Double Diffraction Research Articles

Design of waveguide with double layer diffractive optical elements for augmented reality displays

We investigated a diffraction optical waveguide structure with a double layer coupling configuration. This double layer-coupled diffraction optical waveguide structure modulates light information through wavefront modulation for propagation within the optical waveguide and then reproduces the light information through further wavefront modulation, thus achieving optical information transmission. Analysis indicates that the theoretical maximum field of view can reach 90° × 90°. With an actual field of view set to 53° × 53°, an entrance pupil size of 3.2 × 3.2 mm², an eye relief of 10 mm, and 50 pupil expansion, the system’s total energy transmission efficiency is 37%, with field of view uniformity at 91% and uniformity within the eye movement range reaching 97%.

Effect of metastable precipitate phase transformation on reheat cracking in SS347H welding

Reheat cracking occurred in the welded heat affected zone (HAZ) of the SS347H tube during high temperature applications of approximately 600 °C. The reheat cracks occur when the inside of the grain is strengthened, causing grain boundary embrittlement. In this study, the intra-granular strengthening phase transformation of the HAZ causing the reheat crack was analyzed using TEM.The hardness of SS 347H HAZ with cracks is measured to be 221HV on average, which is about 25HV higher than 196HV of HAZ without cracks. This intra-granular strengthening is due to the formation of intra-granular precipitate phases. The precipitated phase is ultimately NbC, but undergoes an intermediate phase transformation due to diffusion of Nb and C components. The phase transformation consists of the following steps: “(i) SA (solution annealing), (ii) Zone A, (iii) Zone B, and (iv) NbC precipitation.”This is a process in which Nb/C components diffuse and segregate at the reheating temperature from a solid solution state of Nb/C components, and NbC with a size of several tens of nanometers is precipitated. As metastable phases, Zones A and B exist in the intermediate process of precipitation, which is the strengthening stage where intra-granular hardness is maximized. Zone A and B in the pre-precipitation stage means that a new lattice plane is formed as the segregation of component elements forms coherency with the matrix. The relationship between the base and new lattice planes is confirmed by Double Diffraction in the TEM diffraction diagram.The root cause of reheat cracking in SS 347H HAZ is believed to be the intra-granular strengthening phase caused by zone A and zone B as a metastable phase transformation in an intermediate stage before NbC precipitation. In order to suppress reheat cracking, it is desirable to precipitate stable NbC from the metastable phases of Zones A and Zone B through stabilization heat treatment.

Double diffraction imaging of x-ray induced structural dynamics in single free nanoparticles

Because of their high photon flux, x-ray free-electron lasers (FEL) allow to resolve the structure of individual nanoparticles via coherent diffractive imaging (CDI) within a single x-ray pulse. Since the inevitable rapid destruction of the sample limits the achievable resolution, a thorough understanding of the spatiotemporal evolution of matter on the nanoscale following the irradiation is crucial. We present a technique to track x-ray induced structural changes in time and space by recording two consecutive diffraction patterns of the same single, free-flying nanoparticle, acquired separately on two large-area detectors opposite to each other, thus examining both the initial and evolved particle structure. We demonstrate the method at the extreme ultraviolet (XUV) and soft x-ray Free-electron LASer in Hamburg (FLASH), investigating xenon clusters as model systems. By splitting a single XUV pulse, two diffraction patterns from the same particle can be obtained. For focus intensities of about 2×1012 W cm−2 we observe still largely intact clusters even at the longest delays of up to 650 picoseconds of the second pulse, indicating that in the highly absorbing systems the damage remains confined to one side of the cluster. Instead, in case of five times higher flux, the diffraction patterns show clear signatures of disintegration, namely increased diameters and density fluctuations in the fragmenting clusters. Future improvements to the accessible range of dynamics and time resolution of the approach are discussed.

