Uniaxial Crystal Research Articles

Theoretical analysis and correction of a tight focusing field within z -cut uniaxial crystals

Theoretical analysis and correction of a tight focusing field within <i>z</i> -cut uniaxial crystals

Statistical properties of circular and rectangular multi-sinc Schell-model beams propagating in uniaxial crystals

With the extended Huygens–Fresnel principle, we derive the expressions for the spectral intensity, coherence, and effective beam width of circular and rectangular multi-sinc Schell-model (MSSM) beams propagating through uniaxial crystals. Numerical simulations are employed to extensively explore how beam and crystal parameters modulate the optical field. The results reveal that the propagating field exhibits multiple ring-shaped and array-like intensity distributions, with adjustable features such as the number of concentric rings, central brightness, array dimensions, and the morphology and diversity of sub-beams. Additionally, the spectral coherence displays an oscillatory distribution that evolves into a Gaussian distribution as the transmission distance increases. The anisotropy of uniaxial crystals not only influences the morphology of intensity distribution but also affects the evolution rate of coherence and the expansion rate of effective beam width. Our work contributes to optimizing beam propagation through uniaxial crystals, potentially benefiting precision optical systems in laser technology.

The energy of 180° domain walls of uniaxial crystals with the different magnetocrystalline anisotropy type

The main aim of the present work is to analyze the magnetocrystalline anisotropy (MCA) energy function of uniaxial crystals and to derive analytical expressions for the domain wall (DW) energy taking into account two MCA constants. Thus, the article presents a detailed analysis of the magnetocrystalline anisotropy energy function of uniaxial crystals taking into account two MCA constants (K1, K2). The values of the MCA energy extremes and the position of the easy magnetization directions (EMD) and hard magnetization directions (HMD) were determined. The MCA diagram was plotted in “K1”-“K2” coordinates. Six types of MCA have been found for uniaxial crystals. Two of them are simple with one maximum and one minimum of the EA(θ) function, and four are complex with two absolute and one local extreme for each. It is shown that EA(K1, K2) function has the smallest difference between the maximum and minimum values equal to |K1|/4 and the smallest angle between EMD and HMD equal to π/4 when the K1 + K2 = 0 condition is met. Analytical expressions for the 180° Bloch domain wall energy surface density (γ) were derived for uniaxial crystals with each MCA type. It is found that the γ(K1, K2) function has a minimum, equal to γ=2A|K1| when the relation K1 + K2 = 0 between MCA constants is satisfied. The derived analytical expressions are useful for a detailed spin-reorientation transition analysis. To illustrate this, examples of the application of the obtained results to MCA analyses of real crystals and DW energy calculations are given.

Toward the reproducible fabrication of conductive ferroelectric domain walls into lithium niobate bulk single crystals

Ferroelectric domain walls (DWs) are promising structures for assembling future nano-electronic circuit elements on a larger scale since reporting domain wall currents of up to 1 mA per single DW. One key requirement hereto is their reproducible manufacturing by gaining preparative control over domain size and domain wall conductivity (DWC). To date, most works on DWC have focused on exploring the fundamental electrical properties of individual DWs within single-shot experiments, with an emphasis on quantifying the origins of DWC. Very few reports exist when it comes to comparing the DWC properties between two separate DWs, and literally nothing exists where issues of reproducibility in DWC devices have been addressed. To fill this gap while facing the challenge of finding guidelines for achieving predictable DWC performance, we report on a procedure that allows us to reproducibly prepare single hexagonal domains of a predefined diameter into uniaxial ferroelectric lithium niobate single crystals of 200 and 300 μm thickness, respectively. We show that the domain diameter can be controlled with an uncertainty of a few percent. As-grown DWs are then subjected to a standard procedure of current-limited high-voltage DWC enhancement, and they repetitively reach a DWC increase of six orders of magnitude. While all resulting DWs show significantly enhanced DWC values, their individual current–voltage (I–V) characteristics exhibit different shapes, which can be explained by variations in their 3D real structure reflecting local heterogeneities by defects, DW pinning, and surface-near DW inclination.

Square versus hexagonal lattices effects on the optical and dielectric properties of plasmonic Ag–LiNbO[formula omitted] composite

