Biaxial Crystals Research Articles

Поверхностные электромагнитные волны Дьяконова на границе раздела анизотропных двуосных кристаллов

A general approach to analysis of Dyakonov surface waves at the interfaces of anisotropic biaxial crystals is proposed, taking into account arbitrary spatial orientation of the media tensors principal axes. This approach is based on the operator representation of macroscopic Maxwell equations corresponding to the quantum-mechanical equations for photon states in an inhomogeneous anisotropic media. Surface wave dispersion law is investigated in the most general case. It is established that the interface eigenmode dispersion is closely related to the dispersion of bulk waves in the partnering media, which is a specific feature of Dyakonov waves. The electromagnetic field spatial distribution is investigated in the direction orthogonal to the boundary plane. The surface wave angular existence domain is determined. It’s dependencies on the rotation angles of the media optical axes are studied as well.

Dyakonov Surface Waves at the Boundary of Anisotropic Biaxial Crystals

A general approach to analysis of Dyakonov surface waves at the interfaces of anisotropic biaxial crystals is proposed, taking into account arbitrary spatial orientation of the media tensors principal axes. This approach is based on the operator representation of macroscopic Maxwell equations corresponding to the quantum-mechanical equations for photon states in an inhomogeneous anisotropic media. Surface wave dispersion law is investigated in the most general case. It is established that the interface eigenmode dispersion is closely related to the dispersion of bulk waves in the partnering media, which is a specific feature of Dyakonov waves. The electromagnetic field spatial distribution is investigated in the direction orthogonal to the boundary plane. The surface wave angular existence domain is determined. It's dependencies on the rotation angles of the media optical axes are studied as well. Keywords: electromagnetic surface waves, interface photon states, anisotropic media, biaxial materials.

Controlling and Focusing In‐Plane Hyperbolic Phonon Polaritons in α‐MoO3 with a Curved Plasmonic Antenna

Hyperbolic phonon polaritons (HPhPs) sustained in polar van der Waals (vdW) crystals exhibit extraordinary confinement of long-wave electromagnetic fields to the deep subwavelength scale. In stark contrast to uniaxial vdW hyperbolic materials, recently emerged biaxial hyperbolic materials, such as α-MoO3 and α-V2 O5 , offer new degrees of freedom for controlling light in two-dimensions due to their distinctive in-plane hyperbolic dispersions. However, the control and focusing of these in-plane HPhPs remain elusive. Here, a versatile technique is proposed for launching, controlling, and focusing in-plane HPhPs in α-MoO3 with geometrically designed curved gold plasmonic antennas. It is found that the subwavelength manipulation and focusing behaviors are strongly dependent on the curvature of the antenna extremity. This strategy operates effectively in a broadband spectral region. These findings not only provide fundamental insights into the manipulation of light by biaxial hyperbolic crystals at the nanoscale but also open up new opportunities for planar nanophotonic applications.

Wide-angle acousto-optic devices based on isotropic light scattering in biaxial crystals

Using the example of a rhombic crystal of alpha-iodic acid, a detailed study of new variants of acousto-optic isotropic light scattering in oblique sections of biaxial crystals, whose refractive surface contains a concave portion, is carried out. For these cases, the frequency dependences of the Bragg angles and the ranges of acousto-optic interaction are calculated. The possibility of implementing a unique, simultaneously broadband and wide-angle variant of light scattering is established. It is shown that the two-dimensional transfer function of such acousto-optic geometry has a complex X-shaped structure that has no analogues among uniaxial crystals. The possibility of applying this diffraction regime in light beam spatial filtering devices is studied.