University students’ recognition of typical wave optics patterns

The recognition and distinction of typical interference and diffraction patterns are among the expected learning outcomes of studying wave optics. Previous studies have reported high school students’ difficulties with this task. In this study, we investigated university students’ ability to distinguish typical wave optics patterns obtained by the double slit, single slit, and diffraction grating. We also used eye tracking to obtain an insight into the distribution of students’ visual attention during the task. The results showed that university students had similar difficulties in recognizing wave optics patterns as high school students. They mostly struggled with identification of the double-slit interference patterns and diffraction grating patterns of monochromatic light while they were more successful in recognition of the diffraction pattern of white light on an optical grating and single-slit diffraction patterns. The eye-tracking data also revealed that students spent more time attending colourful than grey patterns in questions regarding diffraction of white light on an optical grating, thus suggesting that they were aware that the diffraction grating separates white light into colours. In questions regarding monochromatic light patterns, students overall mostly attended the single-slit diffraction pattern probably because of its distinct central maximum. Furthermore, the longer fixation duration for patterns compared to the text implies that students found it easier to extract information from the text than from the patterns. No prior research has compared the number of transitions during problem solving with the accuracy of the answers. In this study, we observed that students who incorrectly solved a task demonstrated a significantly higher number of gaze transitions between the question and the options, as well as among different options. The results of this study indicate that the recognition of typical wave optics patterns is also difficult for university students, thus suggesting that more attention should be paid to systematic observation and identification of key features of basic wave optics phenomena in lecture demonstrations and student laboratories.

Micro-scale mechanism for cyclic deformation behavior in Zirconium under low-cycle-fatigue loading

Cyclic deformation behaviors and damage mechanisms of pure Zr were systemically investigated at fully reversed strain-controlled tension-compression fatigue experiments (R = −1), followed by detailed microstructural characterization using scanning electron microscopy with electron backscatter diffraction and transmission electron microscopy. The results demonstrated that three stages (Ⅰ, Ⅱ, Ⅲ) of cyclic response behavior were observed for all applied strain amplitudes, and the trend of the cyclic stress response mainly originated from the substructure evolutions. The initial cyclic softening was attributed to the formation of alternating high- and low-dislocation-density regions, enhancing the free path of dislocation motion. The fatigue life prediction model was established based on the hysteresis loops strain energy. SEM/EBSD slip traces analysis and TEM double beam diffraction analysis showed that prismatic <a> dislocation slip was the dominating deformation mechanism, and pyramidal <c + a> dislocations and 101¯2 twins played an essential role in accommodating plastic deformations. Further, fatigue damage behavior was not only influenced by initial texture, but also other factors played an essential role.

Asymmetric transmission devices empowered by a cascaded structure of a dielectric metasurface-photonic crystal.

In this Letter, we theoretically propose an all-dielectric quasi-three-dimensional subwavelength structure constructed by a dielectric metasurface cascaded with a multilayer photonic crystal (PC) to achieve a high-performance asymmetric optical transmission (AOT). The desired optical control of the AOT is realized by combining the predetermined anomalous beam steering of a phase gradient metasurface with a unique bandgap as well as transmission characteristics of the multilayered stacked PC. The simulated results demonstrate that the proposed AOT device operating at the center wavelength of 633 nm with a circularly polarized state exhibits a high transmission of up to 62.4% with a contrast ratio exceeding 606. The excellent performance of AOT is achieved by making disassembled transverse magnetic and transverse electric polarized light under the same deflection angle concurrently match with respective high-efficient transmission bands in the multilayer PC. Furthermore, dependence of the performance of the proposed device on structural dimensions is also explored. Fortunately, the designed AOT structure is applicable to any linearly polarized light but is accompanied by double diffraction channels as compared to the circularly polarized light case. Owing to its planar configuration, passive operation, and compelling performance under various polarization states, the proposed strategy for achieving AOT paves a new road for realizing high-performance optical metadevices in compact optical systems.

