Biaxial Crystals Research Articles

How to eliminate unwanted elasto-optical birefringence from optical devices

There often appears unwanted elasto-optical birefringence in optical devices such as electro-optical, magneto-optical modulators and sensors when they are manufactured and used. This kind of elasto-optical birefringence causes unwanted effect for optical device and needs to be removed. Based on the method of index ellipsoid analysis, we theoretically analyze elasto-optical effects in various point groups of optical crystals and glasses, and accordingly propose some methods to eliminate unwanted elasto-optical birefringences in optical crystals and glasses. Main conclusions show that for orthorhombic biaxial crystal and the light wave propagating along any one crystalline axis of the crystal, if there is no shearing stress and the two external normal stresses applied to the other two crystalline axes can keep a constant ratio related to crystal parameters including refractive index and photoelastic constants, then unwanted elasto-optical birefringence can be eliminated from relevant optical devices, typical crystals include potassium titanium oxide phosphate (KTiOPO4, KTP) crystal and rubidium titanium oxide phosphate (RbTiOPO4, RTP) crystal, which are usually used as electrooptic Q-switchers in laser systems. For all the uniaxial crystyals such as potassium dihydron phosphate (KH2PO4, KDP), beta-barium borate ( -BaB2O4, BBO) and lithiun niobate (LiNbO3, LN) crystals, cubic crystals of 43 m, 432, m3 m point groups such as bismuth germanate (Bi4Ge3O12, BGO) crystal, and optical glasses, if the two normal stresses applied to the x1- and x2- crystalline axes of the crystal are equal to each other and there is no shearing stress, or there exists only one normal stress applied to the x3- crystalline axis of the crystal, then for the light wave propagating along the x3- crystalline axis, unwanted elasto-optical birefringence in relevant optical devices can also be eliminated. The above-proposed method to remove unwanted elasto-optical birefringence is benificial to design, manufacture, and usage of related optical devices.

Transverse spin angular momentum of tightly focused full Poincaré beams.

We show theoretically that by tightly focusing a full Poincaré beam one can create states of light whose average spin angular momentum (SAM) is purely transverse. Moreover, the transverse SAM is significantly increased if a narrow annular aperture is inserted into the Poincaré beam. In this case the state with transverse SAM can exist over an extremely long distance along the optical axis. To avoid diffraction on the aperture and increase the light conversion efficiency we employ the phenomenon of conical diffraction in biaxial crystals to convert a Gaussian beam into a ring-shaped beam, with a high ratio of the ring radius to its width.

Conical refraction in a degenerated two-crystal cascade

When a collimated light beam is passed consequently along the optic axes of two identical biaxial crystals, the conical refraction produces in the focal image plane a specific light pattern consisting of a ring and a central spot. The ring is formed due to the additive action of two crystals, while the spot results from the reversed conical refraction in such a degenerated cascade arrangement. The relative intensity of these two components depends on the azimuth angle between the orientations of the crystals about the beam axis. It is shown that this dependence arises due to the interference of pairs of waves produced by conical refraction in two crystals. If a part of these waves is blocked by polarization selection of beam components, the dependence of the light pattern on the azimuth angle vanishes. In this case, the outgoing light profile consists of a ring and a central spot with fixed intensities so that the total beam power is divided equally between these two components. Depending on the applied polarization, the central spot appears either as a restored input beam or a charge-two optical vortex. The results of numerical simulations of the effect are in a very good agreement with the experimental observations.

Phase behavior of shape-changing spheroids.

We introduce a simple model for a biaxial nematic liquid crystal. This consists of hard spheroids that can switch shape between prolate (rodlike) and oblate (platelike) subject to an energy penalty Δε. The spheroids are approximated as hard Gaussian overlap particles and are treated at the level of Onsager's second-virial description. We use both bifurcation analysis and a numerical minimization of the free energy to show that, for additive particle shapes, (i) there is no stable biaxial phase even for Δε=0 (although there is a metastable biaxial phase in the same density range as the stable uniaxial phase) and (ii) the isotropic-to-nematic transition is into either one of two degenerate uniaxial phases, rod rich or plate rich. We confirm that even a small amount of shape nonadditivity may stabilize the biaxial nematic phase.

