Beam Diffraction Research Articles

Optical vortex beam controlling based on fork grating stored in a dye-doped liquid crystal cell.

In this paper, we investigate the generation and controlling of the optical vortex beam using a dye-doped liquid crystal (DDLC) cell. The spatial distribution of the quasi-sinusoidal orientation of the liquid crystal molecules creates a quasi-sinusoidal phase grating (PG) in the DDLC cell. Depending on the incident light pattern, Trans to Cis photoisomerization of the dye molecules affects the orientation of the liquid crystal molecules. To do so, an amplitude fork grating (FG) is used as a mask, and its pattern is stored in the cell by a pattern printing method as the PG. One of the particular features of the stored grating in the cell is its capability in the diffraction efficiency controlled by the applied electric field. The results show, based on the central defect in the FG pattern, the diffracted probe beam in different orders is optical vortices. As a new technique, this type of stored pattern acts like an amplitude grating but according to the results, its structure is in fact a PG. This technique leads to the vortex beam switching capability by applying an electric field to the cell. The results show that by applying 22V, all the diffraction orders vanish. Meanwhile, the vortex beams reappear by removing the applied voltage. The diffraction efficiency of the vortex beams as well as its generation dependency on the polarization of the incident beam studied. The maximum efficiency of the first diffraction order for linear polarized incident beam was obtained at 0V, about 8%. Based on the presented theory, a simulation has been done which shows the Cis form of the dye molecules has been able to change the angle of LC molecules on average about 12.7°. The study of diffracted beam profiles proves that they are electrically controllable vortex beams.

Reduction of Crosstalk Errors in a Surface Encoder Having a Long Z-Directional Measuring Range

A modified two-axis surface encoder is proposed to separately measure both the in-plane displacement and the Z-directional out-of-plane displacement with minor crosstalk errors. The surface encoder is composed of a scale grating and a small-sized sensor head. In the modified surface encoder, the measurement laser beam from the sensor head is designed to be projected onto the scale grating at a right angle. For measurement of the X- and Y-directional in-plane scale displacement, the positive and negative first-order diffracted beams from the scale grating are superimposed on each other in the sensor head, producing interference signals. On the other hand, the Z-directional out-of-plane scale displacement is measured based on the principle of a Michelson-type interferometer. To avoid the influence of reflection from the middle area of the transparent grating, which causes periodic crosstalk errors in the previous research, a specially fabricated transparent grating with a hole in the middle is employed in the newly designed optical system. A prototype sensor head is constructed, and basic performances of the modified surface encoder are tested by experiments.

Diffraction of Gaussian and Laguerre-Gauss beams from a circular aperture using the moment expansion method.

A method based on the distribution theory is introduced to compute the Fresnel diffraction integral. It is applied to the diffraction of Gaussian and Laguerre-Gauss beams by a circular aperture. Expressions of the diffracting field are recast into a perturbation series describing the near- and far-field regions.

Droplet transition from non-axisymmetric to axisymmetric shape: Dynamic role of lubrication film in a rectangular microfluidic channel

In the past 20 years, droplet microfluidics is burgeoning in many chemical and biological applications due to the unique capability of droplets to act as confined containers. Confinement is ensured even in the case of squeezed droplets within microchannels much smaller than droplet volumes due to the presence of a lubrication thin film that prevents contact between droplets and the channel walls. The thickness of the lubrication film depends on the dynamics of the entire microfluidic system, affecting the actual droplet's shape and velocity. Therefore, this film is extensively studied to obtain insight into the dynamics of flowing droplets, especially when confined in small channels. Circular cross section channels are the most studied for their axial symmetry, but practical applications present most likely non-axisymmetric channels, as a result of fabrication processes, such as soft lithographic rectangular channels. The latter showed unique transitional morphological behavior of droplets, which assumes an axisymmetric or non-axisymmetric shape during their flow inside a non-axisymmetric channel, depending on the lubrication film. This work gives a comprehensive experimental characterization of the dynamics of the lubrication film during the droplet shape transition. We settled on a novel approach based on the optical diffraction of a localized light beam provided by two-facing optical waveguides integrated with the microfluidics circuit. The technique allows for studying the dynamics of flowing droplets and their relationship with the lubrication film thickness. Additionally, this experimental system enables a precise definition of two regimes of lubrication film, and the critical capillary number at which the transition occurs.