Direct observation of the ledge-typed twin boundary in a martensitic steel

The structure at the {112} twin boundaries in martensitic steels has been extensively debated recently. On the one hand, it was claimed to be the omega phase, similar to Ti alloys. On the other hand, it was considered artifacts induced by the double diffraction effect from the overlaps of twin-matrix crystals at their boundaries. In this study, we clarify the twin structure in a martensitic steel providing a detailed investigation of the α′ martensite twin boundaries using experiment and simulation. The fundamental for rejecting the existence of the omega phase in steels is based on the atomic resolution imaging from the <111> direction of twin structure, which was so far challenged to be acquired for such nano-sized twinned systems. The obtained result confirms the ledge-typed twin boundary that causes the visually omega-like forms when observed from other zone axes. The ledges occurred on {110} planes, making them secondary twin planes with coherent characteristics. Furthermore, these ledges were found to transit in a gradual manner from the primary (112) twin plane to (011) and then to (1¯10) secondary twin planes; a perpendicular transition from (112) to (1¯10) was not observed. Such a transitional behavior was explained in view of lowering total twin boundary energy, evaluated by the theoretical prediction of system energy and the geometric phase analysis of the twin planes. Double diffraction and rotational Moiré effects clarified the extra spots in the diffraction pattern obtained at the twin-matrix overlapped regions. This study gives light of understanding twinning in the bcc crystals.

High-Accuracy and High-Tolerance Laser Encoder With a Grating-Pyramid Configuration

Laser encoders is promising positioning sensors for nanometer measurement. It is a key challenge for laser encoders to offer high accuracy while ensuring high tolerance in service. In this paper, we present a laser encoder employing a grating-pyramid configuration. This configuration realizes double diffraction via a single retro-reflector, which offers the following two advantages: (i) providing high-resolution output signals due to optical quadruple frequency; (ii) improving alignment tolerance due to retro-reflection of the single pyramid. Its operating principle is described in detail, and the performance are evaluated. Simulation result presents that stand-off error and pitch error are the critical head-to-scale tolerance for the developed laser encoder. Experiment result shows that the laser encoder offers a stand-off tolerance of ±0.68 mm and a pitch tolerance of ±1.67°. Furthermore, an interpolation accuracy of 3 nm is achieved, which indicates that the laser encoder would achieve nanometer-level resolution. Both simulation and experimental results demonstrate its high-accuracy and high-tolerance.

Production and Characterization of Helical Beams by means of Diffraction Gratings

A description of the intensity distribution patterns of helical beams experimentally generated by forked diffraction gratings is presented. The characterization of the diffraction orders so obtained, using double diffraction gratings as well as the reconstruction of the 2D intensity profiles, is also discussed.

Double Diffraction or ω-Fe Diffraction in Body-Centered Cubic {112}&lt;111&gt;-Type Twinned Martensite

The martensitic substructure in steels plays a major role in understanding the nature of martensite transformation and improving mechanical properties. However, the substructure in the quenched martensite of carbon steel, particularly in high carbon martensite, has not been clarified yet. Local crystal structure in martensite has been characterized by means of transmission electron microscope (TEM). A specimen tilting experiment in TEM is a practical method to simply confirm that the electron diffraction spots are caused by either double diffraction effect or a second crystalline phase. By tilting the TEM specimen containing Fe–C twinned martensite structure, the so-called double diffraction spots of {112}<111>-type twin are still visible even after the diffraction spots from the twinned crystals become invisible. This experimental result is the direct evidence that the so-called twinning double diffraction spots come from a second crystalline phase (ω-phase), which is distributed in the body-centered cubic (BCC){112}<111>-type twinning boundary region. An ideal BCC {112}<111>-type twin is just a model, which has not been reported yet in any experiment.

