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Recent experimental realization of ferroelectric nematic liquid crystalline phases stimulated material development and numerous experimental studies of these phases, guided by their fundamental and applicative interest. In this Perspective, we give an overview of this emerging field by linking history and theoretical predictions to a general outlook of the development and properties of the materials exhibiting ferroelectric nematic phases. We will highlight the most relevant observations to date, e.g., giant dielectric permittivity values, polarization values an order of magnitude larger than in classical ferroelectric liquid crystals, and nonlinear optical coefficients comparable with several ferroelectric solid materials. Key observations of anchoring and electro-optic behavior will also be examined. The collected contributions lead to a final discussion on open challenges in materials development, theoretical description, experimental explorations, and possible applications of the ferroelectric phases.

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The twist-bend nematic phase (N_{TB}) is characterized by a conically twisting director and by a dramatic softening of the bend elastic constant before the transition to the N_{TB} phase. In the recently found splay nematic phase (N_{S}) the splay elastic constant tends to zero, resulting in a splay modulation perpendicular to the director. We model both phases with a single Q-tensor free energy including a term that breaks the degeneracy between the splay and bend elastic constant, and a flexoelectric term coupling the divergence of the Q-tensor with polarization. The N_{TB} or N_{S} phase is obtained by a change of sign of one elastic parameter. Measured elastic constants show that the N-N_{TB} transition is mainly driven by the increase of the nematic order, while the N_{S} transition is due to flexoelectric coupling.

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Ferroelectric ordering in liquids is a fundamental question of physics. Here, we show that ferroelectric ordering of the molecules causes the formation of recently reported splay nematic liquid-crystalline phase. As shown by dielectric spectroscopy, the transition between the uniaxial and the splay nematic phase has the characteristics of a ferroelectric phase transition, which drives an orientational ferroelastic transition via flexoelectric coupling. The polarity of the splay phase was proven by second harmonic generation imaging, which additionally allowed for determination of the splay modulation period to be of the order of 5-10 microns, also confirmed by polarized optical microscopy. The observations can be quantitatively described by a Landau-de Gennes type of macroscopic theory.

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Suspensions of magnetic nanoplatelets in isotropic solvents are very interesting examples of ferrofluids. It has been shown that above a certain concentration ΦNI such suspensions form a ferromagnetic nematic phase, which makes this system a unique example of a dipolar fluid. The formation of a nematic phase is driven by anisotropic electrostatic and long-range dipolar magnetic interactions. Here, we present studies of the evolution of short range positional and orientational magnetic order in suspensions with volume fractions below and above ΦNI, using small angle neutron scattering (SANS). The results show that in the absence of an external magnetic field, short range positional and orientational order already exist at relatively low volume fractions. Polarized SANS revealed that the contribution of ferromagnetic ordering to the formation of the nematic phase is significant. The ferromagnetic correlations can be qualitatively explained by a simple model, which takes into account anisotropic screened electrostatic and dipolar magnetic interactions.

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Successful realization of ferromagnetic nematic liquid crystals has opened up the possibility to experimentally study a completely new set of fundamental physical phenomena. In this contribution we present a detailed investigation of some aspects of the static response and the complex dynamics of ferromagnetic liquid crystals under the application of an external magnetic field. Experimental results are then compared with a macroscopic model. Dynamics of the director were measured by optical methods and analyzed in terms of a theoretical macroscopic model. A dissipative cross-coupling coefficient describing the dynamic coupling between the two system order parameters, the magnetization and the nematic director, is needed to explain the results. In this contribution we examine the dependency of this coefficient on material parameters and the saturation magnetization and the liquid crystal host. Despite the complexity of the system, the theoretical description allows for a proper interpretation of the results and is connected to several microscopic aspects of the colloidal suspension.

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One of the advantages of anisotropic soft materials is that their structures and, consequently, their properties can be controlled by moderate external fields. Whereas the control of materials with uniform orientational order is straightforward, manipulation of systems with complex orientational order is challenging. We show that a variety of structures of an interesting liquid material, which combine chiral orientational order with ferromagnetic one, can be controlled by a combination of small magnetic and electric fields. In the suspensions of magnetic nanoplatelets in chiral nematic liquid crystals, the platelet's magnetic moments orient along the orientation of the liquid crystal and, consequently, the material exhibits linear response to small magnetic fields. In the absence of external fields, orientations of the liquid crystal and magnetization have wound structure, which can be either homogeneously helical, disordered, or ordered in complex patterns, depending on the boundary condition at the surfaces and the history of the sample. We demonstrate that by using different combinations of small magnetic and electric fields, it is possible to control reversibly the formation of the structures in a layer of the material. In such a way, different periodic structures can be explored and some of them may be suitable for photonic applications. The material is also a convenient model system to study chiral magnetic structures, because it is a unique liquid analog of a solid helimagnet.