Acousto-optical modulation of airy light beams in crystals

The non-collinear diffraction of Airy light beams on ultrasound in the regime of weak and strong acousto-optical (AO) interaction is investigated. Expressions are obtained for the complex amplitudes of diffracted waves in the general case of an anisotropic medium. It is shown that with an increase in the dimensionless parameter of the Airy beam, the efficiency of Bragg diffraction decreases. At the same time, however, the shape of the modulation curve remains unchanged. It is established that the greatest efficiency of anisotropic Bragg diffraction is achieved for a case when the diffracted Airy beam propagates along the front of the ultrasonic wave. It is shown that the efficiency of AO diffraction of Airy beam on an amplitude-modulated wave is determined by the diffraction efficiencies of constant components in a diffracted beam.

Self-Calibration of a Large-Scale Variable-Line-Spacing Grating for an Absolute Optical Encoder by Differencing Spatially Shifted Phase Maps from a Fizeau Interferometer

A new method based on the interferometric pseudo-lateral-shearing method is proposed to evaluate the pitch variation of a large-scale planar variable-line-spacing (VLS) grating. In the method, wavefronts of the first-order diffracted beams from a planar VLS grating are measured by a commercial Fizeau form interferometer. By utilizing the differential wavefront of the first-order diffracted beam before and after the small lateral shift of the VLS grating, the pitch variation of the VLS grating can be evaluated. Meanwhile, additional positioning errors of the grating in the lateral shifting process could degrade the measurement accuracy of the pitch variation. To address the issue, the technique referred to as the reference plane technique is also introduced, where the least squares planes in the wavefronts of the first-order diffracted beams are employed to reduce the influences of the additional positioning errors of the VLS grating. The proposed method can also reduce the influence of the out-of-flatness of the reference flat in the Fizeau interferometer by taking the difference between the measured positive and negative diffracted wavefronts; namely, self-calibration can be accomplished. After the theoretical analysis and simulations, experiments are carried out with a large-scale VLS grating to verify the feasibility of the proposed methods. Furthermore, the evaluated VLS parameters are verified by comparing them with the readout signal of an absolute surface encoder employing the evaluated VLS grating as the scale for measurement.

An Ultra-Precision Absolute-Type Multi-Degree-of-Freedom Grating Encoder.

An absolute-type four-degree-of-freedom (four-DOF) grating encoder that can simultaneously measure the three-axis pose (θx, θy, θz) and one-axis out-of-plane position (Z) of an object with high accuracy is demonstrated for the first time in this research. This grating encoder is composed of a stationary reading head and a movable grating reflector. A light beam from the reading head is projected onto the grating, and three diffracted beams (0th-, +1st-, and -1st-order) are generated, collimated, and received by three separate quadrant photodetectors (QPDs). The information of θx, θy, θz, and Z is coded into spot positions of these three diffracted beams on the QPDs. Thus, the modeling and decoupling algorithms were investigated, and an independent calculation of these four-DOF absolute positions was theoretically guaranteed. A prototype was then designed, constructed, and evaluated. Experimental results verified that the proposed grating encoder could achieve the absolute measurement of four-DOF θx, θy, θz, and Z with an accuracy of sub-arcseconds and sub-micrometers. To the best of our knowledge, the proposed encoder in this research is the first one to achieve absolute simultaneous measurements of four-DOF position and pose with a large measurement range. The success of this new grating encoder can benefit various multi-DOF positioning applications, especially for large-scale synthetic aperture optics (SAO), including stitching off-axis parabolic mirrors and pulse compression grating.

Porosity-related high-cycle fatigue strength of nickel-base single crystals: Fatigue experiments and electron back-scattered diffraction analysis

The fatigue limit of nickel-base single crystal (NBSX) is experimentally studied at an elevated temperature of 980 °C. The crack initiation position is revealed as the casting pores in the single crystal under scanning electron microscope (SEM), and distinct “fish-eye” region is observed on the long cycle fatigue fracture surface. The failure mechanism is explored around the “fish-eye” by adopting the focused ion beam (FIB) and electron backscatter diffraction (EBSD) technique. The crystalline motion and the fatigue crack initiation mechanism around the initiation pore are revealed by conducting microscopic analyses.