We investigate the effect on the optical and transport properties of square and hexagonal lattice arrangements of silver nanoparticles (NPs) in uniaxial LiNbO3 as optically active layer within a multilayer configuration. This multilayer is constituted by Indium Tin Oxide (ITO), the polymer PMMA and a substrate of SiO2. The effective dielectric function of the ensemble of Ag NPs and uniaxial LiNbO3 crystal are treated through the Bruggeman approximation. The multilayer absorbance for s- and p-polarization at normal and oblique incidences are determined by means of the Transfer Matrix Method. Changes in the ratio between the diameter of the nanoparticles, D, and the distance between particles or pitch, P, are analyzed. A change in the D/P ratio implies a different filling factor. For small D/P ratio, the calculated absorbance for square- and hexagonal-lattices are equivalent; however, for greater D/P factor, the hexagonal lattice clearly shows higher absorbance values. Moreover, the Brewster angle seems to be sensitive to the Ag NPs size as well as the type of arrangement (square or hexagonal). The ac-electrical conductivity of the effective medium layer of the two arrangements in the perpendicular and parallel directions of the Ag NPs plane were analyzed. Our results demonstrate that the ac-conductivity is higher for hexagonal lattice than for square case, which means a higher density of Ag NPs. In addition, for the perpendicular direction, in the hexagonal-lattice (D/P = 0.5), we have found the negative epsilon (NE) condition, characteristic of metamaterials.

Peculiarities of polarised light scattering in nematic liquid crystals with large-scale director perturbations

ABSTRACT We examine light scattering in a birefringent material, namely uniaxial nematic liquid crystal possessing macroscopic orientation perturbations (variations of director in planar alignment). Our theoretical analysis and direct experiments proved that the polarisation state of the scattered speckle-field is uniform and elliptical (in a common case). The polarisation ellipse azimuth of scattered waves is mirror reflected to one of the directly transmitted waves relative to the optical axis.

Spin–orbit optical broadband achromatic spatial differentiation imaging

Spatial optical analog differentiation allows ultrahigh-speed and low-power-consumption of image processing, as well as label-free imaging of transparent biological objects. Optical analog differentiation with broadband and incoherent sources is appealing for its multi-channels and multi-task information processing, as well as the high-quality differentiation imaging. Currently, broadband and incoherent optical differentiation is still challenging. Here, a compact and broadband achromatic optical spatial differentiator is demonstrated based on the intrinsic spin–orbit coupling in a natural thin crystal. By inserting a uniaxial crystal just before the camera of a conventional microscope, the spin to orbit conversion will embed an optical vortex to the image field and make a second-order topological spatial differentiation to the field, thus an isotropic differential image will be captured by the camera. The wavelength-independent property of the intrinsic spin–orbit coupling effect allows us to achieve broadband analog computing and achromatic spatial differentiation imaging. With this differentiation imaging method, both amplitude and pure phase objects are detected with high contrast. Transparent living cells and biological tissues are imaged with their edge contours and intracellular details protruded in the edge detection mode and edge enhancement mode, respectively. These findings pave the way for optical analog computing with broadband incoherent light sources and concurrently drive the advancement of high-performance and cost-effective phase contrast imaging.

Transformation regulation of the paraxial finite Airy–Gaussian beam array propagating through uniaxial electro-optic crystals

Transformation regulation of the paraxial finite Airy–Gaussian beam array propagating through uniaxial electro-optic crystals

Simulations of optical and dielectric properties of plasmonic Ag–LiNbO[formula omitted] metamaterial: Analysis of the geometrical parameters

We report the optical absorption of a multilayer system and the electrical properties of silver (Ag) naoparticles (NPs) embedded on LiNbO3 that acts as active layer. The multilayer system is constituted by Indium Tin Oxide (ITO), a square lattice of Ag NPs on the uniaxial crystal LiNbO3, the polymer PMMA and a substrate of SiO2. The effective dielectric function of the ensemble aggregates of Ag NPs and uniaxial LiNbO3 crystal are treated through the extended Maxwell–Garnett approximation. The multilayer absorbance for s- and p-polarization at normal and oblique incidences is determined by means of the Transfer Matrix Method. We demonstrate that an adequate choice of structural parameters such as NPs sizes, interparticle distances and layers thicknesses can produce an enhancement of optical absorption in the multilayer system. For filling factor higher, the system absorbance is greater. The Brewster angle is seen to be sensitive to the Ag NPs size, as far as the wavelength is varied. In addition, we evaluate the dielectric modulus parameter and the ac–electrical conductivity of the effective medium layer (active layer) in the perpendicular and parallel directions of the Ag NPs plane. For both directions, at f sufficiently high, we find the negative epsilon condition, typical characteristic observed in metamaterials. For the ac–electrical conductivity, we identify different resonances for the perpendicular and parallel directions. A bigger concentration of Ag NPs induces a higher intensity of ac–conductivity.

Broadband amplification and thermal lensing in a combination of Yb:YLF and Yb:YAG crystals

Broadband amplification of laser radiation in a combination of Yb:YLF and Yb:YAG crystals was demonstrated. It was shown that, with the input spectrum width of 20 nm, the width at the output spectrum can reach 17 nm. A thermal lens induced in the Yb:YAG crystal is partially compensated by the lens in the Yb:YLF crystal due to the different signs of the ∂n/∂T coefficients of the crystals. The thermal lens in the Yb:YLF crystal in the thin and thick (“long-the-side pumped”) rod geometries was studied theoretically and experimentally. An analytical model of thermally induced phase distortions in uniaxial crystals caused by the piezo-optical effect was developed for the thin-rod geometry.

