Uniaxial Crystal Research Articles

Practice of the Visual Determination of the Direction of the Rotation of the Light Polarization Plane in Gyrotropic Uniaxial Single Crystals

Practice of the Visual Determination of the Direction of the Rotation of the Light Polarization Plane in Gyrotropic Uniaxial Single Crystals

Ellipsometry: dielectric functions of anisotropic crystals and symmetry.

The optical functions of anisotropic materials can be determined using generalized ellipsometry, which can measure the cross-polarization coefficients (CPs) of the sample surface reflections. These CPs have several symmetry relations with respect to the symmetry of the crystal. This paper explores the symmetry relations of these CPs for uniaxial, orthorhombic, and monoclinic crystals and the requirements for generalized ellipsometry. Several ellipsometry measurement configurations are examined, including the requirements for the accurate measurements of the dielectric functions of anisotropic crystals.

Topological evolution of acousto-optic transfer functions in biaxial crystals

Modern applications of acousto-optic tunable filters (AOTFs) range from hyperspectral imaging in space research and biomedical optics to optical manipulation and ultrafast laser pulse shaping. The design of all AOTFs is based on optical anisotropy of crystals; until now, however, only uniaxial crystals have been used. Lower symmetry and outstanding acousto-optic (AO) properties of some new biaxial crystals make them promising candidates for qualitative improvements in this field. Anisotropic AO interaction in crystals allows angular noncritical phase-matching (NPM) configurations that are commonly used in different AOTF types. In this work, we perform a comprehensive geometrical and topological analysis of 2D transfer functions of AO interaction under NPM condition in biaxial crystals. The topological classification of the 2D transfer functions under an angular NPM condition is proposed. In principle, in the planes of a biaxial, the same types of transfer function exist as in uniaxial crystals, including cross-like topology of collinear diffraction, circular topology, and ultrawide angle topology. In addition, new topological types of the AO 2D transfer function are reported, which exist only in biaxial crystals.

Exact Solutions for Vector Phase-Matching Conditions in Nonlinear Uniaxial Crystals

The transcendental equations of vector phase matching are transformed into a fourth-order polynomial equation that admits an analytical solution. The real roots of this equation provide the optical axis orientations that are useful for efficient down-conversion in nonlinear uniaxial crystals. The production of entangled photon pairs is discussed in both collinear and non-collinear configurations of the spontaneous parametric down-conversion (SPDC) process. Degenerate and non-degenerate cases are also distinguished. As a practical example, SPDC processes of type-I and type-II are studied for beta-barium borate (BBO) crystals. The predictions are in very good agreement with experimental measurements already reported in the literature and include theoretical results of other authors as particular cases. Some properties that seem to be exclusive to BBO crystals are reported; the experimental verification of the latter would allow a better characterization of these crystals.

Phase-matching properties of Ba2Ga8GeS16

We report experimental results on the phase-matching properties of the quaternary B a 2 G a 8 G e S 16 crystal for second-harmonic generation (SHG) and sum-frequency generation (SFG) of Nd:YAG laser-pumped K T i O P O 4 (KTP) and H g G a 2 S 4 (HGS) optical parametric oscillators (OPOs) and a waveguide C O 2 laser in the 0.8054–10.5910 µm range. Based on these experimental data, we derive refined Sellmeier equations and thermo-optic dispersion formulas that are expected to enable practical applications of this new uniaxial nonoxide nonlinear crystal in the mid-IR part of the spectrum.

Computational Study of Dynamic Susceptibility and Phase-Matching Angle by Two-Photon Entangled Generation.

Two-photon entangled generation is used to produce an entangled photon source which is a key and core element concerning the technology applications of quantum computing, quantum communication, and quantum precision measurement. In this work, we have deduced the formulas of dynamic susceptibility and phase-matching angle of two-photon entangled generation in nonlinear optical crystals. The formulas are employed to compute the susceptibilities and phase-matching angles of these optical processes for uniaxial and biaxial crystals. The susceptibility magnitude and phase-matching condition of two-photon entangled generation affect the performance of the source. The calculated results by these formulas are employed to study properties and estimate the performance of an entangled photon source. In this way, we discuss the phase matching among waves and working wavelength in an entangled source that affects the efficiency of satellite communication with the ground during the day and night.