Fire gilding investigation on early medieval copper-based jewellery by focused ion beam (FIB) on FEG-SEM

The study of ancient gilding is often problematic, as the gilding layers are soft and prone to deformation during sample preparation. In this respect, focused ion beam (FIB) milling on a field emission gun scanning electron microscope (FEG-SEM) provides poorly invasive in situ sampling. The operating process is here detailed and applied on gilded medieval copper-based elite jewellery (10th century) from Prague Castle. Obtained cross-sections and slices of gilded samples were investigated up to nanometer scale without gilding layer deformation. By coupling structural observation with elemental X-ray analysis (EDS) and electron beam diffraction (EBSD), FIB FEG-SEM provided new data on the physical–chemical characteristics of the gilded layer. The gilding has a two-layer metallurgical structure containing a quaternary Au (Hg, Cu, Ag) alloy corresponding to the gold solid solution fcc phase, and a submicrometric inner sublayer formed by a Au-Cu phase, relative to the interdiffusion of copper from the substrate during the fire gilding process. The applied temperature for gilding can be estimated at c. 400 °C. Sintering of the mercury-gold amalgam globules during the fire heating is highlighted. The precise characterisation of the gilding layers provided useful comparative parameters for identifying fire gilding skill levels and assessing the overall quality of the archaeological pieces.

Spatial structure of the refracted field of a Gaussian light beam at total internal reflection.

The two-dimensional spatial structure of a stationary monochromatic refracted field is studied theoretically for the case of its exciting in a transparent homogeneous medium by incidence of a Gaussian light beam under total internal reflection. For that, the exact solution of refracted field in the form of a Fourier integral is used. It is shown that this spatial structure exhibits properties characteristic of the fields in strongly inhomogeneous and absorbing media: field attenuation as it propagates deep into the medium, noticeable diffraction beam divergence near the boundary itself, non-rectilinear nature of propagation in the medium, and non-exponential attenuation along its depth.

Manufacturing of (Al–10Zn) / TiB2 in-situ nanocomposites by reactive liquid metallurgy and hot-extrusion for enhanced interfacial bonding and mechanical properties

This work systematically deals with the development of an (Al–10Zn) die-casting alloy reinforced with in-situ synthesized hexagonal-shaped TiB2 nano-rods through casting and hot-extrusion processes. The cast specimens were extruded at 673 K with an extrusion ratio of 2:1 to orient the micro-texture, generate sub-grains within grains, reorder the reinforced in-situ TiB2 nanoparticles in the matrix, and engender strain fields to improve the mechanical properties. The nanoscale hexagonal TiB2 nano-rods (∼89 nm length and 14 nm edge) were synthesized by the chemical reaction of two halide salts (K2TiF6 and KBF4) with (Al–10Zn). The fabricated AMNCs were characterized using diffracted beams (XRD), scattered beams (FESEM and EBSD) and transmitted beams (TEM) received from the specimen. The diffracted beams from the X-rays reveal the formation of a TiB2 phase with a major α-Al phase and an individual Zn phase. The scattered beams from FESEM and EBSD revealed the homogenous distribution of TiB2 with less particle-free spacing, refinement of grains to an ultrafine level, and the absence of imperfections such as voids and interfacial de-bonding. The strain fields were observed through transmitted beams in the TEM analysis which were engendered by the thermal misfit between the matrix and TiB2 reinforcement. Among the fabricated AMNCs, (Al–10Zn) + 6 wt% TiB2 nanocomposite exhibited higher mechanical strength (160 MPa UTS) whereas (Al–10Zn) + 4.5 wt% TiB2 nanocomposite retained the ductility with improved strength (151.7 MPa UTS and 40% elongation). The strengthening mechanisms were computed using the (a) Zheng and Chen model and (b) Modified Cylne model to estimate the contribution of individual strengthening, and compared with the experimental results. The grain size strengthening contributed more to the total strength owing to the Zener pinning effect by in-situ TiB2 nano-rods.

