Abstract: A heat-dissipating structure for an optical isolator is capable of suppressing an increase in temperature caused by light absorption in a magnetic garnet crystalline film by radiation fins extending from the inside of an external heat conducting cover. The heat-dissipating structure for the optical isolator is formed by housing a magnetic garnet crystalline film (12), first and second heat conductive plates (6, 7, 8 and 9) and magnet 18 in the external heat conducting cover, placing the radiation fins (10 and 11) on the second heat conductive plate, attaching the first heat conductive plates (6 and 7) onto either side of the magnetic garnet crystalline film, arranging the second heat conductive plates (8 and 9) on the outer surface of the first heat conductive plates, and passing the radiation fins through guide openings (2a and 2b) in the isolator holder 2 to the outside of the external heat conductive cover from the extracting opening (3c) to be brought into contact with the outer grooves (4d and 5d).

Abstract: A method for manipulating light comprises receiving an incoming beam of light at a tunable optical device, the tunable optical device comprising an organic material having an optical property that can be selectively varied under the influence of an external bias. The method further comprises applying a selected external bias to the tunable optical device to change an optical property of the tunable optical device. The method also comprises controlling an optical property of a beam of light exiting the tunable optical device as a result of the selected external bias.

Abstract: An imaging apparatus includes a controller executing instructions to form a latent image, and a print engine. The print engine includes a laser source, a micro-electromechanical system (MEMS) device, and a module for mounting the MEMS device. The print engine is communicatively coupled to the controller and configured to form the latent image using the laser source and the MEMS device. The module includes a base having a first support and a second support, the second support having a support guide feature; and a bracket attached to the MEMS device. The bracket has a central axis, a first end, and a second end, the second end having a bracket guide feature, the first end being affixed to the first support to form a cantilever arrangement. The support guide feature engages the bracket guide feature to form a sliding joint having a sliding axis substantially parallel to the central axis.

Abstract: An active optical filter transmits or blocks light according to whether or not a magnetic field is applied, and functions as an optical filter transmitting light having a predetermined wavelength when light is transmitted according to a magnetic field. The active optical filter includes: an optical filter layer for transmitting or blocking light according to whether or not a magnetic field is applied; and a magnetic field applying unit surrounding the optical filter layer for applying a magnetic field to the optical filter layer. The optical filter layer has a multi-layer thin layer structure which is formed of two kinds of thin layers having different respective refractive indices and sequentially and periodically stacked on a substrate.

Abstract: A Faraday rotator having a magnet member constituted of a first magnet standing magnetized in the direction perpendicular to the optical axis and taken toward the optical axis, a second magnet standing magnetized in the direction perpendicular to the optical axis and taken against the optical axis, and a third magnet disposed between these magnets and standing magnetized in the direction parallel to the optical axis and taken toward the first magnet from the second magnet. A through-hole (hollow spaces) inside which a Faraday element is disposed, is provided through the center of these magnets and, where the length of the first magnet and that of the second magnet in the optical-axis direction are both represented by L2 and the length of the third magnet in the optical-axis direction is represented by L3, the relationship of the following Expression (1) is established: L2/10?L3?L2.

Abstract: A Faraday rotator mirror which is compact, allows high workability of manufacturing and has high reliability and high coupling efficiency is provided. The Faraday rotator mirror comprises a graded-index fiber, a Faraday rotator and a reflector mirror, wherein light incident via the graded-index fiber passes through the Faraday rotator to be reflected on the reflector mirror, and the reflected light passes through the Faraday rotator and emerges through the graded-index fiber.

Abstract: An apparatus, method, system, and computer-program product for producing magneto-optic materials in the blue and green wavelengths. The apparatus includes a substrate generally transparent to a light signal including a component at a predetermined visible frequency; a stack of optical multilayers overlying the substrate for transmitting the component with at least about forty percent power therethrough and having at least about twenty-four degrees of Faraday rotation per micron for the predetermined visible frequency less than about six hundred nanometers. The method includes processes for the manufacture and assembly of the disclosed materials, with the computer program product including machine-executable instructions for carrying out the disclosed methods.

