Transverse Focusing Research Articles

Multibeam focusing using single-layer checkerboard metasurface

ABSTRACT In this study, a novel design methodology of multibeam focusing using a checkerboard metasurface is proposed and investigated. The metasurface is designed as a single-layer anisotropic surface consisting of two identical electric field coupled resonators (ELCRs) separated by a dielectric substrate. When a circularly polarized (CP) wave is incident on the unit cell of the metasurface and the unit cell is rotated to angle of θ, the unit cell has a transmitted phase shift of 2θ. The multibeam transverse and longitudinal focusing and control easily can be achieved by a structural rearrangement of metasurface in the form of a checkerboard without mathematical method. The feasibility of the proposed methodology is confirmed by full-wave simulation and measurement results at 5.8 GHz.

Enhanced e–e interaction in suspended 2DEG evidenced by transverse magnetic focusing

Enhanced e–e interaction in suspended 2DEG evidenced by transverse magnetic focusing

Probing the Shape of the Weyl Fermi Surface of NbP Using Transverse Electron Focusing.

Weyl semimetals are defined by their unique Fermi surface, comprising pairs of Weyl points of opposite chirality, connected through topological surface states. Angle-resolved photoemission spectroscopy (ARPES) has been used to verify the existence of the Weyl points and the Fermi arcs. However, ARPES is limited in resolution, leading to significant uncertainty when characterizing the shape of the Fermi surface of semimetals and measuring features such as the distance between the Weyl points. Here, to surpass the resolution of ARPES, we combine quantum oscillation measurements with transverse electron focusing experiments. These techniques offer complementary information, enabling the reconstruction of the distinctive peanut-shaped cross section of the Weyl Fermi surface and accurately determining the separation between Weyl points in the Weyl semimetal NbP. Our Letter showcases the integration of quantum oscillations and transverse electron focusing, allowing for the measurements of complex Fermi surface geometries, concurrently with carriers' transport properties, in high-mobility quantum materials.

Table-top ion-trap experiment on the stability of intense short bunches in linear hadron accelerators

The novel experimental system “S-POD” (Simulator of Particle Orbit Dynamics) is employed to explore the stability of short hadron bunches in high-intensity linacs. In a previous study with the S-POD [M. Goto et al., ], a static potential was used to focus the bunch in the longitudinal direction. We here make a step forward to include the possibility of pure synchrotron resonance, introducing periodic modulation to the longitudinal potential well. The modulation period was taken a half of the transverse alternating-gradient focusing period, which reflects the most typical lattice condition of a drift-tube linac. Detailed stability maps are constructed to reveal dangerous parameter regions where serious beam loss may occur due to resonance. We reconfirm the existence of various betatron and synchrobetatron resonance stop bands whose widths and locations change in tune space depending on the bunch intensity. It turns out that the periodicity of the longitudinal focusing potential brings about no pronounced effect on the resonance feature; the result is very similar to what we obtained in the previous study with a static longitudinal potential. As long as the lattice periodicity mentioned above is maintained, no serious noncoupling synchrotron resonance appears even with a high synchrotron phase advance above 90° per unit alternating-gradient cell. Severe envelope instability may, however, be excited in the longitudinal direction if the axial focusing force includes error components that affect the original lattice periodicity. The experimental observations can be explained with the free from the concept of incoherent tune spread. Published by the American Physical Society 2024

Probing the Anisotropic Fermi Surface in Tetralayer Graphene via Transverse Magnetic Focusing.

Bernal-stacked tetralayer graphene (4LG) exhibits intriguing low-energy properties, featuring two massive sub-bands and showcasing diverse features of topologically distinct, anisotropic Fermi surfaces, including Lifshitz transitions and trigonal warping. Here, we study the influence of the band structure on electron dynamics within 4LG using transverse magnetic focusing. Our analysis reveals two distinct focusing peaks corresponding to the two sub-bands. Furthermore, we uncover a pronounced dependence of the focusing spectra on crystal orientations, indicative of an anisotropic Fermi surface. Utilizing the semiclassical model, we attribute this orientation-dependent behavior to the trigonal warping of the band structure. This phenomenon leads to variations in electron trajectories based on crystal orientation. Our findings not only enhance our understanding of the dynamics of electrons in 4LG but also offer a promising method for probing anisotropic Fermi surfaces in other materials.