Multi-plane photophoretic trapping of airborne particles with a multi-linear optical trap

We investigate the possibility of multi-plane photophoretic trapping of airborne light-absorbing particles using a multi-linear optical trap created with a cylindrical lens. The diffraction of a Gaussian beam on the edge of the lens leads to the generation of a set light lines with decreasing intensities in a transverse plane. Each of the shaped light lines can be used for trapping of different particles because of the photophoretic forces acting on the trapped particles depend on the light intensity. We show that larger particles cannot be trapped by light lines with decreased intensity, while smaller particles can. In addition, initial laser power attenuation leads to intensity fading of the generated non-main light lines and considerable decreasing in trapping robustness which causes to the escape of the smaller particles trapped in these light lines. All these results were experimentally confirmed and can be used for implementation of passive sorting of particles based on their physical properties.

Antifouling paint formulations with ZnO and Fe2O3 nano-paints for marine applications

The specific objective of the work is to develop antifouling paint formulations for coating marine vessels and structures using nanoparticles as functional additives. The Preparation of nano paints was undertaken by embedding the ZnO and Fe2O3 nanoparticles in linseed alkyd resin and mixing them with soya lecithin, mineral turpentine oil, and also thickener was also added. By using these various nano paints formulations, fouling properties was reduced with increased anti-bacterial properties based on which the coatings were examined for their corrosion properties. The development of antifouling paints with nanoparticles as biocides is expected to significantly improve the efficacy of antifouling paints.The results obtained suggest that with an increase in the concentration of nanoparticles, there was an improvement in the antifouling and anti-corrosion. It was also observed that the mild steel specimens were coated with antifouling paint formulations when immersed in the seawater for 120 days for testing and the properties were observed by utilizing Scanning electron microscopy, SEM - EDX, X-ray beam Diffraction, and Fourier transform infrared spectroscopy. It found an improvement in anti-fouling showed by Fe2O3 coated specimens and an improvement utilizing ZnO when contrasted with bare paint.

Design and Testing of a Compact Optical Angle Sensor for Pitch Deviation Measurement of a Scale Grating with a Small Angle of Diffraction

The design and testing of different optical heads were performed to evaluate the pitch deviation of a diffraction scale grating with a small diffraction angle. Based on the proposed pitch deviation evaluation method employing optical angle sensors based on laser autocollimation, a modified optical head with position-sensitive detectors (PSDs) is first designed and constructed by following the conventional optical configuration. Owing to the small angle of diffraction of the first-order diffracted beams, the modified optical head has a large working distance, resulting in poor sensor stability. Therefore, a novel and compact optical head employing a pair of small prisms is designed and developed to shorten the working distance of the optical head. An additional modification was also made to the developed compact optical head in such a way that collimator objectives (COs) in the laser autocollimation units are removed to improve the sensor sensitivity. Experimental comparisons were conducted using the three types of optical heads to verify the feasibility of the developed optical angle sensor with PSDs.

Double-Resolved Beam Steering by Metagrating-Based Tamm Plasmon Polariton.

We consider Tamm plasmon polariton in a subwavelength grating patterned on top of a Bragg reflector. We demonstrate dynamic control of the phase and amplitude of a plane wave reflected from such metagrating due to resonant coupling with the Tamm plasmon polariton. The tunability of the phase and amplitude of the reflected wave arises from modulation of the refractive index of a transparent conductive oxide layer by applying the bias voltage. The electrical switching of diffracted beams of the ±1st order is shown. The possibility of doubling the angular resolution of beam steering by using asymmetric reflected phase distribution with integer and half-integer periods of the metagrating is demonstrated.

Theoretical study on the diffraction-based generation of a 2D orthogonal lattice of optical beams: physical bases and application for a vortex beam multiplication.