Abstract: A magnetic photonic crystal for providing asymmetry of spatial frequencies in the propagation of light is provided. The crystal is formed from at least two materials having different indices of refraction which are aligned along the longitudinal axis of the crystal. And arranged in an array whose symmetry does not include a spatial inversion operator such that (x,y)==/=(?x,?y). One or more of the materials forming the array is magnetic such that the magnetic group representation of the array does not include time inversion as a symmetric operator. In operation, when the magnetic material forming the material is magnetized, the group velocity property of light propagated in one direction along the axis of the array is different from the group velocity property of light transmitted in an opposite direction through the array. The magnetic photonic crystal may be used, for example, as an optical memory device or a high speed modulator/demodulator.

Abstract: A magneto-optical device is provided with a non-magnetic substrate, a magneto-optical crystal embedded in recessed portions formed in the surface of the non-magnetic substrate at positions where pixels are to be located, and a partitioning wall monolithic with the non-magnetic substrate and magnetically separating the magneto-optical crystal from each other at the position of a gap between the pixels, wherein the entire surface of the magneto-optical device is flattened.

Abstract: A polarization controlling apparatus includes a permanent magnet itself or a permanent magnet to which a part capable of being magnetized is applied, an electromagnet capable of changing the magnitude of a magnetic field to be generated thereby, and a Faraday rotation effect element. The Faraday rotation effect element is disposed at a position at which an interaction magnetic field acts on the Faraday rotation effect element. The interaction magnetic field is produced by an interaction between a magnetic field generated by the permanent magnet and a magnetic field generated by the electromagnet. The Faraday rotation effect element thereby produces a Faraday rotation effect on inputted light. The magnitude of the interaction magnetic field in the Faraday rotation effect element is varied by a magnetic field component generated by the electromagnet to vary the amount of the Faraday rotation effect to be had on the inputted light.

Abstract: A flaw detection apparatus includes a coil for producing an alternating-current magnetic field for flowing eddy currents in a magnetic material; a magneto-optical element disposed at the center of an inner peripheral portion of the coil and having a reflective film at an end face thereof opposed to the face of the member to be flaw-detected; an optical fiber for entering light from a light source into the magneto-optical element toward the reflective film via a circulator; an optical fiber for entering reflected light reflected by the reflective film into an analyzer via the circulator; a photoelectric conversion element for converting output light of the analyzer into an electrical signal; and a computing device for processing an output signal of the photoelectric conversion element and detecting a flaw of the member to be flaw-detected, based on the rotation angle of the plane of polarization of the reflected light.

Abstract: A latching magnetic structure in the resonant cavity of magneto-photonic crystal films with in-plane magnetization. Also disclosed is a method for the fabrication and observation of a latching magnetic structure.

Abstract: A thick film bismuth doped rare earth iron garnet greater than 50 ?m in thickness with a growth-induced uniaxial anisotropy less than zero, such that all the magnetic domains in the film have their magnetization vectors in the plane of the film. A preferred embodiment comprises a film of composition Bi1.13Gd1.36Lu0.51Fe4.55Ga0.45O12. Films with such anisotropy solve the problem of devices and sensors that require a continuously varying Faraday rotation without the effective insertion losses that are inherent to discrete perpendicular domains. A similar effect can be achieved with a film of perpendicular domains by launching the light in the plane of the thick film in a non-waveguiding mode as opposed to the conventional perpendicular direction.

Abstract: A reflective magnetic display includes a magnetic material layer region formed between front and rear substrates, wherein the magnetic material layer region has magnetic particles that reflect or absorb incident light when magnetic moments are randomly oriented and reflect or transmit the incident light in, accordance with polarization of the incident light, when the magnetic moments are aligned in a direction and an electrode that is designed to apply a magnetic field inducing a magnetic moment alignment on the magnetic material layer region in accordance with electrical operation.

Abstract: An optical isolator includes a birefringent material and a Faraday rotator. The birefringent material receives a forward light propagating in a forward direction and a backward light propagating opposite to the forward direction. The birefringent material has an optical axis, wherein the forward light has a first polarization aligned perpendicular to the optical axis and is configured to pass the first birefringent material substantially along the forward direction. At least a portion of the backward light has a second polarization not perpendicular to the optical axis. The first birefringent material can displace the backward light to form a first displaced backward light. A Faraday rotator can rotate the forward light, and the backward light or the first displaced backward light by a same predetermined angle along the rotation direction.

Abstract: A light beam scanner may include a polymeric material and a soft magnetic material.