Harmonic generation in a terawatt x-ray free-electron laser

Terawatt x-ray free-electron lasers (XFELs) represent the frontier in further development of x-ray sources and require high current densities with strong transverse focusing. In this paper, we investigate the implications/potentialities of TW XFELs on the generation of harmonics at still shorter wavelengths and higher photon energies. The simulations indicate that significant power levels are possible at high harmonics of the XFEL resonance and that these XFELs can be an important coherent source of hard x-rays through the gamma ray spectrum. For this purpose, we use the MINERVA simulation code which self-consistently includes harmonic generation. Both helical and planar undulators are discussed in which the fundamental is at 1.5 Å and study the associated harmonic generation. While tapered undulators are needed to reach TW powers at the fundamental, the taper does not enhance the harmonics because the taper must start before saturation of the fundamental, while the harmonics saturate before this point is reached. Nevertheless, the harmonics reach substantial powers. Simulations indicate that, for the parameters under consideration, peak powers of the order of 180 MW are possible at the fifth harmonic with a photon energy of about 41 keV and still high harmonics may also be generated at substantial powers. Such high harmonic powers are certain to enable a host of enhanced applications.

‘I like exploring other languages’: primary and lower secondary students’ attitudes towards plurilingual education

ABSTRACT While teachers’ beliefs about plurilingual education are widely studied, there is a gap in research exploring learners’ orientations. Drawing on a conceptualisation of plurilingual education distinguishing between three pluralistic approaches to languages and a transversal dimension focusing on learners’ language resources, the article investigates primary and lower secondary students’ attitudes towards plurilingual education in response to plurilingual education being implemented in the students’ language teaching. Based on interview data collected in a multiple-case study from majority and minority language students in Grades 1, 5 and 7, the analysis displays consistent learner positivity towards plurilingual education, especially emphasising the éveil aux langues approach whereas the integrated didactic approach as well as intercomprehension between related languages receive less attention. The findings indicate that the attitudes towards plurilingual education are linked to the learners’ language resources creating a framework for the students’ encounters and comparisons with other languages. Combining the findings and research literature on plurilingualism as a universal criterion for all learners in a modern, globalised world, the article suggests a continuum of the learner's plurilingualism. However, the findings reveal that experienced plurilingual education contexts do not only foster positive attitudes towards linguistic diversity, but that discriminating language-hierarchising attitudes co-exist.

Rayleigh wave excitation with an elliptical reflector for high-power ultrasound

This study proposes a Rayleigh wave transducer with an elliptical reflector for high-power ultrasound (ELIPS). In contrast to conventional transducers using IDT with single crystal piezoelectric plates or wedge transducers, our ELIPS enables high-power Rayleigh wave excitation in the megahertz range, which will be useful for applications such as surface acoustic wave (SAW) motors, SAW tactile devices, and SAW atomizers. The driving principles of the transducer are Rayleigh wave excitation with a transverse wave source and transverse wave focusing with a dilatational wave source and an elliptical reflection surface. The effectiveness of this mechanism was confirmed with an FEM simulation, and the Rayleigh wave excitation was validated using a prototype transducer. Finally, the high-power characteristics were examined, and a maximum vibration amplitude of 15.5 nm at 1.0 MHz was successfully obtained. It should be noted that this vibration amplitude is not a saturated value, and a much higher value could be realized with higher input power.

Subrelativistic Alternating Phase Focusing Dielectric Laser Accelerators.

We demonstrate a silicon-based electron accelerator that uses laser optical near fields to both accelerate and confine electrons over extended distances. Two dielectric laser accelerator (DLA) designs were tested, each consisting of two arrays of silicon pillars pumped symmetrically by pulse front tilted laser beams, designed for average acceleration gradients 35 and 50 MeV/m, respectively. The DLAs are designed to act as alternating phase focusing (APF) lattices, where electrons, depending on the electron-laser interaction phase, will alternate between opposing longitudinal and transverse focusing and defocusing forces. By incorporating fractional period drift sections that alter the synchronous phase between ±60° off crest, electrons captured in the designed acceleration bucket experience half the peak gradient as average gradient while also experiencing strong confinement forces that enable long interaction lengths. We demonstrate APF accelerators with interaction lengths up to 708 μm and energy gains up to 23.7±1.07 keV FWHM, a 25% increase from starting energy, demonstrating the ability to achieve substantial energy gains with subrelativistic DLA.

