Biaxial Crystals Research Articles

An effective method for calculating phase-matching conditions in biaxial crystals

We present an effective method for calculating phase-matching conditions in biaxial crystals, especially for nonlinear orthorhombic crystals. Exploiting the angle definition introduced by Japanese mathematician Kodaira Kunihiko, we deduce the angular relations in geometry and obtain the expressions of refractive indices depending on angular orientation of wave vector k and optical axis angle. Then, we directly calculate the phase-matching conditions with BIBO crystal in spontaneous parametric down-conversion (SPDC) process and gain the optimum phase matching schemes for the type I and type II. On its basis, we discuss the angular gradients of the pump and emission wave refractive index near the exact phase matching direction and compare the SPDC with double-frequency process in geometrical relations of the refractive index ellipsoids. This method based on angle-dependent refractive index can be applied to three-wave interactions. It is convenient to calculate the phase matching parameters without solving the quadratic Fresnel equations.

Multi-mode technique for the determination of the biaxial Y2SiO5 permittivity tensor from 300 to 6 K

The Y2SiO5 (YSO) crystal is a dielectric material with biaxial anisotropy with known values of refractive index at optical frequencies. It is a well-known rare-earth (RE) host material for optical research and more recently has shown promising performance for quantum-engineered devices. In this paper, we report the first microwave characterization of the real permittivity tensor of a bulk YSO sample, as well as an investigation of the temperature dependence of the tensor components from 296 K down to 6 K. Estimated uncertainties were below 0.26%, limited by the precision of machining the cylindrical dielectric. Also, the electrical Q-factors of a few electromagnetic modes were recorded as a way to provide some information about the crystal losses over the temperature range. To solve the tensor components necessary for a biaxial crystal, we developed the multi-mode technique, which uses simultaneous measurement of low order whispering gallery modes. Knowledge of the permittivity tensor offers important data, essential for the design of technologies involving YSO, such as microwave coupling to electron and hyperfine transitions in RE doped samples at low temperatures.

Transformation of vector beams with radial and azimuthal polarizations in biaxial crystals.

We present both experimentally and theoretically the transformation of radially and azimuthally polarized vector beams when they propagate through a biaxial crystal and are transformed by the conical refraction phenomenon. We show that, at the focal plane, the transverse pattern is formed by a ring-like light structure with an azimuthal node, this node being found at diametrically opposite points of the ring for radial/azimuthal polarizations. We also prove that the state of polarization of the transformed beams is conical refraction-like, i.e., that every two diametrically opposite points of the light ring are linearly orthogonally polarized.

Dyakonov hybrid surface waves at the isotropic-biaxial media interface.

Dyakonov surface waves (DSWs) at the interface of an isotropic dielectric material and a biaxial dielectric crystal were considered in the case in which two principal axes of the biaxial crystal lie in the plane of the interface. Both x-cut and y-cut biaxial crystals were considered, and all permittivity scalars were assumed to be real and positive. A rather simple expression to relate the components of the wave vector of a DSW was derived, and analytical expressions for the limit angles at which the DSWs can propagate and the Poynting vector components of the DSWs were obtained. These expressions were numerically investigated for several biaxial materials. Different conditions for the relative permittivity scalars at which the DSWs can exist were identified. As an example, DSWs can exist not only for the positive, but also for the negative y-cut biaxial crystals.

On the dual-cone nature of the conical refraction phenomenon.

In conical refraction (CR), a focused Gaussian input beam passing through a biaxial crystal and parallel to one of the optic axes is transformed into a pair of concentric bright rings split by a dark (Poggendorff) ring at the focal plane. Here, we show the generation of a CR transverse pattern that does not present the Poggendorff fine splitting at the focal plane, i.e., it forms a single light ring. This light ring is generated from a nonhomogeneously polarized input light beam obtained by using a spatially inhomogeneous polarizer that mimics the characteristic CR polarization distribution. This polarizer allows modulating the relative intensity between the two CR light cones in accordance with the recently proposed dual-cone model of the CR phenomenon. We show that the absence of interfering rings at the focal plane is caused by the selection of one of the two CR cones.

Polarization tailored novel vector beams based on conical refraction.

Coherent vector beams with involved states of polarization (SOP) are widespread in the literature, having applications in laser processing, super-resolution imaging and particle trapping. We report novel vector beams obtained by transforming a Gaussian beam passing through a biaxial crystal, by means of the conical refraction phenomenon. We analyze both experimentally and theoretically the SOP of the different vector beams generated and demonstrate that the SOP of the input beam can be used to control both the shape and the SOP of the transformed beam. We also identify polarization singularities of such beams for the first time and demonstrate their control by the SOP of the input beam.

Biaxial crystal α-BaTeMo(2)O(9): theory study of large birefringence and wide-band polarized prisms design.