Practice of the visual determination of the direction of light polarization plane rotation in the gyrotropic uniaxial single crystals

When studying and applying crystals of the middle category, it is necessary to take into account the manifestations of anisotropy of their properties, in particular, optical anisotropy. One of the manifestations of optical anisotropy is the rotation of the polarization plane (gyrotropy effect), which is observed in the direction of the optical axis of such crystals. The plane of polarization of light can rotate clockwise and counterclockwise. To determine the direction of rotation of the polarization plane, simple visual methods can be used based on studies of samples in converging polarized light – observations of conoscopic figures. In general, the type of conoscopic figures depends on the relative position of the polarizers, the wavelength of light in the system, the cut of the single crystal perpendicular to which the light propagates, the thickness of the sample and the birefringence. The direction of rotation of the polarization plane can be determined by еру change of the type of conoscopic figure of a sample of a gyrotropic crystal cut perpendicular to the optical axis: change of the central spot color during the analyzer rotation; the extinction of the central spot when observing a conoscopic figure using light filters; the direction of movement of the rings in monochromatic light; observation of Airy patterns. According to the experience of working in our laboratory “Single crystals and Stocke on their Base”, the simplest, most operational and unambiguous visual method for determining the direction of rotation of the polarization plane is the observation of Airy figures. A conoscopic pattern in the form of Airy figures (a four-way spiral) occurs when observing in converging polarized light a combination of two superimposed samples of gyrotropic crystals cut perpendicular to the optical axis, rotating the plane of polarization of light in opposite directions. To use this method, a well-known sample of a gyrotropic crystal cut perpendicular to the optical axis is required.

Enhanced edge detection based on spin hall effect in the uniaxial crystal

Optical analog computing and spatial differentiation have received great attention in many fields. In the field of biology and medicine, it is important to get the high contrast of phase images on a subwavelength scale. Compared with other methods, the optical methods based on the photonic spin Hall effect (PSHE) have the advantages of low costs and detailed detections, but this method also has the disadvantages of lower contrasts. Our work is aimed to improve the contrasts for the edges. In the study, we explore the spin Hall effect of light (SHEL) based on uniaxial crystals and investigate the effects of these crystals on spatial differentiation. It can be seen that in the elliptic–hyperbolic crystal, the PSHE can be enhanced significantly and the spatial differentiation contrasts are consistent with the enhancement of PSHE, which implies that this kind of medium would provide more possibilities in micro imaging.

Optical Phase Contrast Microscopy with Incoherent Vortex Phase

AbstractA novel, compact, and broadband optical phase contrast microscopy based on incoherent vortex topological quadrupole is theoretically proposed and experimentally realized. The topological quadrupole, generated in a thin uniaxial crystal, possesses four single‐charge optical vortexes, each of which can act as a two‐dimensional (2D) optical spatial differentiator. The incoherence of light‐emitting diode (LED) light will wash out the optical vortex and the spatial differentiation effect, which can be ingeniously overcome by choosing Kohler illumination and inserting a 1 mm‐thickness uniaxial crystal sandwiched with two polarizers before the camera. By adjusting the polarizers and the tilted angle of crystal to selectively utilize the geometric Berry phase and the angular gradient of Fresnel transmission coefficients of crystal, the 1D, 2D, and second‐order analog spatial differentiations with a spatial resolution better than 0.775 μm can be switched flexibly. A versatile phase contrast microscope is built, which is well compatible with the conventional microscopes. The uniformly incoherent illumination without laser speckle effects results in high‐quality spatial differentiation imaging. Biologically transparent living cells are thus imaged with high contrast.

Angular Quasi-Phase-Matching in Periodically Poled Uniaxial and Biaxial Crystals

This article deals with a general description of Angular Quasi-Phase-Matching (AQPM) in uniaxial and biaxial crystals for second-order nonlinear optical interactions. Such an exhaustive and generalized angular-dependent approach of AQPM reveals new directions of propagation with efficient parametric frequency conversion. These AQPM solutions are studied by depicting the corresponding topologies and associated symmetries. The theoretical overview is fully validated and illustrated by measurements. We clearly demonstrate the benefits of such a generalized approach, both in the case of two emblematic periodically poled (PP) crystals: 5%MgO-doped PPLiNbO3 (5%MgO:PPLN) and Rb-doped PPKTiOPO4 (PPRKTP). These developments should stimulate new potential applications in nonlinear frequency conversion.

Thermally induced polarization distortions in uniaxial crystals

The polarization distortions of high-power laser radiation, which arise when it passes through a solid-state optical element cut from a uniaxial crystal, are studied theoretically and experimentally. The theoretical analysis is carried out taking into account the anisotropy of all physical properties of the crystal for an optical element with an arbitrary orientation of the crystallographic axes. Experimental verification shows convincing agreement with theoretical concepts. The problem of minimizing polarization distortions for optical elements cut in a direction close to the direction of the optical axis is considered.