Neuromorphic computing based on an antiferromagnet-heavy metal hybrid structure under the action of laser pulses

The paper proposes a model of a neuromorphic processor, consisting of excitatory and processing neurons that are oscillators and detectors. The concept of neuromorphic computing, implemented by generating a spin current due to optical excitation of magnetic oscillations in an antiferromagnet is considered. The inverse spin Hall effect causes the generation of an electric current in the heavy metal layer. A constant driving current flows through the common bus. Magnetic oscillations in the receiving neuron occur due to the spin Hall effect. A biaxial nickel oxide crystal was used as a material for the base cells of AFM insulators and platinum was utilized as a heavy metal. The use of optical excitation can significantly increase the processing speed of neuromorphic computing with low power consumption. The presented model implements the simplest operations of neuromorphic computations, such as logical “OR”, “AND”.

Optical parametric generation in biaxial KTA crystal under pumping by YAG:Nd laser in arbitrary directions

Herein, on the basis of expressions for the refractive indices of isonormal waves, the possibility of performing collinear phase matching for optical parametric generation in arbitrary directions of a biaxial KTA crystal under pumping by radiation of a YAG:Nd laser is analyzed. The tuning curves that determine the tuning range of the signal and idler for type-I and II-type phase-matching and arbitrary angles θ and φ in cases where the tuning is carried out along the angle θ at a fixed angle φ and vice versa are calculated. The effective nonlinear coefficient is determined. It is shown that their maximum value is achieved аt a polar angle θ = 90° and type-II phase-matching. For the case of generation of eye-safe radiation the spectral and angular phase matching widths were estimated, as well as gain widths of KTA-OPO under monochromatic pumping.

Optical beam diffraction tensor in birefringent crystals

We demonstrate that anisotropy of Fresnel diffraction in a birefringent medium can be quantitatively characterized by a planar tensor. Eigenvectors of the tensor correspond to directions of minimum and maximum beam divergence. Zero eigenvalues exist for the slow eigenmode near the optic axis of biaxial crystals and correspond to autocollimated beam propagation along the cone of external conical refraction. Applications of the beam diffraction tensor are demonstrated for analysis of noncritical phase matching in acousto-optics and nonlinear three-wave mixing.

Measure by interferential conoscopy of the phase distribution acquired from conical diffraction

We have measured the Pancharatman phase difference between the electrical field emerging from the conical diffraction (CD) phenomenon in the KGd(WO2)4 (KGW) biaxial crystal and a vertical polarized reference, each field traveling in one arm of an interferentiel conoscope. This phase is obtained as the retardation introduced by a liquid crystal retarder in the reference beam which maximizes the interference intensity for each camera pixel. The full characterization of the Uˆkx,ky operator describing the CD was obtained including polarimetric measurements. We have found that the azimuthal variation of the eigen-values of the dielectric tensor was responsible for an azimuthal variation of the phase of the Uˆ operator. The link with the orbital angular momentum of the beam is provided in the cases of a uniformly polarized field and in a vector field.

Noncritical acousto-optic Bragg phase matching: analysis of orthorhombic and monoclinic crystal systems.

Anisotropic acousto-optic diffraction in crystals is the fundamental phenomenon that is used to design acousto-optic tunable filters. Noncritical and quasicollinear phase-matching geometries of Bragg acousto-optic diffraction are compared for acoustic symmetry planes in four crystal systems (tetragonal, trigonal, orthorhombic, and monoclinic). The results for uniaxial crystals are reviewed and generalized for biaxial crystals. It is shown that cubic frequency dependence on the Bragg angle exists in two symmetry planes of orthorhombic crystals and conditionally exists in the symmetry plane of monoclinic crystals. It is also shown that there are two points in the symmetry plane of monoclinic crystals where noncritical phase matching takes place in quasicollinear diffraction geometry that can be used to design high-resolution tunable filters. Phase-matching configurations in α-iodic acid and potassium gadolinium tungstate crystals are analyzed.

First-Principles Calculation of the Optical Rotatory Power of Periodic Systems: Application on α-Quartz, Tartaric Acid Crystal, and Chiral (n,m)-Carbon Nanotubes.