Effects of fiber‐surface treatment on the properties of hybrid composites prepared from oil palm empty fruit bunch fibers, glass fibers, and recycled polypropylene

ABSTRACTIn this article, we report the effects of hybridization and fiber‐surface modification on the properties of hybrid composites prepared from recycled polypropylene (RPP), coupling agents, oil palm empty fruit bunch (EFB), and glass fibers through a twin‐screw extruder and an injection‐molding machine. The surface of the EFB fibers was modified with different concentrations (10–15 wt %) and temperatures (60–90°C) of alkali solutions. The structure and morphology of the fibers were observed with the help of Fourier transform infrared spectroscopy and scanning electron microscopy. Different types of composites were fabricated with untreated, alkali‐treated, and heat‐alkali‐treated fibers. Comparative analysis of the mechanical, structural, morphological, and thermal properties of the composites was carried out to reveal the effects of treatment and hybridization. The analysis results reveal that composites prepared from the alkali‐treated (in the presence of heat) fibers show improved mechanical, thermal, and morphological properties with a remarkably reduced water absorption. Additionally, the crystallinity of RPP also increased with the development of biaxial crystals. The improvement of various properties in relation to the structures and morphologies of the composites is discussed. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 43049.

Perfect interferenceless absorption at infrared frequencies by a van der Waals crystal

Traditionally, efforts to achieve perfect absorption have required the use of complicated metamaterial-based structures as well as relying on destructive interference to eliminate back reflections. Here, we have demonstrated both theoretically and experimentally that such perfect absorption can be achieved using a naturally occurring material, hexagonal boron nitride (hBN) due to its high optical anisotropy without the requirement of interference effects to absorb the incident field. This effect was observed for p-polarized light within the mid-infrared spectral range, and we provide the full theory describing the origin of the perfect absorption as well as the methodology for achieving this effect with other materials. Furthermore, while this is reported for the uniaxial crystal hBN, this is equally applicable to biaxial crystals and more complicated crystal structures. Interference-less absorption is of fundamental interest to the field of optics; moreover, such materials may provide additional layers of flexibility in the design of frequency selective surfaces, absorbing coatings and sensing devices operating in the infrared.

Equivalent variational approaches to biaxial liquid crystal dynamics

Within the framework of liquid crystal flows, the Qian and Sheng (QS) model (Qian and Sheng 1998 Phys. Rev. E. 58, 7475. ( doi:10.1103/PhysRevE.58.7475 )) for Q -tensor dynamics is compared with the Volovik and Kats (VK) theory (Volovik and Kats 1981 Sov. Phys. 54, 122–126) of biaxial nematics by using Hamilton’s variational principle. Under the assumption of rotational dynamics for the Q -tensor, the variational principles underling the two theories are equivalent and the conservative VK theory emerges as a specialization of the QS model. Also, after presenting a micropolar variant of the VK model, Rayleigh dissipation is included in the treatment. Finally, the treatment is extended to account for non-trivial eigenvalue dynamics in the VK model and this is done by considering the effect of scaling factors in the evolution of the Q -tensor.

Conical diffraction thin crystal device on full-scene images

Conical diffraction is an interesting phenomenon that occurs in biaxial crystals. Although the existence of this conical diffraction has been understood for a very long time, it was not until recently that the first applications started to appear, and most of them focus on the manipulation of laser beams. However, the potential use of conical diffraction for all-optical processing in full-scene imaging devices was never addressed. In this article we present a prototype of a general-purpose optical device in order to investigate the applicability of conical diffraction to full-scene imaging. We also show that conical diffraction can obtain the derivative of an image with high resolution. This is the first proof of the theoretical capabilities of conical diffraction in full scenes, and it is just one of its many applications in the field of machine vision.

Implementation and performance of an in-line incomplete Stokes polarimeter based on a single biaxial crystal.

Due to the increasing interest of polarimetric information in numerous applications, different Stokes polarimeter designs are provided in the literature for the measure of light beam polarization. Recently, the concept of polarimeters based on the conical refraction (CR) phenomenon, occurring in biaxial crystals, was proposed. CR polarimeters are snapshot polarimeters that allow controlling the volume of data redundancy without an increase in the acquisition time. We present the implementation, calibration, and analysis of an incomplete CR-polarimeter optimized for the measure of linear polarizations. A simpler and cheaper experimental configuration is achieved, if compared with other polarimeters proposed in the literature. The suitability of the polarimeter is experimentally demonstrated and some of its benefits, such as its performance in low-intensity conditions, are discussed.

On the field-induced switching of molecular organization in a biaxial nematic cell and its relaxation.

We investigate the switching of a biaxial nematic filling a flat cell with planar homogeneous anchoring using a coarse-grained molecular dynamics simulation. We have found that an aligning field applied across the film, and acting on specific molecular axes, can drive the reorientation of the secondary biaxial director up to one order of magnitude faster than that for the principal director. While the π/2 switching of the secondary director does not affect the alignment of the long molecular axes, the field-driven reorientation of the principal director proceeds via a concerted rotation of the long and transversal molecular axes. More importantly, while upon switching off a (relatively) weak or intermediate field, the biaxial nematic liquid crystal is always able to relax to the initial surface aligned director state; this is not the case when using fields above a certain threshold. In that case, while the secondary director always recovers the initial state, the principal one remains, occasionally, trapped in a nonuniform director state due to the formation of domain walls.