α-BaTeMo(2)O(9) is a novel biaxial crystal with wide-band transmittance spectrum. The refractive index dispersion curves and birefringence of the α-BaTeMo(2)O(9) crystal were obtained in spectral range of 0.4~5 μm. The origin of the birefringence for the crystal has been calculated and interpreted on the basis of the crystal structure combined with theoretical studies. The polarized directions and formulations of refractive index of optical waves in biaxial α-BaTeMo(2)O(9) were investigated by solving the refractive index ellipsoid equations. Furthermore, polarized prisms based on the α-BaTeMo(2)O(9) crystal used in spectral ranges of 0.4~2.7 μm and 0.48~4.5 μm were designed and characterized. The extinction ratios of both prisms were determined to be larger than 10000:1, which would satisfy the practical requirements. The impacts on extinction ratio for biaxial and uniaxial crystals were also discussed. To our knowledge, it is the first report about biaxial crystals for the polarized prisms, and the results show that the α-BaTeMo(2)O(9) crystal is a promising material for polarized optical components, especially in the range of 3~5 μm.

Optical Properties of a Monoclinic Insulator Cu(H2O)2(en)SO4

Cu(H2O)2(en)SO4 was recently investigated especially for its magnetic properties: it is an insulating (with a calculated gap of about 2 eV) magnetically quasi-onedimensional spin S = 1/2 antiferromagnet (with the Neel temperature of 0.9K) [1 3]. In this paper we utilize the theoretical electronic structure obtained in [3] to calculate the macroscopic dielectric tensor and compare it to what can be inferred from Mueller-ellipsometry measurements (of the PCRSCRA type) carried out in the 190 to 1700 nm range (6.5 0.7 eV). The material crystal belongs to the monoclinic system and thus is optically biaxial, i.e. displays anisotropy. Contrary to orthorhombic crystals (biaxial crystals of highest crystallographic symmetry), the crystallographic axes of a monoclinic crystal do not x all the axes of the dielectric frame, de ned as the frame where the real part of the (generally complex) dielectric tensor is diagonal. This makes the situation complex on the one hand, but on the other hand more experimental features, such as the orientation of the dielectric frame, can be checked against theory.

Blue-detuned optical ring trap for Bose-Einstein condensates based on conical refraction.

We present a novel approach for the optical manipulation of neutral atoms in annular light structures produced by the phenomenon of conical refraction occurring in biaxial optical crystals. For a beam focused to a plane behind the crystal, the focal plane exhibits two concentric bright rings enclosing a ring of null intensity called the Poggendorff ring. We demonstrate both theoretically and experimentally that the Poggendorff dark ring of conical refraction is confined in three dimensions by regions of higher intensity. We derive the positions of the confining intensity maxima and minima and discuss the application of the Poggendorff ring for trapping ultra-cold atoms using the repulsive dipole force of blue-detuned light. We give analytical expressions for the trapping frequencies and potential depths along both the radial and the axial directions. Finally, we present realistic numerical simulations of the dynamics of a 87Rb Bose-Einstein condensate trapped inside the Poggendorff ring which are in good agreement with corresponding experimental results.

An Alternate Method for the Determination of the Raman Cross Sections of Optical Phonons in Uniaxial Crystals: Application to LiNbO<sub>3</sub>

The present paper is devoted to the derivation of an alternate and simple method based on the rotation of the crystal in view of the determination of the Raman cross-sections of optical phonon in uniaxial and biaxial crystals. The Raman polarisability tensor whose trace remains invariant under an orthogonal transformation is established as function of the crystal rotation position. The resulting angle dependent Raman scattered intensity is finally used to accurately describe the area under the peak which is measured from the polarised Raman spectra of the lithium niobate single crystal recorded under the backscattering scheme; The extracted parameters from the fit such as integrated areas are then plotted as functions of the crystal rotation angles. This allows to quantitatively determinate the relative phase and the relative values of the Raman tensor elements.

Acousto-optics of Biaxial Crystals

An original program is developed for examination of acousto-optic interaction in biaxial crystals. The program makes it possible to calculate for an arbitrary crystal cut all parameters of optical and acoustic waves, frequency dependences of the Bragg angles, acousto-optic figure of merit, as well as angular and frequency characteristics of the acousto-optic effect. The efficiency of the program is demonstrated by the example of an alpha-iodic acid crystal. It is shown that in the vicinity of optical axes the Bragg angle frequency dependences at the anisotropic diffraction have essentially other views in comparison with uniaxial crystals. Crystal cuts with maximal values of the acousto-optic figure of merit are found.