Effects of Thermal Treatment on Microstructure and Wear Properties of Ni60/CeO2 Composite Coating 35CrMoV Steel by Laser Cladding

Laser cladding Ni60/2.0 wt.%CeO2 self-lubricating anti-wear composite coatings on 35CrMoV steel were thermally treated at 25 °C, 500 °C, 600 °C and 700 °C for 1 h, respectively. The macroscopic morphology of composite coatings was characterized by optical microscopy. The evolution of microstructure was studied by scanning electron microscopy. The precipitated phase of the coating was analyzed by X-ray diffractometer. The microhardness and wear properties of the composite coatings were measured by microhardness tester and friction and wear test. The effects of thermal treatment and no thermal treatment on the mechanical properties of the composite coatings were systematically studied by the above experiments. The experimental analysis shows that the main phase composition of Ni60/2.0 wt.%CeO2 composite coating is γ-(Ni, Fe), Cr7C3, Cr23C6, CrB, CrFeB and Cr2Ni3. Meanwhile, in XRD, it can be seen that the diffraction peak has shifted to the left and the single diffraction peak is decomposed into double diffraction peaks with the thermal treatment at 700 °C, which indicates that the lattice in the coating phase has a certain distortion. Compared with the coatings without thermal treatment, Ni60 cladding layer has more uniform solute distribution and a denser and more uniform structure after thermal treatment at 700 °C. The laser cladding anti-wear composite coating demonstrates that the wear resistance performance shows the greatest improvement after thermal treatment at 700 °C.

Bragg-diffraction-induced imperfections of the signal in retroreflective atom interferometers

We present a detailed study of the effects of imperfect atom-optical manipulation in Bragg-based light-pulse atom interferometers. Off-resonant higher-order diffraction leads to population loss, spurious interferometer paths, and diffraction phases. In a path-dependent formalism, we study numerically various effects and analyze the interference signal caused by an external phase or gravity. We compare first-order single and double Bragg diffraction in retroreflective setups. In double Bragg diffraction, phase imperfections lead to a beating due to three-path interference. Some effects of diffraction phases can be avoided by adding the population of the outer exit ports of double diffraction.

Attenuated phase shift masks: a wild card resolution enhancement for extreme ultraviolet lithography?

Background: The successful introduction of extreme ultraviolet (EUV) lithography to high volume manufacturing has increased the interest to push this technology to its ultimate limits. This will require photoresist materials, which enable a better tradeoff between resolution, linewidth roughness and sensitivity, and the adaptation of optical resolution enhancements that were originally developed for deep ultraviolet (DUV) lithography. Aim: We review published research on attenuated phase shift masks (attPSM) for EUV with special emphasis on modeling and fundamental understanding of the imaging characteristics of alternative absorber materials. The overview on previous work is intended to summarize typical observations and learning on obtained results and to serve as a reference for further research on this important topic. Review approach: The review starts with a summary of related work on attPSM for DUV lithography. It is shown that the understanding and mitigation of mask topography (or mask 3D) effects is key for the analysis and optimization of attPSM for EUV lithography. Observations from several research groups and application of dedicated modeling approaches help to understand the physical mechanisms behind observed lateral image shifts and pitch-dependent shifts of the best focus position. Results: The imaging physics of attPSM for EUV lithography differs significantly from attPSM imaging in DUV lithography. The “double diffraction” of EUV light from the absorber, the reflection characteristics of the multilayer blank, and the guidance of light through the openings in a low-refractive-index (low-n) absorber introduce important effects that need to be considered in the design and use of attPSM in EUV lithography. It is important to use the optical properties (n and k) and the thickness of the absorber as predictive design parameters of attPSM for EUV lithography (instead of phase and reflectivity). The refractive index of the absorber material is important for binary masks as well. The discussion of low-n absorbers includes both “traditional” attPSM for EUV and low reflectivity absorbers, which exploit the guidance of light inside patterned layers. Conclusions: In-depth modeling investigations of attPSM and first experiments suggest that absorbers with a refractive index around 0.9 (low-n materials) can help to push high NA EUV lithography into the low k1 regime. Comprehensive optimization of source and mask is required to exploit the advantages of low-n absorbers. Further enhancements can help to push EUV imaging to its ultimate limit.

Visible-light metalens far-field nanofocusing effects with active tuning of focus based on MIM subwavelength structures used in an integrated imaging array.