The self-consistent coupled-perturbed (SC-CP) method in the CRYSTAL program has been adapted to obtain electromagnetic optical rotation properties of chiral periodic systems based on the calculation of the magnetic moment induced by the electric field. Toward that end, an expression for the magnetic transition moment is developed, which involves an appropriate electronic angular momentum operator. This operator is forced to be hermitian so that the chiroptical properties are real. In our formulation, the trace of the optical rotatory power matrix is gauge-origin-invariant as long as the electric dipole transition matrix elements are obtained using the velocity (rather than position) operator. On the other hand, the component along the optic axis is invariant in general for uniaxial and biaxial crystals. Under the same conditions, these properties also do not depend on the so-called missing integers that occur in the treatment of the electric dipole moment of quasi-one-dimensional periodic systems or the analogue of missing integers for the case of higher dimensionality. Tests on a model H2O2 polymer confirm the formalism and, as desired, show that the calculated properties are independent of the size and definition of the unit cell. In addition, an empirical relation to a finite oligomer gauge-including atomic orbital (GIAO) calculation is found. Applications, with comparison to experiment, are carried for α-quartz, tartaric acid crystal, and carbon nanotubes. Future developments of this initial approach to chiroptical properties in the solid state are noted.

Temperature dependent refractive index, thermo-optic coefficient and birefringence of negative biaxial imidazolium l-tartrate non-linear optical crystal

Imidazolium L-tartrate (IMLT) single crystal has been grown by slow cooling seed rotation technique. The temperature dependent refractive index (RI) has been measured along the principal axes in the temperature range 30–125 °C. The prism coupling technique has been used to determine the refractive index with accuracy ~ 5 × 10−4. The transmission spectra depict good transparency in the range 340–1350 nm. The principal axes directions have been identified using polarized light microscopy. Principal directions have been found rotated by 44° in the orthogonal xz-plane with respect to the crystallographic x-axis. The generalized temperature dependent equations for the Sellmeier’s and thermo-optic (dn/dT) coefficients have been determined. The thermo-optic coefficients (TOC) in the above-specified range have been found to be negative and are ~10−5/°C. An important set of empirical relations between TOC and wavelength (407–1551 nm) has also been established which is useful for estimating TOC in the temperature range of 30–125 °C. Based on the birefringent measurement it has been confirmed that the IMLT crystal is a negative biaxial crystal.

Algorithm to visualize a 3D normal surface in anisotropic crystals and the polarization states of the o- and e-waves in uniaxial crystals

Of the many topics generally taught in undergraduate or graduate optics courses, the propagation of light through crystals with electrical anisotropy is one of the most difficult topics for students and for teachers who do not work in this field. In particular, the mathematics and equations are complex vectorial equations, and this complicates the visualization of the implications of the theory. Also, the standard textbooks and papers on the subject have led to some misconceptions on this problem by presenting results only for specific cases of the theory in graphical form. For example, it is a general belief that after refraction of an incident wave on the crystal, the polarization state of the two waves propagating inside the crystal, given by their displacement vectors D, are always orthogonal to each other. However, this is not the case, as explained and illustrated for uniaxial crystals by Alemán-Castañeda and Rosete-Aguilar [J. Opt. Soc. Am. A 33(4), 677–682 (2016)]. The purpose of this paper is to help students and teachers visualize the solution to Maxwell's equations in electrical anisotropic crystals. An algorithm has been written in mathematica so the reader can use it to visualize the normal surface in uniaxial and biaxial crystals. This algorithm can be used as the basis of computational projects for students to better understand the equations involved, or as a visualization tool for teachers in class.

Group velocity of light in biaxial crystals.

