or two circularly polarized beams of coherent light [5]. We developed a tunable photonic crystal with strong polarization dependence by embedding a uniform lying helix (ULH) structure in a planar MC [6]. LC driving allows us to tune a periodic potential and modifies the photonic band gaps of polarized optical modes in the dispersion of “massive photons”. Furthermore, dye doping allows for tunable lasing that preserves the polarization properties of the photonic bands. Acknowledgments: This work was funded by project NCN UMO-2022/47/B/ST3/02411. The authors acknowledge EU project No. 964770 – TopoLight. References: [1] T. Ozawa et al., Reviews of Modern Physics 91, 015006-1-76 (2019). [2] S. Abreu et al. Reviews in Physics 12, 100093 (2024), [3] K. Rechcinska et al. Science 366, 727 (2019). [4] K. Lekenta et al., Light Sci. Appl. 7, 74 (2018), [5] K. Łempicka-Mirek et al., Nanophotonics, 13 (14), 2659 (2024)

Liquid crystal elastomers (LCE) are lightly cross-linked elastomeric materials containing liquid crystal components [1]. Recently a series of sidechain liquid crystal elastomers with varying crosslink density was studied. Higher crosslink density samples display an auxetic response [2,3]. Refractive index and order parameters temperature dependencies were reported in [4]. To theoretically describe these dependencies we suggest modifying the Maier-Saupe (M-S) theory of nematics by including in the M-S free energy of mesogenic groups three additional terms: the term responcible for coupling between the orientational order parameter and strain, the term accounting for stress, acting on the elastomer, which is a combination of the applied stress and the internal stress due to anisotropic cross-linking, and the term describing the elastic part of the LCE free energy [5.6]. By minimizing the total free energy we calculate the order parameter dependence on the temperature which happens to be in a good agreement with the experimental data. The first two ferroelectric nematic (FN) liquid crystals (NF) RM734 and DIO were synthesized and reported in [7,8]. These materials possess large dielectric permittivities and spontaneous polarization. Recently it was reported the temperature dependence of the order parameters of FN RM734 [9]. A dip in the birefringence and order parameters was observed at the N to NF transition. This dip in the order parameters has not been previously reported or predicted theoretically. Understanding the physics of the non-monotonic change in the order parameters dependence on the temperature is necessary for future studies and applications of FN. We present a modified M-S theory which in addition to the terms suggested in [10,11] accounts for the coupling between the spontaneous and induced polarizations, and non-monotonic behaviour of the density vs temperature. The modified version of the M-S theory allows a dip in the order parameters and spontaneous polarization temperature dependencies nearby the NF-N transition and agrees well with the experimental data. Acknowledgments: This work was supported by the British Academy through a Researchers at Risk Fellowship. HFG and TR are grateful to the UK Engineering and Physical Sciences Research Council for funding through grant EP/V054724/1. We are grateful to Merck for funding (DN) and the provision of materials. References: [1] M. Warner, and E. M. Terentjev. Liquid crystal elastomers. OUP, 2013, Oxford. [2] D. Mistry et al., Nature Communications, 9(1), 5095 (2018). [3] T. Raistrick et al., Physical Review Research, 3(2), 023191 (2021). [4] Emily J. Cooper et al., Macromolecules, 57, 2030 (2024). [5] Jonathan V. Selinger et al.,, Phys.Rev.Lett., 89, 225701 (2002). [6]. P.G. de Gennes, C. R. Acad. Sci. 281B, 101 (1975). [7] R. J. Mandle et al., Chem. Eur. J. 23, 14554 (2017). [8] H. Nishikawa et al., Adv. Mater. 29, 1702354 (2017). [9] T. Raistrick et al., Phys. Rev. E 110, 044702 (2024). [10] B. Par et al., Phys. Rev. E 63, 021707 (2001). [11] J. Etxebarria et al., Liq. Cryst. 49, 1719 (2022).