We propose a structure of a far-field nanofocusing metalens with focal shifting that is actively tuned at visible wavelengths. Surface plasmon polaritons (SPPs) can be excited by the metal-insulator-metal (MIM) subwavelength structure at visible wavelengths. The coherent interference of SPPs emitted by subwavelength nanostructures can form a nanoscale focus. When the SPPs are excited and pass through several concentric ring gratings with specific aspect ratios, the extraordinary optical transmission phenomenon occurs. Two metal concentric ring gratings achieve double diffraction, scattering light to the far field. An anisotropic or isotropic electrically adjustable refractive index material, such as liquid-crystal or optical phase change material, is filled in a dielectric layer between two metal layers, and the effective refractive index is modulated by electronically controlled active tuning. The focal shift is achieved by changing the effective refractive index of the intermediate dielectric. In addition, different incident wavelengths correspond to different effective refractive indices to achieve time-division-multiplexing multi-wavelength achromatic focusing. The finite-difference time-domain method was used to simulate the effect of substrate effective refractive index variation on achromatic superfocusing. The results show that the super-resolution focal spot (FWHM=0.158λ0) with long focal length (FL=5.177λ0) and large depth of field (DOF=3.412λ0) can be achieved by optimizing the design parameters. The visible plasma metalens has potential applications in high-density optical storage and optical microscopic imaging, especially in three-dimensional display for light field and integral imaging.

Hand and Body Blockage Measurements With Form-Factor User Equipment at 28 GHz

Blockage by the human hand/body is an important impairment in realizing practical millimeter-wave wireless systems. Prior works on blockage modeling are either based on theoretical studies of double knife-edge diffraction or its modifications, high-frequency simulations of electromagnetic effects, or measurements with experimental millimeter-wave prototypes. While such studies are useful, they do not capture the form-factor constraints of user equipments (UEs), such as moderate array sizes, gains, and beamwidths. In this work, we study the impact of hand/body blockage with a UE at 28 GHz built on commercial millimeter-wave components. We report five controlled studies with different types of hand holdings/grips, antenna types, and directional/narrow beams. For both hard and loose hand grips, we report considerably lower blockage loss estimates than prior works. Critical in estimating the loss is the definition of a “region of interest” (RoI) around the UE where the impact of the hand/body is seen. Toward this goal, we define an RoI that includes the spatial area where significant energy is seen in either the no blockage or blockage modes. Our studies show that significant spatial area coverage improvement can be seen with a loose hand grip due to hand reflections.

The Performance of a Low Berm in Reducing Traffic Noise

Traffic noise measurements were made behind a low, earth berm and in an adjacent open field to estimate insertion loss. The traffic was comprised of a mix of light vehicles, heavy trucks, and some medium trucks. The berm had a height of 1.65 meters above the roadway and began at the outside shoulder of a four-lane highway along U.S. Highway 101 in Northern California. Two microphone positions were located on the far side of the berm at distances of 28 and 40 meters from the center of the near lane of vehicular traffic. Away from the berm, a microphone was placed in an open field at 28 meters from the highway at a site upstream of the berm. The difference between the open location and those behind the berm were 11.6 and 9.9 dB for the 28- and 40-meter locations, respectively. The reductions obtained with the berm are compared to double edge diffraction theory and acoustic scale model results from the literature. The results of this study are reviewed in this paper and a comparison to FHWA Traffic Noise Model results is presented.

Characterization and strengthening effects of different precipitates in Al–7Si–Mg alloy