A comprehensive theoretical study on the generation of a 2D orthogonal lattice of optical beams based on the near-field diffraction and Talbot effect is presented. First we investigate the near-field diffraction of an optical beam with a finite lateral extension from an infinite 2D orthogonal grating. It is shown that the resulting diffraction patterns over the Talbot planes depend on the following parameters: the period and opening ratio (OR) of the grating, wavelength and spatial spectral bandwidth of the incident beam, and the propagation distance. In terms of these parameters, we find multiplication conditions: the certain conditions under which a 2D orthogonal lattice of the Fourier transform of the incident beam is generated on the Talbot planes. Therefore, if the incident beam is Fourier-invariant and all the established multiplication conditions are fulfilled, the intensity profile of each of the individual Talbot images resembles the intensity profile of the incident beam. We consider the Laguerre-Gaussian beams having zero radial index as an important class of the vortex beams. We explicitly show that these beams are Fourier-invariant and we calculate their spatial spectral bandwidth. As a result, in the illumination of a 2D orthogonal binary grating with this kind of vortex beam, a 2D orthogonal lattice of the incident optical vortex is generated at the Talbot planes. Considering the obtained multiplication conditions, for the first time, to our knowledge, we determine a multiplication interval. This interval covers the propagation distances at which the vortex beam multiplication occurs. Moreover, we obtain the maximum possible value of the grating's OR for the realizations of the vortex multiplication. It is shown that both the multiplication interval and the maximum value of the OR depend on the topological charge (TC) of the incident beam. With the aid of some practical examples and defining a multiplication quality factor, the mentioned results are verified quantitatively. In addition to the vortex beam multiplication effect, we consider another interesting phenomenon that results from the interference of the grating's first diffraction orders. We call this phenomenon the first diffraction orders interference (FDOI) effect. We show that both the multiplication and the FDOI effects occur simultaneously but at different propagation distances. It is also shown that the multiplication and FDOI intervals separate and distance from each other by increasing the TC of the incident beam.

Optical Enhancement of Diffraction Efficiency of Texas Instruments Phase Light Modulator for Beam Steering in Near Infrared.

Phase light modulator (PLM) by MEMS mirror array operating in a piston-mode motion enables a high-speed diffractive beam steering in a random-access and flexible manner that makes a lidar system more intelligent and adaptive. Diffraction efficiency is determined by the range of the piston motion of the MEMS array; consequently, a larger range of the piston motion is required for beam steering in infrared, such as for lidar. We demonstrated how the range of the piston motion is optically enhanced by a factor of two with a light-recycling optics based on Talbot self-imaging. The proposed optical architecture extends the usable range of the wavelength so that a MEMS-PLM designed for visible wavelength is applicable for a high-efficiency beam steering at an infrared wavelength of 1550 nm with an improved diffraction efficiency of 30%.

Thickness profiling of electron transparent aluminium alloy foil using convergent beam electron diffraction.

Convergent beam electron diffraction (CBED) was used to profile the thickness of aluminium alloys foils prepared by using the twinjet electropolishing method. The two-beam CBED condition was obtained by exciting the and aluminium diffracted g-vector. The aluminium alloy foil thicknesses were calculated at different distances from the sample hole edge. In areas where only one Kossel-Möllenstedt (K-M) minima fringe was obtained, the thickness was determined by matching the experimental with simulated convergent beam diffraction patterns. In areas far away from the sample edge, the thickness of foils was high enough to generate at least two (K-M) minima fringes, required for linear regression fitting.

Spectrally Scanning LiDAR Based on Wide-Angle Agile Diffractive Beam Steering

Spectral scan, or beam steering by only wavelength tuning enables inertia-less fast-scanning LiDAR, while the field of view is fundamentally limited by the total available wavelength range and the dispersion ability of common gratings. Here, we propose to relieve the restriction by combining a diffraction grating and a low-cost diffractive element, which enables wide-angle two-dimensional beam steering. An FoV far beyond the reach of other spectral scan methods can be achieved. Several diffractive elements samples are fabricated to demonstrate spectrally scanning field of views of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7.7^{\circ } \times 10^{\circ }$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7.7^{\circ } \times 29^{\circ }$ </tex-math></inline-formula> from an 100-nm wavelength tuning range. Also, to show the potential to further extend the spectral scan range, blazed diffractive elements are fabricated with high diffraction efficiency, which corresponds to a spectral scan range up to 40.3°. Based on the structure, a solid-state coherent LiDAR system is built. Three-dimensional imaging with mm-level range resolution is demonstrated.

Probing order within disorder in oxide glasses and liquids by quantum beam diffraction

Probing order within disorder in oxide glasses and liquids by quantum beam diffraction