New Method to Calculate Spatial Distribution of Acousto-Optic Figure of Merit in Crystals

We propose a novel method to calculate acousto-optic gure of merit in crystals. Calculations are performed in laboratory coordinate system where Z′-axis is collinear with wave vector of ultrasound and the Fresnel equation is considered as an equation on the third component of refractive index vector. The method is applicable to both uniaxial and biaxial crystals. In this paper, we compared obtained values of acousto-optic gure of merit with values from literature data for uniaxial crystals such as paratellurite, lithium niobate, tellurium and for biaxial crystals such as lead and strontium tetraborates. Calculations in paratellurite were carried out for slow-shear acoustic wave propagating along [110] crystal axis. In lithium niobate crystal, we perform comparison with results for geometry of acousto-optic interaction where acoustic wave vector forms 88◦ angle with X crystal axis and 150.4◦ angle with Z crystal axis. In tellurium crystal, we investigate geometries applied in infrared de ectors. In SrB4O7 and PbB4O7 crystals we analyze acousto-optic characteristics of slow-shear mode propagating along [100] crystal axis. Spatial distributions of acousto-optic gure of merit and acoustic frequency for the mentioned acousto-optic interaction geometries are presented.

Characterizing conical refraction optical tweezers

Conical refraction occurs when a beam of light travels through an appropriately cut biaxial crystal. By focusing the conically refracted beam through a high numerical aperture microscope objective, conical refraction optical tweezers can be created, allowing for particle manipulation in both Raman spots, and in the Lloyd/Poggendorff rings. We present a thorough quantification of the trapping properties of such a beam, focusing on the trap stiffness, and how this varies with trap power and trapped particle location. We show that the lower Raman spot can be thought of as a single-beam optical gradient force trap, while radiation pressure dominates in the upper Raman spot, leading to optical levitation rather than trapping. Particles in the Lloyd/Poggendorff rings experience a lower trap stiffness than particles in the lower Raman spot, but benefit from rotational control.

Crystal System Determination from X-ray Diffraction of Magnetically Oriented Microcrystal Suspensions

A procedure for determining the crystal system of a microcrystalline powder is described. In this procedure, in situ X-ray diffraction measurements are performed on a microcrystal suspension oriented uniaxially under static and rotating magnetic fields. This is followed by the classification of the obtained diffraction images using a flowchart proposed in this study. To demonstrate the validity of this procedure, diffraction images were recorded for microcrystalline suspensions prepared from known crystal systems including triclinic (d-arabitol), monoclinic (cellobiose), orthorhombic (l-alanine), tetragonal (urea), trigonal (bismuth, calcite), hexagonal (zinc), and cubic (sodium chloride) systems. The crystals were classified into their respective crystal systems following the proposed procedure. The determined crystal systems for biaxial crystals were consistent with the reported crystal systems of the microcrystalline powders investigated. Herein, determination of the lattice parameters and space groups...

Polarization properties of lasing near an optical axis in the KGd(WO4)2:Nd biaxial crystal

Fluorescence and stimulated emission were obtained for propagation directions in the vicinity of the optical axis from the biaxial Nd-doped KGd(WO4)2 crystal. We visualized the peculiar role of the optical axis by fluorescence conoscopy. A fourth spectroscopic parameter due to the monoclinic symmetry was exhibited. Intra-laser-cavity conoscopy was performed in conjunction with the lasing in order to indicate the role of the elliptical modes. The lasing efficiency was found to be in agreement with the relative intensity of the left and right circular polarized components of the fluorescence near the optical axis.

Conical diffraction illumination opens the way for low phototoxicity super-resolution imaging

We present a new technology for super-resolution fluorescence imaging, based on conical diffraction. Conical diffraction is a linear, singular phenomenon, taking place when a laser beam is diffracted through a biaxial crystal. We use conical diffraction in a thin biaxial crystal to generate illumination patterns that are more compact than the classical Gaussian beam, and use them to generate a super-resolution imaging modality.While there already exist several super-resolution modalities, our technology (biaxial super-resolution: BSR) is distinguished by the unique combination of several performance features. Using BSR super-resolution data are achieved using low light illumination significantly less than required for classical confocal imaging, which makes BSR ideal for live-cell, long-term time-lapse super-resolution imaging. Furthermore, no specific sample preparation is required, and any fluorophore can be used. Perhaps most exciting, improved resolution BSR-imaging resolution enhancement can be achieved with any type of objective no matter the magnification, numerical aperture, working distance, or the absence or presence of immersion medium.In this article, we present the first implementation of BSR modality on a commercial confocal microscope. We acquire and analyze validation data, showing high quality super-resolved images of biological objects, and demonstrate the wide applicability of the technology. We report live-cell super-resolution imaging over a long period, and show that the light dose required for super-resolution imaging is far below the threshold likely to generate phototoxicity.

