Uniaxial Crystal Research Articles

Automated calculations of exchange magnetostriction

We present a methodology based on deformations of the unit cell that allows to compute the isotropic magnetoelastic constants, isotropic magnetostrictive coefficients and spontaneous volume magnetostriction associated to the exchange magnetostriction. This method is implemented in the python package MAELAS (v3.0), so that it can be used to obtain these quantities by first–principles calculations and classical spin–lattice models in an automated way. We show that the required reference state to obtain the spontaneous volume magnetostriction combines the equilibrium volume of the paramagnetic state and magnetic order of the ground state. In the framework of a classical spin–lattice model, we find that the analysis of volume dependence of this method jointly to the knowledge of the spatial derivative of the exchange interactions can reveal the equilibrium volume of the paramagnetic state and spontaneous volume magnetostriction unambiguously without involving any calculation of the paramagnetic state. We identify an error in the theoretical expression of the isotropic magnetostrictive coefficient λα1,0 for uniaxial crystals given in previous publications, which is corrected in this work. The presented computational tool may be helpful to provide a better understanding and characterization of the relationship between the exchange interaction and magnetoelasticity.

Propagation of finite-wright and mainardi beams in uniaxial crystals orthogonal to the optical axis

Propagation of finite-wright and mainardi beams in uniaxial crystals orthogonal to the optical axis

The effect of parabolic potential on the generation of higher harmonics of nematicons

We investigate the behavior of nonlocal spatial optical solitons in a uniaxial nematic liquid crystal with a parabolic potential. The equations governing the system are solved using semi-analytic and numerical methods. We found that nematicons exist in the parabolic potential. These nematicons exhibit periodic oscillations in the presence of the parabolic potential. The wavelength of periodic oscillations was found to decrease linearly with increasing potential strength. Higher harmonics of nematicons can be generated by varying the strength of the parabolic potential. Using Bogoliobov-De-Genes equations, the stability of the stationary solution against small perturbation has been investigated.

Indicatrix of TE and TM- polarized wave velocities in crystal of classes 4mm, 3m, 6mm with magneto-electric effect

This work is devoted to the theoretical study of the laws of propagation of electromagnetic waves of TE and TM polarization in anisotropic media belonging to classes 4mm, 3m, 6mm, etc. having a magnetoelectric effect. The directions of the vectors of the phase and group velocities of the polarization waves TE and TM at the boundary of a uniaxial crystal with magnetoelectric properties are considered. In the analytical form, the values of the directions of the phase and group velocities of the TE and TM waves are indicated, depending on the direction of the wave vector of the incident wave. The consequences of the obtained results for uniaxial crystals in the absence of magnetoelectric properties are discussed. The solution of the tasks set in this paper is based on the use of the matrix method. On its basis, various problems of wave processes in an isotropic elastic medium, electromagnetic waves in crystals, the distribution of coupled elastic and electromagnetic waves in piezoelectric and piezomagnetic media with a magnetoelectric effect were previously considered. In the presence of a magnetoelectric effect for electromagnetic waves propagating through uniaxial crystals, the parameters of the wave vector, phase and group velocities are determined. The obtained results are analyzed for electromagnetic waves propagating through uniaxial crystals in the absence of a magnetoelectric effect. The indicatrices of the wave vectors propagating in the plane and the phase velocities of the TM polarization waves are limited ( 0 ) x z. Based on the Rayleigh equation, the values of the group velocity are obtained. The density of electromagnetic energy fluxes and their components are determined for TE and TM waves. The energy transfer rate and its direction are determined. It is shown that the group velocities and directions obtained from the Rayleigh equation and the Umov-Poynting vector do not coincide.

Brillouin Scattering Study of Ferroelectric Instability of Calcium–Strontium–Barium Niobate Single Crystals

Uniaxial ferroelectrics with tetragonal tungsten bronze structure are important functional materials with photorefractive, electrooptic, piezoelectric, and pyroelectric properties. SrxBa1-xNb2O6 (SBN100x) with x > 50 is known as a typical uniaxial relaxor ferroelectric, while CaxBa1-xNb2O6 (CBN100x) undergoes nearly normal ferroelectric phase transitions. Single crystals of CSBN100x = [x(CBN28) + (1 - x) (SBN61)] = xCa0.28Ba0.72Nb2O6 + (1 - x) Sr0.61Ba0.39Nb2O6 with nominal x = 0.00, 0.25, 0.50, 0.75, and 1.00 were studied to clarify the dynamical properties at the crossover from relaxor (x = 0) to normal (x = 1) ferroelectric behavior. The longitudinal acoustic (LA) and transverse acoustic (TA) modes and a central peak (CP) related to the relaxation process of polarization fluctuations along the polar c-axis were studied in uniaxial ferroelectric CSBN single crystals as a function of temperature via Brillouin scattering spectroscopy. A CBN28 (x = 1.00) crystal shows the sharp elastic anomaly of the LA mode in the gigahertz range toward Curie temperature, Tc. However, those of CSBN25 (x = 0.25) and SBN61 (x = 0.00) crystals show diffusive anomalies due to stronger random fields. The relaxation time determined from the width of a CP shows a critical slowing down in the vicinity of Tc. The elastic anomaly and slowing down of relaxation time of CSBN100x crystals become diffusive in the vicinity of Tc as the CBN28 content decreases. The origin of the crossover from relaxor to normal ferroelectric phase transitions is discussed in terms of the difference in the A1 and A2 sites' occupancies.