Athermal directions and their dispersion in KGd(WO4)2 and KLu(WO4)2 crystals

An analysis of the existence of athermal properties for optically biaxial crystals KGd(WO4)2 and KLu(WO4)2 is performed and compared with that of KY(WO4)2 for monolithic and laser cavity configurations. Short-wavelength limits for athermal behavior in the principal planes of optical indicatrix are found. In KGd(WO4)2 they lie near or in the absorption band. In KLu(WO4)2, one of the two isonomal waves and both isonomal waves in the Np–Nm principal plane of KGd(WO4)2 for the laser cavity configuration have also long-wavelength limits. It is shown that for some wavelengths (one or two in the visible spectrum) and light wave polarization, the optical indicatrix axes can be athermal. In KLuW, for the monolithic configuration, the Np axis is athermal at three wavelengths, two of which lie in the IR region (0.843 and 1.975μm). All-space athermal directions are determined for KLu(WO4)2 at 2μm. For the monolithic configuration, they form a cone with its axis parallel to the Np axis and oval cross-section.

Generalized Jones matrix method for homogeneous biaxial samples.

The generalized Jones matrix (GJM) is a recently introduced tool to describe linear transformations of three-dimensional light fields. Based on this framework, a specific method for obtaining the GJM of uniaxial anisotropic media was recently presented. However, the GJM of biaxial media had not been tackled so far, as the previous method made use of a simplified rotation matrix that lacks a degree of freedom in the three-dimensional rotation, thus being not suitable for calculating the GJM of biaxial media. In this work we propose a general method to derive the GJM of arbitrarily-oriented homogeneous biaxial media. It is based on the differential generalized Jones matrix (dGJM), which is the three-dimensional counterpart of the conventional differential Jones matrix. We show that the dGJM provides a simple and elegant way to describe uniaxial and biaxial media, with the capacity to model multiple simultaneous optical effects. The practical usefulness of this method is illustrated by the GJM modeling of the polarimetric properties of a negative uniaxial KDP crystal and a biaxial KTP crystal for any three-dimensional sample orientation. The results show that this method constitutes an advantageous and straightforward way to model biaxial media, which show a growing relevance for many interesting applications.

Reexamination of the mean-field phase diagram of biaxial nematic liquid crystals: Insights from Monte Carlo studies.

Investigations of the phase diagram of biaxial liquid-crystal systems through analyses of general Hamiltonian models within the simplifications of mean-field theory (MFT), as well as by computer simulations based on microscopic models, are directed toward an appreciation of the role of the underlying molecular-level interactions to facilitate its spontaneous condensation into a nematic phase with biaxial symmetry. Continuing experimental challenges in realizing such a system unambiguously, despite encouraging predictions from MFT, for example, are requiring more versatile simulational methodologies capable of providing insights into possible hindering barriers within the system, typically gleaned through its free-energy dependences on relevant observables as the system is driven through the transitions. The recent paper from this group [Kamala Latha et al., Phys. Rev. E 89, 050501(R) (2014)], summarizing the outcome of detailed Monte Carlo simulations carried out employing an entropic sampling technique, suggested a qualitative modification of the MFT phase diagram as the Hamiltonian is asymptotically driven toward the so-called partly repulsive regions. It was argued that the degree of (cross) coupling between the uniaxial and biaxial tensor components of neighboring molecules plays a crucial role in facilitating a ready condensation of the biaxial phase, suggesting that this could be a plausible factor in explaining the experimental difficulties. In this paper, we elaborate this point further, providing additional evidence from curious variations of free-energy profiles with respect to the relevant orientational order parameters, at different temperatures bracketing the phase transitions.

Interferometric characterization of the structured polarized light beam produced by the conical refraction phenomenon

The interest on the conical refraction (CR) phenomenon in biaxial crystals has revived in the last years due to its prospective for generating structured polarized light beams, i.e. vector beams. While the intensity and the polarization structure of the CR beams are well known, an accurate experimental study of their phase structure has not been yet carried out. We investigate the phase structure of the CR rings by means of a Mach-Zehnder interferometer while applying the phase-shifting interferometric technique to measure the phase at the focal plane. In general the two beams interfering correspond to different states of polarization (SOP) which locally vary. To distinguish if there is an additional phase added to the geometrical one we have derived the appropriate theoretical expressions using the Jones matrix formalism. We demonstrate that the phase of the CR rings is equivalent to that one introduced by an azimuthally segmented polarizer with CR-like polarization distribution. Additionally, we obtain direct evidence that the Poggendorff dark ring is an annular singularity, with a π phase change between the inner and outer bright rings.