Abstract: Methods and systems for PMD compensation in an optical communication system are implemented by transmitting multiple optical signals through a common optical conduit to an optical compensator that adjustably rotates the polarization states of the multiple optical signals and transmits the rotated optical signals to an optical receiver. The receiver, upon sensing an excessive error condition, commands the optical compensator to change the polarization state of rotation, which changes the PMD profile of the received optical signals.

Abstract: An integrated micro-optical system includes at least two wafers with at least two optical elements provided on respective surfaces of the at least two wafers, at least one of the two optical elements being a spherical lens. The resulting optical system presents a high numerical aperture. One of the optical elements may be a refractive element formed in a material having a high index of refraction.

Abstract: A variable focal length lens (12) includes a central transparent elastic portion (120) having a first wall (1200) and a second wall (1202) intersecting an optical axis and a peripheral portion (122) surrounding the body. The first wall and the second wall joined with the periphery form a container (124). The container is filled with magnetic fluid (126).

Abstract: An optical element comprises a fluid chamber and a device for providing a magnetic field over at least a portion of the fluid chamber The fluid chamber has side portions and end portions, and contains a first fluid and a second fluid. The fluids are non-miscible and the second fluid is capable of being influenced by a magnetic field. The end portions of the fluid chamber are connected together only by the side portions.

Abstract: Methods for optical isolation in high peak power fiber-optic systems prevent damage to a facet within a fiber-optic isolator caused by back-reflected light from, for example, an optical amplifier. Preventing damage to the facet may include expanding a mode area of the back-reflected light and/or reducing a change in refractive index.

Abstract: Magneto-optical crystals of each pixel of a magneto-optical device are magnetically and completely separated, and the entire surface thereof is flattened. Disclosed is a magneto-optical device including a non-magnetic substrate, a magneto-optical crystal embedded in recessed portions formed in the surface of the non-magnetic substrate at positions where pixels are to be located, and a partitioning wall monolithic with the non-magnetic substrate and magnetically separating the magneto-optical crystal from each other at the position of a gap between the pixels, wherein the entire surface of the magneto-optical device is flattened.

Abstract: Provided are a magnetic display pixel using an optical shutter having a magnetic material layer, and a magnetic display panel including the magnetic display pixel. The magnetic display pixel includes a magnetic material layer that transmits light when a magnetic field is applied and does not transmit the light when the magnetic field is not applied, a first electrode arranged on a lower surface of the magnetic material layer, a second electrode arranged on an upper surface of the magnetic material layer, and a spacer arranged at a side surface of the magnetic material layer to electrically connect the first electrode and the second electrode.

Abstract: An optical element comprises a fluid chamber, the fluid chamber having side and end walls, and contains a first fluid (20) and a second fluid (22). The fluids are non-miscible and the second fluid is capable of being influenced by a magnetic field. A device (19) for providing a magnetic field over at least a portion of the fluid chamber is provided, with the magnetic field being capable of moving the second fluid so that the positions of the first an second fluids in the fluid chamber are altered. The second fluid may be a ferrofluid.

Abstract: Provided are an active reflective polarizer and a magnetic display panel comprising the same. The active reflective polarizer includes a magnetic material layer in which magnetic moments are arranged in one direction when a magnetic field is applied; and electrodes for applying magnetic fields to the magnetic material layer in two different directions.

Abstract: A method for modifying the polarization state of light with a magnetically uniaxial crystal which initially has a specific multidomain structure, wherein light enters via predefined areas of the crystal, and wherein a magnetic field pulse having a magnetic intensity H1 is applied to the crystal (1), wherein the crystal (1) is transformed into a reversible monodomain state. In order to obtain an enlargement of the useful aperture, while at the same time keeping switching and response times to a minimum, a retention magnetic field of transition of the crystal (1) into a reversible monodomain state, wherein the magnetic field intensity H2 is lower than the magnetic field intensity H1 and the reversible monodomain state is maintained.

Abstract: A condenser lens is incorporated into the end portion of a magnetic field measuring apparatus including a magneto-optical crystal. Alternatively, the end portion of the magnetic field measuring device includes an optical fiber having a core diameter smaller than that of a normal single-mode optical fiber.