RF-Acceleration Studies for the HBS-Linac Applying Alternating Phase Focusing Concepts

The recent layout of the Jülich High Brilliance Neutron Source (HBS) driver linac is based on short crossbar H-mode (CH) cavities operated at a fixed synchronous phase. In the last decades the computing power for the development of linacs, available to physicists and engineers, has been increased drastically. This also enabled the accelerator community to finally carry out the required R&D to generate further the idea of drift tube linacs with alternating phase focusing (APF) beam dynamics, originally proposed in the 1950s. This focusing method uses the electric fields in between the drift tubes (i.e., gaps) to provide subsequent transverse and longitudinal focusing to the beam along multiple gaps. The beam focusing properties within each gap are adjusted individually by means of the synchronous phase. As a result of the alternating phase focusing method, these linacs can operate completely without internal magnetic lenses. The R&D-program for the high brilliance neutron source HBS offered the opportunity to investigate the APF concept further in order to open this advanced concept for high duty-factor, high intensity hadron beam acceleration. Besides, a prototype APF-interdigital H-mode (IH)-cavity has been designed and is going to be build and tested in the next future.

Andreev reflection imaging and longitudinal shift of pseudospin-1 fermions in two-dimensional materials

In this work, the transverse magnetic focusing of pseudospin-1 fermions in two-dimensional materials with a superconducting contact is studied. The transmission coefficient and Andreev reflection coefficient from injector lead to collector lead are calculated based on the Landauer–Büttiker formula combined with the non-equilibrium Green's function method. The local state density diagrams of the electron and hole transmission in the center region are given, which provide a complete image of the ballistic electron–hole cyclotron orbits. Using these images, the positive longitudinal shift in Andreev reflection of the pseudospin-1 fermion can be obviously seen. Furthermore, it is found that the total offset is proportional to the number of Andreev reflection occurrence. This setup provides the possibility of detecting this shift experimentally.

Integration of large-extinction-ratio resonators with grating couplers and waveguides on GaN-on-sapphire at O-band.

Photonic integrated circuits (PICs) based on gallium nitride (GaN) platforms have been widely explored for various applications at C-band (1530 nm∼1565 nm) and visible light wavelength range. However, for O-band (1260 nm∼1360 nm) commonly used in short reach/cost sensitive markets, GaN-based PICs still have not been fully investigated. In this article, a microring resonator with an intrinsic Q-factor of ∼2.67 × 104 and an extinction ratio (ER) of 35.1 dB at 1319.9 nm and 1332.1 nm, is monolithically integrated with a transverse electric-polarized focusing grating coupler and a ridge waveguide on a GaN-on-sapphire platform. This shows a great potential to further exploit the optical properties of GaN materials and integrate GaN-based PICs with the mature GaN active electronic and optoelectronic devices to form a greater platform of optoelectronic-electronic integrated circuits (OEICs) for data-center and telecom applications.

Development of the heavy ion RFQ for CAFE2

A radio frequency quadrupole (RFQ) accelerator which accelerates particles with a mass-to-charge ratio up to 3 to over 1.33 MeV/u was developed. This RFQ was designed based on the existing 162.5 MHz solid-state power sources of the Chinese Accelerator Driven System (C-ADS) injector II. The frequency is relatively high to a heavy ion RFQ which means a weak transverse focusing strength and brings challenges to the beam loss and quality control. The average radius r0 of the RFQ was appropriately chosen to make a compromise between the transverse focusing strength and the maximum surface field. The beam dynamics parameters were carefully optimized to improve the quality of the RFQ output beam so that the beam could be well transported in the following superconducting structure. Beam dynamics simulations and an error study have been performed to evaluate the RFQ and a method which is more suitable for the analyses of small acceptance RFQs has been adopted. And the results of the beam commissioning have been proved to agree well with the simulations.

Ballistic transport spectroscopy of spin-orbit-coupled bands in monolayer graphene on WSe2

Van der Waals interactions with transition metal dichalcogenides were shown to induce strong spin-orbit coupling (SOC) in graphene, offering great promises to combine large experimental flexibility of graphene with unique tuning capabilities of the SOC. Here, we probe SOC-driven band splitting and electron dynamics in graphene on WSe2 by measuring ballistic transverse magnetic focusing. We found a clear splitting in the first focusing peak whose evolution in charge density and magnetic field is well reproduced by calculations using the SOC strength of ~ 13 meV, and no splitting in the second peak that indicates stronger Rashba SOC. Possible suppression of electron-electron scatterings was found in temperature dependence measurement. Further, we found that Shubnikov-de Haas oscillations exhibit a weaker band splitting, suggesting that it probes different electron dynamics, calling for a new theory. Our study demonstrates an interesting possibility to exploit ballistic electron motion pronounced in graphene for emerging spin-orbitronics.