Reflection from uniaxial crystals: symmetries, and formulae for near-normal incidence.

The following symmetries and interrelationships are established: the direct reflection amplitudes r ss,r pp are independent of the signs of the direction cosines of the optic axis. For example, they are unchanged by ϕ→π-ϕ or ϕ→-ϕ, where ϕ is the azimuthal angle of the optic axis. The cross-polarization amplitudes r sp a n d r ps are both odd in ϕ; they also satisfy the general relations r sp(ϕ)=r ps(π+ϕ) and r sp(ϕ)+r ps(π-ϕ)=0. All of these symmetries apply equally to absorbing media with complex refractive indices, and thus complex reflection amplitudes. Analytic expressions are given for the amplitudes which characterize the reflection from a uniaxial crystal when the incidence is close to normal. The amplitudes for reflection in which the polarization is unchanged (r ss a n d r pp) have corrections which are second order in the angle of incidence. The cross-reflection amplitudes r sp a n d r ps are equal at normal incidence and have corrections (equal and opposite) which are first order in the angle of incidence. Examples for normal incidence and small-angle (6°) and large-angle (60°) incidence reflection are given for non-absorbing calcite and absorbing selenium.

Controlling the spin Hall effect of grafted vortex beams propagating in uniaxial crystal.

Though numerous studies of spin-orbit interaction (SOI) of light beams propagating along the optic axis of uniaxial crystals have been carried out, in previous studies, the initial input beams have cylindrical symmetry. In this case, the total system preserves cylindrical symmetry so that the output light after passing through the uniaxial crystal doesn't exhibit spin dependent symmetry breaking. Therefore, no spin Hall effect (SHE) occurs. In this paper, we investigate the SOI of a kind of novel structured light beam, grafted vortex beam (GVB) in uniaxial crystal. The cylindrical symmetry of the system is broken by the spatial phase structure of the GVB. As a result, a SHE determined by the spatial phase structure emerges. It is found that the SHE and evolution of the local angular momentum are controllable both by changing the grafted topological charge of the GVB and by employing linear electro-optic effect of the uniaxial crystal. This can open a new perspective to investigate the SHE of light beams in uniaxial crystals via constructing and manipulating the spatial structure of the input beams artificially, hence offers novel regulation capabilities of spin photon.

Analysis and design of transition radiation in layered uniaxial crystals using tandem neural networks

With the flourishing development of nanophotonics, a Cherenkov radiation pattern can be designed to achieve superior performance in particle detection by fine-tuning the properties of metamaterials such as photonic crystals (PCs) surrounding the swift particle. However, the radiation pattern can be sensitive to the geometry and material properties of PCs, such as periodicity, unit thickness, and dielectric fraction, making direct analysis and inverse design difficult. In this paper, we propose a systematic method to analyze and design PC-based transition radiation, which is assisted by deep learning neural networks. By matching boundary conditions at the interfaces, effective Cherenkov radiation of multilayered structures can be resolved analytically using the cascading scattering matrix method, despite the optical axes not being aligned with the swift electron trajectory. Once properly trained, forward deep learning neural networks can be utilized to predict the radiation pattern without further direct electromagnetic simulations. In addition, tandem neural networks have been proposed to inversely design the geometry and/or material properties for the desired effective Cherenkov radiation pattern. Our proposal demonstrates a promising strategy for dealing with layered-medium-based effective Cherenkov radiation detectors, and it can be extended to other emerging metamaterials, such as photonic time crystals.