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Dynamic light scattering (DLS) experiments were performed on stretched sheets of liquid crystal elastomers (LCEs) swollen with a nematic solvent with different swelling ratios. We show that the obtained stress-strain curve and DLS data can still be explained with the concepts of semisoft elasticity. The stress-strain curve shows a typical semisoft response with a threshold strain and a plateau region where stress increases only a little with the applied strain. The width of the plateau decreases with the increase of the swelling ratio because the polymer backbone anisotropy reduces during the swelling. The relaxation rate of thermally excited director fluctuations, however, still shows a typical response, and our measurements indicate the presence of a soft dynamic director-shear mode, as predicted by the theory of semisoft elasticity.

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We have studied the response of ferromagnetic liquid crystals to external magnetic and electric fields, and compared it to the usual response of nematic liquid crystals (NLCs). We have observed effects, which are not present in a pure NLC and are a consequence of the coupling between the nematic director and the magnetization. The electro-optic effect, which is in the ferromagnetic phase the same as in the pure NLC, is accompanied by a converse magnetoelectric effect. The magneto-optic effect differs completely from the one observed in the pure NLC, where it is a quadratic effect and it only appears when a magnetic field larger than a critical field is applied perpendicular to the director. In the ferromagnetic NLC in addition to the response to the perpendicular field, there is also a qualitatively different response to the parallel field. Contrary to the pure NLC no critical field needs to be exceeded for the system to respond to a perpendicular field, but a critical field needs to be exceeded to observe a response to the field parallel to the director and antiparallel to the magnetization. The critical field is in this case two orders of magnitude smaller than the critical field of the magnetic Frederiks transition in the pure NLC. The experimental observations are well described by a simple macroscopic theory.

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More than four decades ago, Brochard and de Gennes proposed that colloidal suspensions of ferromagnetic particles in nematic (directionally ordered) liquid crystals could form macroscopic ferromagnetic phases at room temperature. The experimental realization of these predicted phases has hitherto proved elusive, with such systems showing enhanced paramagnetism but no spontaneous magnetization in the absence of an external magnetic field. Here we show that nanometre-sized ferromagnetic platelets suspended in a nematic liquid crystal can order ferromagnetically on quenching from the isotropic phase. Cooling in the absence of a magnetic field produces a polydomain sample exhibiting the two opposing states of magnetization, oriented parallel to the direction of nematic ordering. Cooling in the presence of a magnetic field yields a monodomain sample; magnetization can be switched by domain wall movement on reversal of the applied magnetic field. The ferromagnetic properties of this dipolar fluid are due to the interplay of the nematic elastic interaction (which depends critically on the shape of the particles) and the magnetic dipolar interaction. This ferromagnetic phase responds to very small magnetic fields and may find use in magneto-optic devices.

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We describe the complex time dependence of the buildup of force exerted by a clamped photoelastomer under illumination. Nonlinear (non-Beer) absorption leads to a bleaching wave of a significant cis isomer dye concentration deeply penetrating the solid with a highly characteristic dynamics. We fit our experimental response at one temperature to obtain material parameters. Force-time data can be matched at all other temperatures with no fitting required; our model provides a universal description of this unusual dynamics. The description is unambiguous since these are clamped systems where gross polymer motion is suppressed as a possible source of anomalous dynamics. Future experiments are suggested.

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We give a detailed theory of nematic fluctuations in liquid-crystal elastomers (LCEs) and calculate relaxation rates as obtained by dynamic light scattering (DLS). In ideal LCEs, a nematic state is formed by a spontaneous orientational symmetry breaking of an isotropic state, manifesting itself in an existence of a coupled director-shear soft mode (Goldstone mode). The relaxation rate of the soft mode (a pure bend and a pure splay mode) goes to zero in a long-wavelength limit. In a real, nonideal sample with a locked-in anisotropy, on the other hand, the relaxation rates of these modes become finite. Nonideal elastomers are characterized by a plateau in the stress-strain curve, and the soft mode can be detected only upon stretching to the point of elastic instability at which the director starts to rotate. We use the semisoft model of Gaussian elasticity to derive relaxation rates as a function of deformation for different scattering geometries. We show that the bend-mode relaxation rate goes to zero at the threshold strain, so it is the soft mode. The splay mode, on the other hand, is not soft because the relaxation rate is finite at the threshold strain. We provide experimental evidence and compare DLS measurements of splay and bend modes of two side-chain LCE samples differing in crosslinking densities. Results of both samples are in complete agreement with the predictions of the semisoft model, which indicates that director relaxation properties are not influenced much by the crosslinking conditions.

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We investigate light-induced patterning of a monodomain side-chain liquid crystal elastomer (SC-LCE) doped with light-sensitive azobenzene moiety in the temperature region close to the nematic-paranematic phase transition. We show that a strongly nonlinear relationship between the concentration of the cis isomers of the azomesogens and the refractive index modification of the material, which is characteristic for the phase transition region, results in nonmonotonous time dependence of the diffraction efficiency of a probe beam. From this effect we determine the sensitivity of the nematic transition temperature on the molar fraction of the cis isomers. The relation between the cis isomer molar fraction and nematic order also provides a possibility for recording hidden holograms, which can be made visible by cooling the sample from the paranematic to the nematic phase.