The microstructure of the nanoscale precipitates (especially the β phase) formed in the primary a-Al grains of a cast Al–7Si–Mg alloy during ageing at different temperatures, and the strengthening effects of them on the mechanical properties have been systematically investigated by transmission electron microscopy (TEM) and tensile test. The interactions of dislocations with different types of precipitates were analyzed in depth. It was found that the GP zones and β″ phase can be easily sheared by dislocations along the close-packed {111}Al planes, leading to good deformation compatibility and elongation. The step-like planar defects were found in the deformed β″ phase, indicating that this needle-shaped precipitate can be sheared not only along the short axis but also along the long axis. The β phase and nanoscale Si particles are usually bypassed by dislocations, showing a typical Orowan strengthening mechanism, leading to the highest strength. This may be related to their large size (about 100 nm in diameter), high shear modulus and modest number density. In addition, the moiré fringes and FFT pattern of β phase were discussed by calculation of diffraction vectors. The moiré fringes with about 2.389 nm and 2.664 nm spacing displayed in HRTEM image results from the interactions between the 004Al/006β and 2¯22Al/3¯33β diffraction respectively. The corresponding complex FFT pattern is caused by strong double diffraction of [110]β and [110]Al reflections. Furthermore, an interesting phenomenon that the β phase tends to nucleate and grow on the surface of Si particle was firstly observed and discussed in depth.

A new time-domain heuristic diffraction coefficient for characterization of diffracted and transmitted field with UWB applications

In this paper, a novel heuristic diffraction coefficient in the frequency-domain (FD) for non-perfectly conducting wedges and buildings is proposed. The six-terms diffraction coefficient which is an extension of the four-terms UTD coefficient is proposed to include the effect of transmitted ray for a lossy dielectric wedge with arbitrary low wedge angle, thus, attaining the continuity of the total field all around the structure. This new six-terms UTD diffraction coefficient is verified with the earlier available finite-difference time-domain (FDTD) result. Further, the time-domain (TD) solution based on the classical frequency domain result is proposed for UWB applications in indoor environments. Finally, a case of double diffraction for two consecutive buildings scenario is presented based on slope diffraction and their corresponding TD solution is also presented. The different input pulses and building materials are considered to test the overall behavior of the TD model. All the TD results are verified with inverse fast Fourier transform (IFFT) of the FD results in both the soft and hard polarization and the results are found to be in very good agreement. The channel impulse response is also presented to determine the distortion on the input pulse. The computational efficiency of the proposed TD solutions is demonstrated by comparing them with IFFT-FD solutions.

Light Strands: Visualization of Free Space in Double Slit Diffraction

Modern understanding of light has fluctuated between particle and wave theory. The classic double slit experiment provided seemingly conclusive support for wave theory of light with its resultant fringe patterns thought to only be due to wave interference. However, interference junctures of light have never been directly visualized. We investigated the double slit experiment and its fringe pattern through novel techniques of direct visualization of light propagation in the free space after slit exit in order to validate this interference principle. A cloud chamber and gel media were developed to visualize otherwise invisible light pathways. Coherent light was observed in these environments in settings of diffraction, refraction, and reflection. Experimental generation of distinct, isolated light strands after diffraction through double slits were visualized. Discrete light strands, not waves, were noted as light propagated through free space. Light strands were visualized directly creating the pseudo-interference fringe pattern, counter to the concept of wave interference. Novel visualization of light strands supports the particle theory of light and provides an alternative to wave theory. The finding that diffractive fringe patterns and other observations of light can be explained in some situations by the phenomena of discrete radiating strands, not wave interference, may have implications in physics, quantum mechanics, and technology.

Dense rotational twins in superconducting (111)-orientated δ-NbN epitaxial films on 4H-SiC substrates

In order to confirm the superconductivity observed in hexagonal ϵ-NbN reported recently, we have deposited NbN film on (0001) 4H-SiC substrate, with good lattice match, intentionally to grow hexagonal NbN phase. The detailed structural analysis show that the deposited films are (111)-orientated δ-NbN phase with dense rotational (60°) twins. Double diffraction effect in selected area electron diffraction and Moiré fringes in high resolution transmission electron microscope images confirm the existence of rotational twins in nanometer scale. The growth of highly twined film results from no energy preference for the two rotational twins of (111)-orientated δ-NbN to bond with the Si-faced (0001) 4H-SiC substrate. These highly twined δ-NbN epitaxial films exhibit high normal state resistivity, lower T C, but good spatial uniformity of superconducting energy gap. No ϵ-NbN phase was observed in this study which is might due to a low growth temperature of thin film.