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Liquid crystals (LCs) are intriguing materials of interest due to their potential applications in smart devices. Incorporating the LCs with polymer has attracted significant attention because of their application in the range of electro-optic systems. The liquid crystal polymer composite (LCPC) is explored for light scattering devices. A free-standing optical diffuser film is fabricated using the nematic LC and cellulose bio-polymer. The sub-micron and micron-sized LC droplets in the polymer matrix effectively diffuse the light. The high haze value (≈99 %) and full width at half maximum of the angular distribution of the transmitted light, similar to the Lambertian distribution, is achieved through the optimization of the LC concentration with the polymer. Through the incorporation of the LCs with pseudopeptide polymer, light-scattering devices are fabricated, without the need for thermal or UV-curable process. The pseudopeptide polymer forms the microspheres in the LCs through precipitation. The polymer microsphere improves the light-scattering properties of the cholesteric LC in the focal conic state and reduces the voltage required for the scattering state. In the negative dielectric anisotropy LC (nLC), the polymer alters the ionic properties of LC. The light scattering in the nLC, due to the electrohydrodynamic instability (EHDI) state, is influenced by the change in the ionic properties. The pseudopeptide polymer microsphere in the nLC significantly enhances light-scattering abilities, offers a high contrast ratio, and substantially decreases the voltage required to generate the scattering state. These devices can be employed in electro-optic systems that depend on this light-scattering phenomenon, such as smart windows and tunable light diffusers. LC has also been explored in surface profilometry. An angular shearing interferometer has been fabricated using a liquid crystal cell, and its application in surface profilometry has been demonstrated. A wedge-shaped liquid crystal cell spatially separates the two orthogonal polarizations of light, which are then made to interfere with the help of a polarizer. The liquid crystal cell produces stable and high-contrast interference fringe patterns, which are essential for surface metrology.

Time crystals are recently discovered, unexpected states of matter that spontaneously break time translation symmetry either in a discrete or continuous manner. However, spatially-mesoscale classical space-time crystals that continuously break both the space and time symmetries have not been reported. Here we describe the observation of continuous space-time crystal in a nematic liquid crystal driven by ambient-power unstructured light. We numerically construct multi-dimensional configurations that exhibit a good agreement with experiments. Both experiments and computer simulations reveal a continuous space-time crystallization phase controlled by varying light intensity, sample geometry and temperature. The robustness against temporal perturbations and spatiotemporal dislocations shows the stability and rigidity of the studied classical continuous space-time crystals, which may relate to their locally topological nature with many-body interactions of particle-like solitonic building blocks. Furthermore, the lecture will discuss potential utility in optical devices, photonic space-time crystal generators, telecommunications, anti-counterfeiting designs, and cryptography, among many other.

Conventional optical microscopes convert the static inhomogeneity of physical quantities such as density, concentration, and orientation of molecules in materials as a two-dimensional image. For this reason, it is difficult to obtain significant information about the internal structure of materials when observing an isotropic, liquid, and transparent state with a conventional optical microscope. However, many solutions such as beverages, alcoholic beverages, cosmetics, pharmaceuticals, and emulsified products, as well as many chemical compounds such as paints, adhesives, and lubricants, and states such as glass and gel, in other words, many useful materials, have isotropic and highly transparent liquid properties. Here, we have invented the principle of a new “Fluctuation Microscopy” and have also developed a prototype device. Fluctuation Microscopy is also possible to observe the transient changes in materials driven by change of temperature, external field application, or polymerization, drying, and evaporation processes, as moving images.