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By dynamic light scattering we studied the temperature dependence of scattered intensities and relaxation rates for pure twist and pure bend modes in a colloidal system of BaTiO(3) single domain nanoparticles and liquid crystal octylcyanobiphenyl (8CB) close to the nematic to smectic-A phase transition. From the experiments we obtained the critical exponents for the smectic correlation lengths, which in suspensions differ from the values for pure 8CB. The phase transition temperatures from isotropic to nematic phase (T(NI)) and from nematic to smectic-A phase (T(NA)) are both affected by the presence of the particles in two ways. The electric field around the ferroelectric particles increases the transition temperatures, whereas the disorder and probably also the excess of the surfactant cause a decrease of the transition temperatures compared to pure 8CB. The net effect is lower T(NI) and almost unchanged T(NA) in suspensions. After prolonged exposure to the external field the ferroelectric particles irreversibly aggregate, which results in the decrease of the internal electric field and, consequently, in the decrease of both transition temperatures.

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The optical mechanism for imprinting one-dimensional grating structures into thin films of a light-sensitive monodomain liquid crystal elastomer is investigated by analyzing the time dependence of optical diffraction properties. The recording kinetics shows an irregular oscillatory behavior, which is most expressed at small grating spacings and at temperatures close to the nematic-isotropic phase transition. The oscillations are attributed to the opto-mechanical response of the film, i.e., to contraction of the film during the recording process. At temperatures far below the nematic-isotropic phase transition, the spontaneous erasure kinetics exhibits exponential relaxation with relaxation time following the Arrhenius activation law. However, at temperatures close to the nematic-isotropic phase transition, the erasure process shows an interesting nonmonotonic behavior that we attribute to the non-linear relation between the concentration of the photo-transformed chemical groups and the nematic order parameter.

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We investigated nonlinear absorption and photobleaching processes in a liquid-crystal elastomer doped with light-sensitive azobenzene moiety. A conventional one-dimensional holographic grating was recorded in the material with the use of two crossed UV laser beams and the angular dependence of the diffraction efficiency in the vicinity of the Bragg peak was analyzed. These measurements gave information on the depth to which trans to cis isomerization had progressed into the sample as a function of the UV irradiation time. Using a numerical model that takes into account the propagation of writing beams and rate equations for the local concentration of the absorbing trans conformer, we computed the expected spatial distribution of the trans and cis conformers and the shape of the corresponding Bragg diffraction peak for different irradiation doses. Due to residual absorption of the cis conformers the depth of the recording progresses logarithmically with time and is limited by the thermal relaxation from the cis to trans conformation.

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We report on the operation and performance of a gain-switched Er:ZBLAN fiber laser based on an active pulsed diode pump system. The produced laser pulses offer high peak powers while retaining the high average powers and efficiency of the cw regime. The measured pulse duration was about 300 ns and nearly independent of the pump repetition frequency. The maximum obtained 68 W of peak power is the highest reported, to our knowledge, for diode-pumped Er:ZBLAN fiber lasers, and the 2 W of average power at the repetition frequency of 100 kHz is 2 orders of magnitude higher than previously reported average power in a pulsed regime. The obtained slope efficiency was 34%.

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Dynamic light scattering on a nematic liquid-crystal elastomer was performed as a function of deformation perpendicular to the director and along the director. We show that the relaxation rate of the nematic director fluctuations increases with strain along the director, as expected from the theory of semisoft elasticity. Deformation applied perpendicular to the director, on the other hand, decreases the relaxation rate to a very small value at the onset of the soft elastic response, revealing the existence of a dynamic soft mode. The results are in complete agreement with the theory of semisoft elasticity and allow us to determine all the constants of the model.

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We investigate diode pump absorption and temperature distribution in three erbium-doped double-clad fluoride fibers. Absorption is measured via fluorescence intensity and temperature distribution is measured with thermal imaging. Ray-tracing calculations of absorption and heat-equation modeling of temperature distribution are also conducted. We found excellent agreement between measurements and calculations for all fibers. Results indicate that erbium-doped fluoride fiber lasers have already reached maximum output powers allowed under natural convection cooling, with fiber end being the most critical. We propose cooling and fiber design optimizations that may allow an order-of-magnitude further power-scaling.

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In monodomain liquid crystal elastomers a symmetry-breaking locked-in anisotropy causes a semisoft elastic response characterized by a plateau in the stress-strain curve. We show by dynamic light scattering performed as a function of deformation that the relaxation rate of the nematic director fluctuations decreases with strain to a very small value at the onset of the soft elastic response, revealing the existence of a dynamic soft mode. The results are in complete agreement with the theory of semisoft elasticity and allow us to determine all the constants of the model.