Propagation Characteristics of Circular Airy Vortex Beams in a Uniaxial Crystal along the Optical Axis

Circular airy vortex beams (CAVBs) have attracted much attention due to their “abruptly autofocusing” effect, phase singularity, and their potential applications in optical micromanipulation, communication, etc. In this paper, we numerically investigated the propagation properties of circular airy beams (CABs) imposed with different optical vortices (OVs) along the optical axis of a uniaxial crystal for the first time. Like other common beams, a left-hand circular polarized (LHCP) CAVB, propagating along the optical axis in a uniaxial crystal, can excite a right-hand circular polarized (RHCP) component superimposed with an on-axis vortex of topological charge (TC) number of 2. When the incident beam is an LHCP CAB imposed with an on-axis vortex of TC number of l = 1, both of the two components have an axisymmetric intensity distribution during propagation and form hollow beams near the focal plane because of the phase singularity. The phase pattern shows that the LHCP component carries an on-axis vortex of TC number of l = 1, while the RHCP component carries an on-axis vortex of TC number of l = 3. With a larger TC number (l = 3), the RHCP component has a larger hollow region in the focal plane compared to the LHCP component. We also studied cases of CABs imposed with one and two off-axis OVs. The off-axis OV makes the CAVB’s profile remain asymmetric throughout the propagation. As the propagation distance increases, the off-axis OVs move near the center of the beam and overlap, resulting in a special intensity and phase distribution near the focal plane.

Numerical Tool for Calculating Birefringence in Mirror-Substrates for Gravitational-Wave Detectors

The influence of birefringence on rays entering and exiting a non-isotropic medium is a complex process that depends on its dielectric tensor, the orientation and geometry of the medium, the surrounding material, and the inclination of the incident ray. Thus, when aiming for a calculation of the effects, many parameters need to be taken into account while simplifications are generally not applicable. Moreover, the complexity of the general issue makes it almost impossible to find an analytical solution for backward calculations of stress-birefringence from polarization measurements. In this paper, a report is given on the formulation of a birefringence ray-tracing program in Python for the convenient evaluation of optical effects inside uniaxial crystals under stress. The aim thereby is to have an easily applicable tool that can be used in interferometer commissioning for current and future gravitational-wave detectors. Results from test simulations using realistic parameters for a sapphire mirror as used in the gravitational-wave detector KAGRA are implemented and show the capabilities of this tool.

Asymmetrical spiral spectra and orbital angular momentum density of non-uniformly polarized vortex beams in uniaxial crystals

To explore the effect of non-uniform polarization on orbital angular momentum (OAM) in anisotropic medium, in this work investigated are the evolution of the spiral spectra and OAM densities of non-uniformly polarized vortex (NUPV) beams in uniaxial crystals propagating orthogonal to the optical axis, and also the case of uniformly polarized vortex (UPV) beams with left-handed elliptical polarization. In the input plane, the NUPV beams present their spiral spectra of m-mode concentrated at m = l ± 1 modes rather than m = l mode, and reveal the relation among topological charge l, mode of spiral spectra m and the power weight value Rm expressed by . The relation is still satisfied for UPV beams in uniaxially anisotropic crystals, whereas for NUPV beams their relations are no longer valid owing to non-uniform polarization. Furthermore, the analysis indicates that the asymmetrical distribution of power weight of spiral spectra and the non-zero value in the sum of longitudinal OAM densities originate from the initial non-uniform polarization and anisotropy in uniaxial crystals rather than topological charges. In addition, the relation between spiral spectrum and longitudinal OAM density is numerically discussed. This work may provide an avenue for OAM-based communications, optical metrology, and imaging by varying the initial non-uniform polarization.

Superposition of vortex beams generated by polarization conversion in uniaxial crystals

An optical system comprising a c-cut uniaxial crystal positioned between two axicons and illuminated by a Gaussian or a Laguerre–Gauss mode was used to demonstrate the generation of various vector vortex beams. We focused the generated beams using a 1 m focal length lens and we investigated their intensity profile and the polarization state in the focal plane of the focusing element. We showed that the achieved intensity profile can be controlled by changing the polarization state of the beam incident on the crystal. We observed that, for a particular configuration of the system, the initial circular symmetry of the beam is no longer preserved. The experiments were performed with Ti:Sapphire lasers that were operated in continuous wave mode, as well as in pulsed regime. The optical system presented here ensures a convenient way to generate a great variety of vector vortex beams and it is expected to be of interest for applications that use low and high-power laser sources, such as STED microscopy, light trapping, or material processing.