Efficient methodology with potential uses of Fresnel diffractometry for real-time study of uniaxial nematic liquid crystal phase transitions

Due to the different features of their various phases and expanding physical understanding, liquid crystals (LCs) play a fundamental and crucial role in contemporary technology. Recently, they have also been utilised in adaptive optics, active switching, and next-generation displays for augmented and virtual reality. In order to determine relevant quantities for thermotropic uniaxial nematic liquid crystals (NLCs), our aim is to assess the applicability of a ground-breaking method. The method being discussed is based on Fresnel diffraction (FD) from phase objects, which has been employed over the past 20 years in several accurate and precise metrological applications. Using a phase step and quantitatively registering the visibility of the diffraction patterns, diffractometry can transform any change in the order of LCs brought on by a change in temperature into a change in the optical phase. Owing to its low sensitivity to environmental vibrations, inherent compactness, and ease of set up, diffractometry can be used much more effectively than interferometry. Additionally, as a special major feature, if the various phases of a LC have the required transparency, it is possible to record the number of phases in the bulk of the LC, the surface ordering, and the approximate temperature of the phase transitions in a single-shot imaging by applying a suitable temperature gradient. The numerical computations and practical data comparisons from our theoretical considerations demonstrate a very high level of agreement with the output from other currently used methodologies. As we shall see, by addressing some of the faults and inadequacies of existing techniques, this strategy has the potential to both complement and strengthen them.

Nematic liquid crystals in lens shape geometry

ABSTRACTSessile nematic droplets provide a possibility to study the combined effect of anchoring at solid and gas interfaces. The combination of various alignments at the two surfaces and external fields results in a variety of director distribution schemes, ranging from a defect-free, almost homogeneous state to configurations with point-, line- and wall defects. This paper reviews recent results obtained on sessile droplets of uniaxial nematic liquid crystals, such as temperature-controlled anchoring transitions, formation and dynamics of Néel wall type metastable inversion walls in magnetic and/or electric fields. The structures of the recently discovered twist-bend and ferroelectric nematic liquid crystals will also be briefly discussed.

Spin Hall Effect of Nonlinear Photons

AbstractPhotonic spin Hall effect (SHE) refers to the transverse separation of spin photons in refraction and reflection phenomena. The photonic SHE has been investigated in various optical systems including air–glass interfaces, interfaces containing 2D materials, random media, etc. Here, the spin–orbit coupling (SOC) in nonlinear uniaxial crystals is investigated, and the SHE of second‐harmonic photons is demonstrated theoretically and experimentally. The generation and evolution processes of nonlinear spin photons within the crystal are visualized by the derived four wave coupling equations and wavevector‐varying Berry phases. For a focused fundamental beam, two cascaded SOCs occurring in the fundamental and second‐harmonic fields are connected by the nonlinear wave mixing near the focal position. Thus the SHE of nonlinear photons depends on the focal position, different strongly from linear photons whose SHE is independent of the focal position. Similar to the focal‐position‐dependent SHE, the focal‐position‐dependent optical vortex generations are also demonstrated for the nonlinear fields. Finally, a high‐speed modulation scheme for the SHE is proposed based on an electro‐optical polarization controller, which routes nonlinear spin photons into different destinations. These findings deepen the understanding of spin–orbit coupling in nonlinear systems and facilitate the development of spin multiplexed electrooptic devices.

Nodal degeneracy of guided modes in uniaxial crystal slabs

We study the dispersions of the guided modes in the continuous uniaxial crystal slab waveguide and engineer their degeneracies through dielectric anisotropy. By switching the uniaxial positivity and negativity, we can obtain distinctive nodal types, point and line, for the lowest degeneracy in frequency. The mirror symmetry protections, Mx and My, are pointed out, and the degeneracy properties are intuitively analyzed through comparing the approximate slopes of the guided modes. Our results reveal a link between the lowest nodal types and the positivity/negativity of the uniaxial crystal, and provide a new approach to regulate the topology of degeneracy in two-dimensional photonic bands.

ПОЛЯРИЗАЦИОННЫЕ ЭФФЕКТЫ ПРИ ОТРАЖЕНИИ СВЕТА ОТ ГРАНИЦЫ ОДНООСНОГО КРИСТАЛЛА

In this paper, the boundary conditions for plane electromagnetic waves at the interface between an isotropic medium and a uniaxial crystal have been obtained and analyzed. Elements of the reflection matrix that relates components of the electric field of the reflected wave back to those of the incident electromagnetic wave have been determined. Using the elements of the reflection matrix, we show that the possibility exists for polarization of light to be preserved upon reflection at the interface with anisotropic media. The conditions for the Jones vectors conservation upon reflection from the surface of a uniaxial crystal are obtained. The existence of the Brewster effect at the interface with such an anisotropic medium has been studied and verified. The Brewster’s polarizations have been shown to be almost p-polarizations with just little admixture of s-polarization.