Fredericks transitions in biaxial nematics.

Much of our understanding (and applications) of biaxial nematic liquid crystals requires the study of the textural transformations in external electric or magnetic fields. To that end, one should employ theoretical approaches which could have bearing on the minimization problem of the multi-parametric free energy. The immediate shortcoming of the direct free-energy minimization (widely used for uniaxial nematics) is the need to resolve several non-linear constraints. To overcome this difficulty, in what follows we shall use the "angular velocity", which describes space rotations of the order parameter, and is in fact a vector internal curvature of the texture. This method provides a means to resolve the constraints imposed on the order parameter. Thus, we have obtained the set of equations to find all possible one-dimensional textures of biaxial nematics in the external field. To illustrate our method, we calculate the critical fields corresponding to some basic configurations for textural transitions in the biaxial nematics. We feel that this result could be useful to determine the intrinsic degree of biaxiality for liquid crystalline materials.

Conical refraction healing after partially blocking the input beam

In conical refraction, when a focused Gaussian beam passes along one of the optic axes of a biaxial crystal, it is transformed into a pair of concentric bright rings at the focal plane. We demonstrate both theoretically and experimentally that this transformation is hardly affected by partially blocking the Gaussian input beam with an obstacle. We analyze the influence of the size of the obstruction both on the transverse intensity pattern of the beam and on its state of polarization, which is shown to be very robust.

Voigt wave investigation in the KGd(WO4)2:Nd biaxial laser crystal

We have investigated the Nd3+-doped KGd(WO4)2 biaxial laser crystal for wave propagation directions in the vicinity of the optical axis at wavelengths tunable around 800 nm. The angular absorption distribution was found to be strongly anisotropic. Increasing absorption, the optical axis splits in two new ones able to propagate unchanged a left or a right circularly polarized light and able to propagate a circularly polarized Voigt wave with a linear spatial dependence. The intensities of the transmitted light in different configurations of polarizations were investigated. The angular displacement of the two optical axes versus the absorbed wavelengths was measured and explained with a single oscillator model. The light energy propagation was found distributed inside a crescent-shaped area.

Statistical thermodynamics of thermotropic biaxial nematic liquid crystals: An effective, molecular-field based theoretical description by means of a closed approximate form of the orientational partition function

In this work, we show that the use of a molecular-field approach and of a closed, effective (even though approximate) form of the orientational partition function, leads to trustworthy predictions of order parameters and other important thermodynamic functions (as heat capacity, orientational internal energy and entropy) of real and/or virtual biaxial nematic mesophases. As a matter of fact, when the partition function Z is explicitly known, all about the thermodynamics of the studied systems becomes in principle accessible, since the thermodynamic functions can be directly calculated through the usual formulas provided by the statistical mechanics. We were successful in obtaining such an approximate expression for Z that works well and allows for almost instantaneous, reliable simulations (it is worthwhile to emphasize that, being available in the present case an analytical expression of Z, the derivatives occurring in the statistical mechanics formulas can be calculated analytically and instantaneously). Several examples of the performances of our approach are presented where, besides the second-rank order parameters, also heat capacities and changes in entropy and internal energy are quantitatively assessed, often for the first time, for the treated cases; moreover, an evaluation of some of the most important fourth-rank order parameters for the treated phases has been carried out. The results are good and our treatment proves to be suitable and promising also for future studies.

Light propagation in biaxial crystals

We present a formalism able to predict the transformation of light beams passing through biaxial crystals. We use this formalism to show both theoretically and experimentally the transition from double refraction to conical refraction, which is found when light propagates along one of the optic axes of a biaxial crystal. Additionally, we demonstrate that the theory is applicable both to non-cylindrically symmetric and non-homogeneously polarized beams by predicting the transformation of input beams passing through a cascade of biaxial crystals.

Variable two-crystal cascade for conical refraction.

The cascade conical refraction occurs when a collimated light beam is passed consequently along the optic axes of several biaxial crystals arranged in a series. For commonly used optical arrangements, the general structure of light emerging from such a cascade is rigorously determined by the used crystals, leaving few possibilities for the variations of the established light pattern. A simple modification of a two-crystal arrangement where one of the two crystals is placed beyond the imaging lens is reported. This modification adds an extreme versatility to the effect and allows one to tune continuously the actual cascade parameters. As a result, practically any pattern of two-crystal cascade conical refraction can be obtained for any pair of biaxial crystals.