Enhancing the efficiency of the topological phase transitions in spin–orbit photonics

A light beam reflected and refracted at a sharp interface can acquire a momentum-dependent Pancharatnam–Berry (PB) phase, which produces a topological phase transition from one kind of spin–orbit interaction (e.g., spin-controlled vortex generation) to another (e.g., photonic spin-Hall effect). However, this process is extremely inefficient and difficult to observe directly in experiments, which also hinders its applications. Here, we propose to enhance significantly the topological phase transitions by c-cut uniaxial crystals. We first give a full-wave theory to describe the spin–orbit interactions of a beam passing through a c-cut uniaxial crystal and experimentally observe the topological phase transition process of the transmitted beam when the angle between the beam propagation direction and the optical axis direction changes. It is found that the efficiency of the spin–orbit interactions caused by the momentum-dependent PB phase can be increased as high as 50%, which is much larger than that at isotropic sharp interfaces. Our findings provide an alternative approach for manipulating the spin and orbital angular momenta of light and exhibit potential applications in the future spin–orbit photonic components.

Propagation of the odd-Pearcey Gauss beam in the uniaxial crystals with the Pockels effect

In this paper, the propagation dynamics of an odd-Pearcey Gauss beam (OPGB) in uniaxial crystals along the optical axis governed by the Pockels effect is analytically and numerically investigated. In this case, the left-hand circularly polarized OPGB gives rise to the right-hand vortex component possessing a topological charge of 2. Results show that the focusing intensity, the focusing distance, the focal point size, the efficiency of the power exchange between these two contributions and the conversion between spin angular momentum (SAM) and orbit angular momentum (OAM) can be controlled by choosing an appropriate external electric field. Furthermore, the right-hand vortex component can be utilized to trap the nanoparticles whose refractive index is lower than that of the surroundings. The energy flow and the angular momentum of the OPGB are also studied. Particularly, with increasing the ratio of the extraordinary index to the ordinary index in a uniaxial medium, both two contributions perform bifocusing behavior.

Hyperbolic phonon polaritons with positive and negative phase velocities in suspended α -MoO3

Sample suspension is a valuable method to improve the mechanical, thermal, electronic, and optical properties of low-dimensional materials. In terms of confined light-matter waves—the polaritons, sample suspension can elongate the wavelength of polaritons with a positive phase velocity. Previous work demonstrates a wavelength elongation of ∼10% for hyperbolic phonon polaritons (HPPs) in uniaxial crystals of hexagonal boron nitride (hBN). In this work, we report the alteration of HPPs in biaxial α-phase molybdenum trioxide (α-MoO3) by sample suspension. Our combined infrared nano-imaging experiments and electromagnetic theory reveal a wavelength elongation > 60% and a propagation length increase > 140%, due to the simultaneous wavelength elongation and dissipation elimination in the suspended specimen. We have also examined HPPs in α-MoO3 with a negative phase velocity. The sample suspension shortens the HPP wavelength and simultaneously reduces the dissipation due to the unique permittivity tensor. The HPPs with improved figures of merits in the suspended specimen may be developed for nano-polaritonic circuits, biochemical sensing, emission engineering, and energy transfer.

Bulk lateral shearing interferometry for spatiotemporal study of time-varying ultrashort optical vortices

The spatiotemporal measurement of ultrashort laser beams usually involves techniques with complex set-ups or limited by instabilities that are unable to accurately retrieve the frequency-resolved wavefront. Here, we solve these drawbacks by implementing a simple, compact, and ultra-stable spatiotemporal characterization technique based on bulk lateral shearing spectral interferometry using a birefringent uniaxial crystal. We apply it to retrieve complex spatiotemporal structures by characterizing ultrafast optical vortices with constant and time-varying orbital angular momentum. This technique can operate in all the transparency range of the anisotropic elements, enabling the characterization in different spectral ranges like infrared, visible, or ultraviolet.

Shear direction switching phenomena in twisted nematic liquid crystal cells for novel differential interference contrast imaging systems

AbstractA lateral shear occurs between ordinary and extraordinary rays in general optical uniaxial crystals, and we can observe a double image through the crystal, indicating a typical birefringence phenomenon. Small lateral shears occur in typical liquid crystal (LC) cells under small voltage applications, where the molecular alignment direction is generally inclined. The small lateral shear is useful for differential interference contrast (DIC) imaging systems, although it must be negligible in a typical LC display panel. In particular, unique lateral shearing properties are exhibited by twisted nematic (TN) LC cells, which are popular and important LC display modes. The 45°‐oblique lateral shear occurs according to the direction of the surface molecular alignment, and the inclination direction (+45° or −45°) depends on the molecular twist direction. If it is possible to switch the twist direction in the TN cell, the lateral shear direction can be switched by 90°, and a full DIC imaging system can be attained because the normal DIC system can obtain one‐directional derivative information along the shear direction. In this work, twist direction switching phenomena in TN cells are investigated by applying a magnetic field in the direction parallel to the cell surface.