Dispersion Analysis of Perpendicular Modes Using a Hybrid Two-Trace Two-Dimensional (2T2D) Smart Error Sum.

Using linear dichroism theory, one would assume that a z-cut of a uniaxial crystal is equivalent to an x-cut to determine the perpendicular component of the dielectric tensor and the corresponding oscillator parameters. However, Fresnel's equations show that the effect of interfaces in the form of the continuity relations of the different components of the electric field must be considered. A consequence of the continuity relations is that perpendicular modes increase less significantly in strength with increasing angle of incidence than expected. This is a consequence of the fact that it is the inverse of the perpendicular component of the dielectric function that increasingly becomes important with a growing angle of incidence. An inverse dielectric function, however, has typically much smaller values than the dielectric function. An additional consequence is that perpendicular modes are blueshifted and coupled in such a way that oscillator strength is transferred to the higher wavenumber mode. Thus, the spectral signatures of perpendicular modes are often weak and masked by the parallel modes when two modes overlap. Accordingly, to enable dispersion analysis, it is suggested to use a hybrid of the conventional residual sum of squares and the two-trace two-dimensional (2T2D) smart error sum, which can correct systematic multiplicable errors in the experimental spectrum. As demonstrated for fresnoite (Ba2TiSi2O8), this is an important step toward determining the perpendicular component of the dielectric tensor and the corresponding oscillator parameters using dispersion analysis, since asynchronous 2T2D correlation spectra are, in particular, sensitive to perpendicular modes.

Polarization structure of optical vortices in inclined Laguerre–Gaussian beams passed through a uniaxial crystal

The work shows that in linearly polarized Laguerre–Gaussian beams passing through an anisotropic medium at an angle to the optical axis of the crystal, the distribution of optical vortices is devoid of axial symmetry. It is shown that the trajectories of movement of polarization singularities in the plane of the Laguerre–Gauss beam are different for different cases of input linear polarization at angles γ=±45∘ and there is an exchange of optical vortices, provided that the sign of the topological charge is preserved. It is shown that when the axis of an anisotropic medium is tilted, the movement of optical vortices occurs, accompanied by topological reactions of creation, destruction, or displacement of optical vortices to the periphery of the beam. It is characteristic that at angles of inclination by linear polarization γ=+45∘, topological reactions of creation and annihilation occur, and at angles γ=−45∘, topological reactions of displacement of optical vortices to the periphery of the beam occur.

Properties of a Lorentz correlated beam in uniaxial crystal

AbstractThe equation of a Lorentz‐correlated Schell‐model beam (LCSMB) in a uniaxial crystal is derived, and the relation of spreading properties and coherence with and are analyzed during propagation. The intensity of an LCSMB in the uniaxial crystal will evolve from Lorentz distribution into diamond distribution, and the LCSMB with smaller will evolve from Gaussian distribution into Lorentz distribution faster. The distribution of coherence of an LCSMB will lose the Lorentz distribution and become an elliptical distribution as increases.

Adjustable anomalous hollow vortex beam and its properties

AbstractA new beam named adjustable anomalous hollow vortex beam (AAHVB) is proposed, and the expressions of an AAHVB in uniaxial crystal are derived. The evolutions of intensity distributions of an AAHVB in free space and uniaxial crystal are investigated. The relationships between intensity distributions with beam parameters, uniaxial crystal, and distance are analyzed in detail. It is found that intensity distributions of an AAHVB in uniaxial crystal can be manipulated by setting source parameters , , , , and .

Controllable photonic hooks generated by typical shapes composed of uniaxial crystals

This work reports on the theoretical study and results on the generation and control of photonic hooks (PHs) through uniaxial crystals (calcite as an example). Completely different mechanisms and effects are obtained in typical rectangular and cylindrical structures, respectively. PHs generated by the rectangular structure no longer have a single inflection point but have a specific dual-inflection-point feature. The calcite cylindrical structure can generate a PH with a size comparable to that of the structure, and dynamic adjustment can be achieved through the angle between the incident and optical axes. By changing the polarization state of the incident field, active switching between photonic nanojet and PH can be achieved in both types of structures. The proposed generation and modulation scheme can be extended to other anisotropic materials.

High-energy single-longitudinal-mode Q-switched double-cladding fiber laser based on the injection seeding technique.