Abstract: A system and method to detect angular rotation, linear displacement and/or surface deformations is presented. The method is based on the ability of a linear polarized light to interact with magnetic materials and to change its polarization angle due to Faraday effect. A basic structure of the system consists of a magneto-optic (MO) film with a two-domain structure and a single domain wall which are generated by gradient magnetic field produced by opposite polarity permanent magnets placed near the film. An AC magnetic field applied perpendicular to the MO film surface causes the magnetic domain wall in the MO film to oscillate at the same frequency. This leads to a detected output AC modulated signal. By measuring the temporal changes in this signal, information on angular rotation, linear displacement and/or surface deformation can be obtained.

Abstract: Methods and apparatus for optical isolation in high peak power fiber-optic systems prevent damage to a facet within a fiber-optic isolator caused by back-reflected light from, for example, an optical amplifier. Preventing damage to the facet may include expanding a mode area of the back-reflected light and/or reducing a change in refractive index.

Abstract: Methods and systems for PMD compensation in an optical communication system are implemented by transmitting multiple optical signals through a common optical conduit to an optical compensator that adjustably rotates the polarization states of the multiple optical signals and transmits the rotated optical signals to an optical receiver. The receiver, upon sensing an excessive error condition, commands the optical compensator to change the polarization state of rotation, which changes the PMD profile of the received optical signals.

Abstract: A hard magnetic Bi-substituted rare earth iron garnet material with excellent Faraday rotary moment, temperature property, wavelength property and insertion loss is provided. A Bi-substituted rare earth iron garnet material having a chemical composition of (Bi3-a-b-cGdaTbbYbc) Fe(5-w)MwO12 (where, M is at least one element selected from the group consisting of Ga, Al, Ge, Sc, In, Si and Ti, 0.5?a+b+c?2.5, 0.2?w?2.5) can be provided with hard magnetism and have excellent Faraday rotary moment, temperature property, wavelength property and insertion loss.

Abstract: A single side band modulation device includes a first Mach Zehnder interferometer and a second Mach Zehnder interferometer. The first Mach Zehnder interferometer includes at least two output arms, and the second Mach Zehnder interferometer includes at least two output arms. Terminals of the output arms are connected with one another.

Abstract: A microelectrical mechanical system (MEMS) actuator having electrically conductive coils that create first magnetic fields that are opposed by a second magnetic field is disclosed. The actuator includes two coils having dual, interspersed Archimedean spirals. Within an actuator, one coil is arranged with spirals that proceed clockwise, while the other coil is provided with spirals that proceed counterclockwise. An electrically conductive bridge mechanically couples the two coils of each actuator to a mirror. Opposing magnetic fields are created to provide a force that urges the coils to expand so that the outermost portions of the coil extend upward, away from the substrate, and lift the bridge and mirror. Control current may then be modulated to increase and decrease the coil's magnetic field strength thereby increasing and decreasing the coil's extension to raise and lower relative to the substrate.

Abstract: A Faraday rotator for a Faraday isolator with an input polarizer, with an output polarizer, with a roller-shaped optical crystal that is arranged therebetween and that is arranged symmetrical to its axis of symmetry, with a right hollow cylinder that surrounds this and has a hollow space made of a permanent magnetic material, which cylinder is axially magnetized and the magnetic field of which extends in the hollow space approximately parallel to the axis of symmetry that runs in only one direction from the north pole to the south pole, and with terminal magnets attached to each of the two end faces in the plane perpendicular to the y- and z-directions of the axis of symmetry, each of which is embodied as a hollow right cylinder and has a through-aperture in the extension of the axis of symmetry, is characterized in that each terminal magnet is largely radially magnetized with regard to the axis of symmetry at least by region, in that the one of the two terminal magnets is magnetized radially from interior to

Abstract: There are provided a manufacturing method of an optical device excellent in expediency, and a technique for stably manufacturing a high performance optical device. After a single crystal film which constitutes a Faraday rotator and can exhibit a substantially rectangular magnetic hysteresis, is obtained, the single crystal film is magnetized in a state where this single crystal film is incorporated in an optical device such as an optical isolator. By performing a magnetizing step after the Faraday rotator is incorporated in the optical device, it becomes unnecessary to discriminate between the front and back surfaces of the single crystal film, and the characteristics of the optical device are also improved.