Based on the wave vector surface, we have derived the analytical expressions for the group velocity of light traveling in an optically biaxial crystal in an arbitrary direction. Our formulas are in terms of either the wave vector direction or the ray direction. An axis dispersion vector is introduced to specify the rotation of the dielectric frame in monoclinic and triclinic crystals, which is found to be responsible for the asymmetry of the group velocity surfaces of these two crystal systems when compared to their phase and ray velocity surfaces. Our formulas confirm that the group velocity of light in a nondissipative medium equals the ratio between the Poynting vector and the total energy density of the electromagnetic field. The group index of light is found to be decomposable into three parts: the ray index, the group index due to principal refractive index dispersion, and that due to axis dispersion. Numerical calculations are performed for the group velocity of light in ${\rm Sn}_2{\rm P}_2{\rm S}_6$ crystal at 550 nm wavelength. Our results show that the dispersion of the principal refractive indices has a considerable contribution to the group index.

Bricked Subwavelength Gratings: A Tailorable On‐Chip Metamaterial Topology

AbstractIntegrated metamaterials are redefining the capabilities of silicon photonic chips. In providing lithographic control over dielectric permittivity, dispersion and anisotropy, they are enabling photonic devices with unprecedented performance. However, the implementation of these materials at telecom wavelengths often requires a fabrication resolution of the order of 100 nm and below, pushing current wafer‐scale fabrication technology to its limits and hindering the widespread exploitation of on‐chip metamaterials. Herein, a subwavelength grating metamaterial with bricked topology is proposed, that provides lithographic control over the metamaterial dispersion and anisotropy using a single etch Manhattan‐like geometry with pixel dimensions up to 150 × 150 nm2, thereby easing the path toward fabrication at wafer‐scale. The behavior of these structures as biaxial crystals is analytically shown, validating their use in high performance on‐chip beam‐splitters. Through engineering of the metamaterial anisotropy tensor, the splitters are shown to exhibit sub‐decibel insertion losses and imbalance over a 400 nm design bandwidth, via 3D FDTD simulations. The excellent device performance is demonstrated over a 140 nm bandwidth, limited by the measurement setup.

Switching in a Biaxial Smectic A - like Phase

ABSTRACT Comments and the work presented in this paper aim at initiating discussion within the liquid crystalline community about the nature of different biaxial phases and their switching mechanisms. The mechanisms have the potential for applications in switching devices for displays and photonics. Claire Meyer et. al. interestingly report recently a fast Freedericksz-like transition of the secondary director in the biaxial Smectic Ab phase of a mixture of two compounds. Fast switching in liquid crystals occurs through a coupling of the biaxiality with the electric field. To realise this potential, one of the major goals of the liquid crystal community had been to discover biaxial nematic liquid crystals. In a biaxial liquid crystalline phase, the refractive indices along the three orthogonal axes are all different [n11≠ n22 ≠ n33] as opposed to these being different only along the two orthogonal directions n11 ≠ n22 = n33 in uniaxial nematics. In this notation 1, 2 and 3 are the three orthogonal axes that coincide with the major and the two minor directors. The biaxial nematic phase has been elusive for over half a Century. It has therefore proven to be almost impossible to meet the goal of achieving fast switching using biaxial nematics. Ferroelectric and antiferroelectric liquid crystals were discovered in 1975 and 1989 by R. Meyer in the USA and Atsuo Fukuda in Japan, respectively, for fast switching. These have been used in devices for niche but limited high-resolution applications as the devices using these liquid crystals suffered not only from achieving proper alignment at surfaces but also showed poor recovery of alignment following repeated cycles of switching.

Existence of solutions to incompressible biaxial nematic liquid crystals flows

The recent paper considers the incompressible hydrodynamic flow of biaxial nematic liquid crystal in dimensions N with N = 2 or 3. The unique local solutions are firstly derived for in dimensions 2 and 3. Then the unique global solution is obtained for and small initial energy: .

Asymmetry of the group velocity of light in monoclinic crystals.

We have proved that compared to phase velocity and ray velocity surfaces, the group velocity surface of a monoclinic crystal has a reduced symmetry, due to the loss of the two mirror planes that contain the crystallographic b axis. We have derived a formula for calculation of the group velocity of the extraordinary light traveling in a principal plane of a biaxial crystal, which takes into account the rotation of the dielectric frame due to frequency dispersion. The maximum asymmetry of the group velocity of light traveling in the a-c plane is found to be 2.4% at 365 nm in BiB3O6 and 1.4% at 550 nm in Sn2P2S6.