Device and method of optically orienting biaxial crystals for sample preparation

An optical instrument we refer to as the "biaxial orientation device" has been developed for finding the optical plane, acute bisectrix, and obtuse bisectrix in biaxial crystals by means of optically aligning conoscopically formed melatopes and measuring the angular coordinates of the melatopes, where the angular values allow for determination of the optical plane containing the optical axes using a vector algebra approach. After determination of the optical plane, the instrument allows for the sample to be aligned in the acute bisectrix or obtuse bisectrix orientations and to be transferred to a simple mechanical component for subsequent grinding and polishing, while preserving the orientation of the polished faces relative to the optical plane, acute bisectrix, and obtuse bisectrix during the grinding and polishing process. Biaxial crystalline material samples prepared in the manner are suitable for accurate spectroscopic absorption measurements in the acute bisectrix and obtuse bisectrix directions as well as perpendicular to the optical plane.

Calculation of phase-matching conditions based on angle-dependent refractive index in biaxial crystals

We present a straightforward method for the calculation of phase-matching conditions based on the angle-dependent refractive index in biaxial crystals. Considering the refractive indices relying on angular orientation of wave vector and optical axis angle, we acquire the numerical curves of phase-matching angles. We then obtain the effective nonlinear coefficient for a spontaneous parametric down conversion (SPDC) process in BiB3O6 (BIBO) crystal, and ascertain the optimal phase-matching directions for types I and II. Moreover, we focus on the angular gradient of the pump and emission wave refractive indices near the exact phase-matching direction, and compare the SPDC with the double frequency process in the geometrical relations of the refractive index ellipsoids. This method is superior in ascertaining the space distribution of pump and emission waves, and it is convenient for deciding the parameters of phase matching without solving the quadratic Fresnel equations.

X-ray Natural Circular Dichroism

Natural Circular Dichroism was only recently discovered in the x-ray range[1]. This effect stems from the interference terms which mix multipole transition moments of opposite parity: the Electric Dipole-Electric Quadrupole (E1.E2) and the Electric Dipole-Magnetic Dipole (E1.M1) exist only in structures with broken space inversion symmetry. The scalar E1.M1 term known to be responsible for Circular Dichroism at optical wavelengths is usually considered to be vanishingly small for core level spectroscopies. The E1.E2 interference term, on the contrary, can be large in the X-ray region, but it is a parity odd second rank tensor and therefore observable only in 13 non-centrosymmetric crystal classes. X-ray Natural Circular Dichroism has now been detected in the XANES region for several uniaxial and biaxial crystals. It can give access to the absolute configuration of chiral absorbing centers. On the other hand, Chiral-EXAFS, i.e. the analog of Magnetic-EXAFS for Natural Circular Dichroism has also been measured recently using a uniaxial optically active crystal of paratellurite (TeO2). Chiral-EXAFS originates from symmetry allowed multiple scattering paths. In this presentation, we wish to report on recent advances in X-ray natural circular dichroism and its applications. Determination of absolute configuration is illustrated with measurements of both E1.E2 and E1.M1 terms in chiral alpha-Ni(H2O)6·SO4 single crystals. Manifestation of X-ray optical acitivity in magnetoelectric crystals will be illustrated with various dichroisms measured at the Fe K-edge in multiferroic GaFeO3 crystal. Finally, we will review briefly the perspectives open by our experiments.

Crystal Structure Analysis of Magnetically Oriented D-Arabinitol Microcrystal

We have proposed magnetically oriented microcrystal array (MOMA) technique as a new technique of crystal structure analysis. With this technique, single crystal X-ray diffraction analysis is made possible from a microcrystalline powder. Biaxial crystals, having three different values of magnetic susceptibility (χ1>χ2>χ3), are aligned three dimensionally under a frequency-modulated elliptical magnetic field. Biaxial microcrystal suspended in an ultraviolet (UV) light-curable monomer matrix is aligned three dimensionally under the magnetic field, followed by consolidation of the alignment by the photopolymerization the matrix. Biaxial crystal group has three crystal systems: orthorhombic, monoclinic and triclinic systems. The analysis of crystals belonging to the triclinic system is important because ca. 23 % of organic crystals are triclinic. We have so far succeeded in determining crystal structures of orthorhombic and monoclinic systems by using the MOMA technique[1, 2, 3] but crystals of triclinic system have not been examined yet. Therefore, in this report, we attempt to determine the crystal structure of D-arabinitol, belonging to the triclinic system, by using the MOMA technique. 10 wt% D-arabinitol / XVL14 (UV light-curable monomer) suspension was subjected to 8-T magnetic field (the speed of rotation changed between 10 rpm and 40 rpm at every 900) and was consolidated by irradiation of UV light. The prepared MOMA was subjected to the X-ray diffraction measurement. The obtained diffraction spots were well resolved and the average of half widths was about 3.90. These results indicate that the D-arabinitol microcrystals were aligned three dimensionally in the MOMA and the high quality of alignment was achieved. These results indicate that the obtained diffraction patterns are equivalent to those obtained from corresponding single crystal.