Abstract: According to one aspect of the invention, a method and apparatus for polarizing electromagnetic radiation is provided. The electromagnetic radiation may be divided into first and second portions, substantially all of the first portion may be linearly polarized in a first direction and substantially all of the second portion may be linearly polarized in a second direction, the first direction being substantially orthogonal to the second direction. The linear polarization of at least one of the first and second portions may be changed such that substantially all of both of the first and second portions are linearly polarized in a third direction. At least one of the first and second portions may be redirected such that substantially all of both the first and second portions are propagating in a fourth direction.

Abstract: Augmented magic sphere rotator permanent magnetic structures are provided by augmenting a magic sphere augmented with an interior magnet that attains significant decreases in mass, bulk and length of the optically active element. Also provided is a multiple augmented magic sphere rotator permanent magnetic structure with two augmented magic spheres positioned in tandem that provides an advantageously significant reduction in mass. The augmented magic sphere rotator permanent magnetic structures of the present invention provide the desirable advantages of specifically decreased mass and bulk of the structure and decreased total length of the optically active elements. The augmented magic sphere rotator permanent magnetic structure and multiple augmented magic sphere rotator permanent magnetic structure can be used as Faraday rotator structures.

Abstract: A magnetic, single-axis crystal is used to modify the polarization state of light, whereby light passes through pre-determined areas of the crystal. To change the polarization state of the light, a magnetic field pulse is applied to the crystal with a magnetic field amplitude, at which the crystal no longer remains in the single-domain state at the end of the pulse, but returns to a defined multi-domain state that is determined by the direction of the applied magnetic field, thus achieving large usable apertures of the switching element and extremely short change periods. According to the invention, energy is only required for the change operation and not for maintaining a specific state.

Abstract: A photo magnetic field sensor includes a Faraday rotator made of a paramagnetic material, a polarizer, an analyzer, a light-irradiating element, and a light-sensing element. The Faraday rotator is made of a paramagnetic garnet single crystal including at least Tb and Al.

Abstract: An optical element having characteristics suitable for use in a Faraday rotator has bonded to each of the adjacent radiation-receiving surfaces thereof with a chamber or water conducting conduit affixed therein includes a water cooled Faraday rotator element having: a base magnet plate substrate; a flowing water filled conduit fixed on the top surface of the base magnet plate substrate; a ferrite waffle iron grid with a binary top surface which reflects radiation and which has a bottom surface; and a fused copper layer fixed between the bottom surface of the ferrite waffle iron grid and the flowing water filled conduit.

Abstract: An optical sensor unit, free from electrical noise, includes a sensor case which has both lateral sides having high frequency connectors mounted thereon, and a metallic plate mounted inside the case. The metallic plate has both ends connected to inner conductors of the high frequency connectors, and its upper surface having a current and a voltage sensor unit mounted thereon for measuring the high frequency current and voltage, respectively. The current sensor unit includes total-reflection mirrors and a current sensor, and the voltage sensor unit includes further total-reflection mirrors and a voltage sensor. The voltage sensor has its upper surface having an electrode provided thereon to be connected to the sensor case. The laser light from outside is input to the current and voltage sensor units over optical fibers. The signal light output from the current and voltage sensor units is taken outside on output optical fibers.

Abstract: An optical isolator is disclosed for transmitting light in a first direction and blocking light in a second direction along an optical pathway. The optical isolator includes an input polarizer having a pass axis at first angle, an output polarizer having a pass axis at second angle, a Faraday rotator material between the polarizers having a Verdet constant and an axis of maximum length therethrough, generation means for generating a magnetic field around and inside the rotator material, and at least one reflector configured to define an optical length through the rotator material which is longer than the axis therethrough. The optical pathway length through the rotator material, the magnetic field strength, and the Verdet constant are selected so as to rotate light through the Faraday rotator material from the first angle to the second angle.

Abstract: A Faraday rotator of multilayer film type is provided which can achieve excellent optical characteristics with a reduced number of layers. In the Faraday rotator, a metal reflection film, a periodic dielectric multilayer film made of silicon dioxide SiO2 and tantalum pentoxide Ta2O5, a magneto-optical thin film, and another periodic dielectric multilayer film made of tantalum pentoxide Ta2O5 and silicon dioxide SiO2 is formed sequentially. Light incident on a polarizer goes therethrough, is reflected at the metal reflection film while traveling trough the periodic dielectric multilayer films, and goes through an analyzer to exit out.