This paper demonstrates a high-energy, single-longitudinal-mode (SLM), actively Q-switched fiber laser based on the injection seeding technique. The large-mode-area double-cladding fiber is used as the gain medium to improve energy storage. Simultaneously, by using the linear electro-optic effect of the negative uniaxial crystal (β-B a B 2 O 4, BBO), a matching frequency-shift-free Q-switch with high damage threshold and high extinction-ratio is designed. Before reaching the stimulated Brillouin scattering threshold, the SLM Q-switched pulses can be achieved with energy higher than 15µJ over a wide range of repetition rates from 10 to 80kHz, and the maximum output power reaches 1.2W at the repetition rate of 80kHz, which may be the highest output pulse energy for such a SLM Q-switched fiber laser so far, to our best knowledge.

Unsupervised topological analysis of polarized light microscopy: application to quantitative birefringence imaging.

The determination of birefringence (magnitude and axis orientation) of optical materials is of significant interest in various fields. In the case of composite samples, this task becomes complicated and time-consuming; therefore, a partially automated procedure for reconstructing birefringence spatial distribution becomes valuable. Herein, we propose a procedure to reconstruct the spatial distributions of the retardance and optical axis orientation in a geological thin section from sparse quantitative birefringence measurements, using automatic boundary detection on cross-polarized light microscopy images. We examine two particular areas on the selected geological thin section: one that presents a uniaxial crystal with a circular cross-section of its refractive index ellipsoid and the other with grains of varying orientations. The measurement gives the orientation of the grain's optical axis both in and out of the plane of the thin section, which explains the qualitative observations with the cross-polarized light microscope. Future work will connect the measured orientation of the rock thin section with its 3D geological orientation in the field.

The effect of anisotropic field on magnon numbers, magnetization and heat capacity of antiferromagnetic materials

This article provides a theoretical examination of the impact of anisotropic fields on the magnetization and heat capacity thermodynamic properties of sublattice antiferromagnetic spin systems. The analysis begins with the classical Heisenberg model and considers uniaxial anisotropic fields in the antiferromagnetic system. Quantum field theory and the double time temperature dependent Green’s function technique, which incorporates the random phase approximation, are used to decouple and diagonalize the higher order terms. The study utilizes a dispersion of uniaxial symmetric AFM crystal lattice to examine the thermodynamic parameters of magnetization and heat capacity as a function of excitation temperature at low temperatures and long wavelength approximation. The results demonstrate that the magnetization and heat capacities of AFM are sensitive to anisotropic fields, with the magnetization deviation moving up and the heat capacity maximum peak reducing with increased anisotropy. These findings may have implications for the use of antiferromagnetic materials with similar anisotropy sources and stability in real-world applications.

Propagation of Lorentz-Gaussian elliptical multi-Gaussian correlated Schell-Model beam in uniaxial crystal

The evolution behavior of the intensity profile, beam spreading, and spectral degree of coherence of the Lorentz-Gaussian elliptical multi-Gaussian correlated Schell-Model beam propagating in uniaxial crystal are studied. The expression of the cross spectral density of the beam in uniaxial crystal is obtained based on Huygens-Fresnel integration, and the expressions of spectral coherence and root mean square (rms) beam width are derived. The beam spot is circular or elliptical while the ordinary and extraordinary refractive indices of the crystal are equal or unequal, respectively. The ellipticity of the light spot is affected by the Lorentz parameters. The larger the ratio of ordinary to extraordinary refractive index in uniaxial crystal is, the larger the spectral coherence of beam and rms beam waist width is. The spectral coherence increases with the increase of the Gaussian beam waist and the decrease of the Lorentz parameters. The rms beam width of the beam increases with the increase of the Gaussian beam width and Lorentz partial parameters. With the increase of the transmission distance, the influence of the light source parameters on the rms beam width gradually weakens. The total number of terms of multi-Gaussian correlated Schell-Model (MGSM) source and the spatial coherence lengths add additional degree of freedom for adjusting the spot pattern inside crystal.

Polarization helicity and the optical spin-orbit Hall effect

The optical spin-orbit Hall effect manifests the separation of the spin angular momentum (SAM) and the orbital angular momentum (OAM), yet it can be obtained for the radially polarized light and well controlled by the initial phase of the polarization state which leads to the twist of its distribution. In this paper, we introduce the polarization helicity to characterize the effect of the initial phase of the polarization states in the optical spin-orbit Hall effect. We find the polarization helicity of the radial polarization state can be modulated by changing its initial phase, and the polarization helicity of the high-order polarization state always is zero. We show that the separation magnitude of the SAM and the OAM reach the maximum value when the initial phase of the radial polarization state equals π/4 (or −π/4). The sign of the SAM and the OAM are determined by the polarization helicity of incident light and the anisotropy of uniaxial crystal, and its evolution follows a sinusoidal function. Furthermore, the polarization state of the incident radially polarized light will evolve into the left-handed (or right-handed) elliptical polarization state as the change of the polarization helicity of incident light. Our studies further deepen the understanding of the spin-orbit coupling of the vector beams, and provide a potential technique for modulating the polarization state of the light in uniaxial crystal.