The 4x4 matrix method was first formulated by Berreman and others to deal with propagation of electromagnetic waves in one-dimensionally varying optical media such as multilayer optical coatings and planar-aligned cholesteric liquid crystals. In recent years, there is a rapidly growing interest in electro-optic liquid-crystal devices based on the Pancharatnam-Berry (PB) phase effect due to its potentiality to achieve 100% efficient wave-front manipulation, thereby allowing for the loss-less thin film optical components. Although the concept of the PB phase is formally straightforward to understand using the Jones 2x2 matrix, quantitatively reliable analysis of wave propagation is difficult even for the simplest structures due to the diversion of wave front and internal reflections. In this talk, I will attempt to generalize the 4x4 matrix method by employing the circularly polarized waves as the basis vectors. In so doing, the PB phase naturally emerges in association with the optical anisotropy of the medium. Unlike the original 4x4 matrix method, we do not assume the uniformity of optical properties in the plane perpendicular to the propagation direction. We, instead, rigorously transform Maxwell’s equations into a 4x4 matrix form with an arbitrarily chosen (fictitious) direction of propagation using the circularly polarized bases. As an example, when we apply the new 4x4 matrix method to a planar-aligned cholesteric liquid crystals, the 4x4 matrix can be split into two 2x2 matrix equations that allow for an easy derivation of analytical solutions of optical waves propagating along the helical axis as **************** **************** where E_+ [φ] and E_- [φ] are the right- and left-handed circularly polarize electric vectors with the appropriate PB phase factors associated with the angle φ, and n_ij is the effective “refractive index” tensor made by combinations of principal values of dielectric and magnetic permeability tensors, and β is the wave vector of the cholesteric helix. This formalism enables us to capture the physical origin of the selective reflection band as a result of the interference of the PB phase, essentially distinct from the Bragg reflection which emerges when the propagation occurs in the oblique direction.

Topological soft matter: selected examples of use in optics and photonics Slobodan Žumer Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia Condensed Matter Physics Department, Jozef Stefan Institute, 1000 Ljubljana, Slovenia Understanding topology's role in numerous areas of physics has grown immensely. Here, we focus on topological soft matter, fluids characterized by the orientational ordering of constituting elements, including liquid crystals, colloids, and biological systems. Due to its softness, topological soft matter is rarely homogenously oriented. The frustration caused by the conflicting effects of anisotropic elasticity, chirality, confining geometries, surface anchoring, and external fields leads to stable and metastable point defects, disclination lines, and solitons in the orientational order parameter field. Integrating sophisticated experiments and theoretical approaches with efficient numerical simulations enables the development of techniques that control the formation and interaction of defects in diverse topological soft matter systems and opens new possibilities for applications in optics, photonics, and plasmonics. Basic concepts with theoretical and simulation approaches needed for topological soft matter and its interaction with light will be briefly given and illustrated by selected examples. • Optical modes in chiral nematics confined to cylindrical cavities [1]: Simulations demonstrate non-propagating modes with mixed features of edge modes, defect modes, and whispering gallery modes. The mixtures and their quality factors depend on the ratio between cylinder radius and degree of birefringence. Controlling the modes is crucial for use in lasers and other photonic elements. • Enhancement of geometric phase vortex coronagraphs [2]: The intrinsic features of self-engineered nematic liquid crystal topological defects are used to enhance the rejection capabilities of spectrally tunable vector vortex coronagraphs. This approach's simplicity and moderate performance offer an amateur astronomy community the possibility to consider vortex coronagraphy. • Solitonic optomechanics [3]: Topological and optical solitons in unwound chiral nematic layers can coexist. Their interaction is based on the light-to-matter momentum transfer and the force due to the nonlocal orientational elasticity of chiral nematic liquid crystals. It enables dynamic control and spatial localization of topological solitons, which nicely illustrates optomechanics. Acknowledgments: Studies were done and funded in collaboration with groups in Ljubljana (U. Mur, G. Poy, M. Ravnik, J. Zaplotnik; ARIS Grant No. P1-0099 and EU 2020 MSC Grant No. 834256), Boulder (I. Smalyukh; NSF Grant No. DMR-1810513), and Bordeaux (N. Kravets, E. Brasselet; Conseil Regional de Nouvelle Aquitaine, Project HELIXOPTICS). References: [1] U. Mur, et al., in preparation (2025). [2] N. Kravets, et al., Appl. Phys. Lett. 121, 241104 (2022). [3] G. Poy, et al., Nature Photonics 16, 454 (2022).