Abstract: A variable optical filter comprises a first polarizer, a first phase difference element operable to generate a phase difference, a variable Faraday rotator operable to impart a variable Faraday rotation, a second phase difference element operable to generate a phase difference, and a second polarizer, wherein said polarizers, said variable Faraday rotator, and said phase difference elements are arranged in the mentioned order along the optical axis, and wherein when the angles formed by the optic axes of said first and second phase difference elements and the transmitted polarization azimuth of the first polarizer are assumed respectively to be ?1 and ?2, these ?1 and ?2 are set to different angles.

Abstract: There are provided a small optical deflector that can be driven at a high speed with a low voltage, provides a large angle of deflection, has a low distortion even in high speed operation and has a high static flatness of a reflective surface, and a method of producing the optical deflector. The optical deflector drives a movable plate relative to a supporting substrate to deflect a light incident on a reflective surface and has a configuration in which at least two recesses are formed in a surface of the movable plate on which the reflective surface is not formed, and a magnetic material is provided in the recesses.

Abstract: This application describes optical monitoring devices and applications in optical systems for monitoring various optical parameters of light, including the signal to noise ratio, the degree of polarization, and the differential group delay (DGD).

Abstract: An optical modulation element is capable of forming a reflective diffraction grating in which heights of a plurality of elements each having a reflecting surface periodically change. The reflecting surfaces of at least one of the plurality of elements are driven in a direction of height by piezoelectric elements. The plurality of elements each having the surface as the reflecting surface are two-dimensionally arrayed by juxtaposing long sides. A rear surface side of an effective reflecting portion of each of the elements is fixed to the piezoelectric element.

Abstract: An object of the invention is to easily realize an optical element using an etalon type structure, capable of changing a periodic transmission wavelength characteristic in an axial direction of transmissivity, and also capable of changing a periodic characteristic with respect to wavelength. To this end, a transmission wavelength characteristics variable optical element according to the invention comprises: a light interference section including a pair of wedge shape magneto-optic crystals arranged with taper faces thereof in close contact, that can change a distance between reflecting films formed on parallel planes of the magneto-optic crystals, by relatively moving the magneto-optic crystals by movable sections, permanent magnets for applying a fixed magnet field to the pair of magneto-optic crystals, an electromagnet for applying a variable magnetic field in a direction different to the fixed magnetic field, and a variable current source controlling the current flowing into the electromagnet.

Abstract: Optical devices including a Faraday rotation devices improved in wavelength and temperature characteristics and an optical attenuator reduced in wavelength dependence and temperature-dependent loss. The Faraday rotation device has permanent magnets magnetized in an axial direction of through-holes, and Faraday elements having a same Faraday rotation direction with respect to a same magnetization direction. The permanent magnets are directed in the same magnetization direction along an optical path, where part of the Faraday elements are accommodated in the through-hole of the permanent magnet, and the remaining Faraday elements are arranged between the magnets, whereby the Faraday elements are to be applied by magnetic fields in opposite directions. For a device variable in Faraday rotation angle, an electromagnet is provided. An input fiber collimator and polarizer are provided on an input side of with the Faraday elements while an analyzer and output fiber collimator are on an output side.

Abstract: A magnetooptic element whose size is essentially that of a lattice, namely several angstroms in size of magnetic material and which at the same time has its exhibiting magnetooptic effect detectable is provided along with a magnetooptic disk, a memory device and a magnetooptical picture or image display with a storage capacity of several terabits per square inch or more, each using such a magnetooptic element. The magnetooptic element utilizes a gigantic effective magnetic filed based on a spin chirality formed by geometrically configuring the spin orientation and crystallographic structure of a certain solid material.

Abstract: A biological implantable pressure sensor element comprises a fixed volume pouch formed by a sealed, flexible, impermeable membrane comprising therewithin a gel mass contained in a gel volume, said gel being hydrated with an aqueous solution comprising an agent having at least a first and a second NMR-detectable form, the proportion of the first to the second form of the agent in the gel volume being determined by their electrolytic interaction with the gel, whereby when an external pressure is applied to the sensor element a d (chemical shift)/d(.sigma./K) greater than 0.0001 ppm is attained, wherein .sigma. is the external pressure and K is the modulus of the gel. A kit contains sterile, individually wrapped sensor elements.