Approximated dielectric tensor of the biaxial α-SnSe crystal

We present the principal components of the dielectric tensor for α-SnSe biaxial single crystal in the spectral range from 0.74 to 6.42 eV at room temperature (300 K) using spectroscopic ellipsometry. Aspnes’ first-order approximation method was applied to obtain approximated pseudodielectric response from the pseudodielectric tensor measured at an angle of incidence of ϕ = 68.8°. Multilayer calculations were then performed to extract the pure dielectric tensor without surface roughness artifacts. The Tauc–Lorentz model was applied to describe the critical point structures, and the optical constants along the principal axes of biaxial α-SnSe single crystal can be now calculated at arbitrary wavelength for device applications.

THE COMBINED ELLIPSOMETRIC METHOD OF COMPLETE OPTICAL CHARACTERIZATION OF CRYSTALS. II. DETERMINATION OF THE OPTICAL CONSTANTS OF CRYSTAL

This part of the article describes the second stage of the combined ellipsometric method of complete optical characterization of crystals. The testing of the second stage was carried out on crystals of lithium niobate (LiNbO 3 ) and cadmium tungstate (CdWO 4 ). The obtained results of measurements of an optically uniaxial LiNbO 3 crystal fully confirmed the correctness of the proposed method and its applicability for optical characterization of crystals. In particular, the values of the principal refractive indices { n o = 2.280(±0.003), n e = 2.202(±0.002)} and birefringence {Δ n = – 0.0775(±0.0015)} of the LiNbO 3 crystal are in good agreement with the values of these quantities, obtained by other researchers by other methods. Studies of the optically biaxial CdWO 4 crystal were important for analyzing the accuracy of determining the optical constants. For generality of this analysis, measurements were performed in different measurement configurations at several angles of incidence of the laser beam. In particular, according to the results of measurements in two configurations (angle of incidence 45°), the following values of the principal refractive indices of the CdWO 4 crystal (doped from the melt 0.375 wt.% PbO) were obtained: n g = 2.249±0.002, n m = 2.185±0.002, n p = 2.130±0.008. Based on these values of n g , n m , and n p , the angle between the optical axes and the optical sign of the crystal were determined. It has been shown experimentally that the CdWO 4 crystal is a pronounced biaxial crystal with an angle between the optical axes close to 90°. Possible ways to improve the accuracy of determining the optical constants of crystals are also analyzed. Key words : ellipsometry, optical indicatrix, principal refractive indexes, uniaxial and biaxial crystals.

Passive Polarized Light Guiding and Thermally Induced Visible Fluorescence in Histidine Microstructures with Optical Switching Function

AbstractThe increasing interest in implantable medical devices that incorporate photonic components has accelerated the search for new, biocompatible optical materials at micro‐ and nano‐scale. This work proposes use of the polar amino acid L‐histidine as a candidate for bio‐photonic devices. L‐histidine is self‐assembled into diverse solid‐state crystallized microstructures, one of which—the elongated hexagonal microplate—is shown to have passive waveguiding capability of polarized light. The interaction of polarized light with histidine microplates having different orientations and thicknesses is studied from Stokes parameters and Mueller matrix. The linear birefringence of histidine microplates is estimated by using the theory of generalized Jones matrix for biaxial crystals. Visible fluorescence in heated histidine microplates is discovered and its origin is discussed. The phenomenon of passive waveguiding capability of polarized light by such an elongated hexagonal microplate means that the microplate can be used as a part of an optical switch. The findings show that besides the known chemical and biological characteristics of the amino acid histidine, it also has optical properties that can be exploited in multifunctional biophotonic applications, such as waveguides, polarizers, interconnects, and light sources.