Composition-Related Dielectric, Ferroelectric and Electrocaloric Properties of Pb5Ge3O11 Single Crystals Modified by Ba Ions

In this paper, we studied some ferroelectric properties of archetypal oxide uniaxial ferroelectric single crystals of Pb5Ge3O11 modified by Ba ions. They include dielectric, DSC, ferroelectric polarization, and electrocaloric effect (ECE) measurements. The measurements show that increasing Ba doping considerably influences all the measured parameters, mainly by lowering the Curie temperature, gradually diffusing the phase transition, and decreasing values of polarization as well as the coercive field. The decrease in overall ECE is influenced by decreasing polarization. Compared with the pure PGO single crystals, this decrease is from 1.2 K to 0.2 K. However, the effect of diffusing the phase transition increases the range of its occurrence (up to 30 K), which might be beneficial in applications.

Molecular cluster analysis using local order parameters selected by machine learning.

Accurately extracting local molecular structures is essential for understanding the mechanisms of phase and structural transitions. A promising method to characterize the local molecular structure is defining the value of the local order parameter (LOP) for each particle. This work develops the Molecular Assembly structure Learning package for Identifying Order parameters (MALIO), a machine learning package that can propose an optimal (set of) LOP(s) quickly and automatically for a huge number of LOP species and various methods of selecting neighboring particles for the calculation. We applied this package to distinguish between the nematic and smectic phases of uniaxial liquid crystal molecules, and selected candidate LOPs that could be used to precisely observe the nematic-smectic phase transition. The LOP candidates were used to observe the nucleation and subsequent percolation transition, and the effect of the choice of LOP species and neighboring particles on the statistics of local molecular structures (clusters) was examined. The procedure revealed the time evolution of the number of clusters and the dependence of the percolation curve on the number of neighboring particles for each LOP species. The LOP species with the lowest dependence on the number of neighboring particles was the best-performing LOP species in the MALIO screening strategy. These results not only show that machine learning can powerfully screen a huge number of LOP species and suggest only a few promising candidates, but also indicate that MALIO can select the best LOP species.

Two-Dimensional Talbot Effect in Uniaxial Crystals Orthogonal to Optical Axis

Two-Dimensional Talbot Effect in Uniaxial Crystals Orthogonal to Optical Axis

First measurements of second-order frequency conversion phase-matching conditions in the new CTAS crystal

We report that Ca3TaAl3Si2O14 is a positive uniaxial crystal and provides second-order frequency conversion. Indeed, we performed direct measurements of phase-matching conditions for second-harmonic generation and sum-frequency generation up to 3.5 µm. The simultaneous fitting of recorded data provided the Sellmeier equations of the two principal refractive indices and the magnitude of the nonlinear coefficient.

Acousto-optic k-space filtering for multifrequency laser beam shaping

One of emerging applications of acousto-optic tunable filters (AOTFs) is spatial filtering of optical beams. A noncollinear AOTF has a tunable ring-shaped transfer function determined by geometry of the refractive index surface in a uniaxial crystal. We rigorously derive the geometrical parameters of the AOTF’s elliptic transfer function under noncritical phase matching condition in uniaxial crystals. This basic family of transfer functions can be used for synthesis of axially symmetric transfer functions with the help of multifrequency ultrasonic signals. A two-color tunable optical trap configuration is proposed based on a single AOTF used for laser beam shaping.

Controlling the Abrupt Autofocusing of Circular Airy Vortex Beam via Uniaxial Crystal

The propagation of many kinds of structured light beams in uniaxial crystal has been investigated. However, the investigation of the evolution of these structured light beams after the uniaxial crystal is lacking. In this paper, an evolution formula of a light beam after passing through a uniaxial crystal is derived. Based on the formula, controlling the autofocusing of a circular Airy vortex beam (CAVB) via a uniaxial crystal is studied. It is found that a uniaxial crystal can prolong the focal length of the autofocusing. By changing the crystal length, the relative weight of the left- and right-hand circular polarization components and the relative value between the orbital and spin angular momentum densities of the beam’s focal plane can be adjusted flexibly. In addition, other optical elements can be inserted between the crystal and the focus to further adjust the focal plane field distribution. The influences of inserting x- and y-polarization polarizers on the intensity distribution are calculated as examples.

Spectral-Polarization Systems of Three-Dimensional Computer Vision Based on Acousto-Optic Filtering

Development of two-channel acousto-optic spectral devices with enhanced functionality is described. Approaches to development of multifunctional acousto-optic devices capable to register different types of optical information (spatial distribution, spectra, polarisation characteristics) are discussed. Opportunities to register multi-dimensional complementary data based on Bragg light diffraction on ultrasonic waves in a uniaxial crystal are analysed. It is demonstrated that such approach may be developed on the basis of implementation of simultaneous diffraction of two light beams in planes rotated relative to each other by a small angle. Such enhancement of the acousto-optic filter operational concept allows to go beyond the classic constraints imposed on their characteristics.