Spatiotemporal response of concave VLS grating to ultra-short X-ray pulses.

In soft X-ray free-electron laser (FEL) beamlines, variable-line-spacing (VLS) gratings are often used as dispersive components of monochromators and spectrometers due to their combined dispersion and focusing properties. X-ray FEL pulses passing through the VLS grating can result in not only transverse focusing but also spatiotemporal coupling effects, such as pulse front tilt, pulse front rotation, and pulse stretching. In this paper, we present a theoretical study of the spatiotemporal response of concave VLS gratings to ultra-short X-ray pulses. The theoretical analysis indicates that the tilt angle of the non-zero diffraction orders varies with the propagation distance, and disappears at the focus, where the focal lengths and pulse stretching differ for different diffraction orders. The model demonstrates the pulse duration after the concave VLS grating is the convolution of the initial pulse duration and the stretching term induced by dispersion, while the beam size at the focus in x dimension is the convolution of the geometric scaling beam size and the dispersion term. This work provides a mathematical explanation for the spatiotemporal response of concave VLS grating to ultra-short X-ray pulses and offers valuable insights into the design of FEL grating monochromators, spectrometers, pulse compressors, and pulse stretchers.

Probing miniband structure and Hofstadter butterfly in gated graphene superlattices via magnetotransport

The presence of periodic modulation in graphene leads to a reconstruction of the band structure and formation of minibands. In an external uniform magnetic field, a fractal energy spectrum called Hofstadter butterfly is formed. Particularly interesting in this regard are superlattices with tunable modulation strength, such as electrostatically induced ones in graphene. We perform quantum transport modeling in gate-induced square two-dimensional superlattice in graphene and investigate the relation to the details of the band structure. At low magnetic field the dynamics of carriers reflects the semi-classical orbits which depend on the mini band structure. We theoretically model transverse magnetic focusing, a ballistic transport technique by means of which we investigate the minibands, their extent and carrier type. We find a good agreement between the focusing spectra and the mini band structures obtained from the continuum model, proving usefulness of this technique. At high magnetic field the calculated four-probe resistance fit the Hofstadter butterfly spectrum obtained for our superlattice. Our quantum transport modeling provides an insight into the mini band structures, and can be applied to other superlattice geometries.

High-energy quasi-monoenergetic proton beam from micro-tube targets driven by Laguerre–Gaussian lasers

High-energy proton beams with low energy spread and angular divergence are highly valuable in various applications, such as proton therapy, ultrafast science, and nuclear physics. Laser-driven ion sources are being explored as a more compact and cost-effective alternative to conventional accelerators. However, producing high-quality proton beams using lasers has been a significant challenge. In this study, we propose a novel approach to achieve high-energy quasi-monoenergetic proton beams by utilizing a Laguerre–Gaussian (LG) laser to irradiate a solid hollow tube target. Our three-dimensional particle-in-cell simulations demonstrate that the LG laser efficiently pulls out and accelerates electrons. As these electrons exit the rear side of the tube, a charge-separation electric field for proton acceleration is self-established. Meanwhile, a considerable part of the electrons are confined to the laser axis by the ponderomotive force of the LG laser, generating a longitudinal bunching field and transverse focusing field. As a result, protons are accelerated and focused in these fields, producing a high- quality proton beam with high energy (247 MeV) and low energy spread (∼2%) using an LG laser with an intensity of W cm−2 and a tube target with an electron density of 40nc . In comparison to a standard Gaussian laser, the LG laser exhibits superior performance in terms of proton cut-off energy, energy spread, and angular divergence.

Transmission of hydrogen detonation across a curtain of dilute inert particles

Transmission of hydrogen detonation wave (DW) in an inert particle curtain is simulated using the EulerianLagrangian approach. A detailed chemical mechanism is used to predict the detonative combustion of a stoichiometric hydrogen-air mixture and parametric studies are conducted based on a two-dimensional computational domain. A detonation map of propagation and extinction corresponding to various particle sizes, concentrations, and curtain thicknesses is plotted. It is shown that the critical curtain thickness decreases considerably when the particle concentration is less than the critical value. The effects of curtain thickness on the trajectories of peak pressure, shock front speed, and heat release rate are examined. Three propagation modes of the DW in particle curtain are found: detonation transmission, partial extinction and detonation re-initiation, as well as detonation extinction. The first two modes are analyzed with the evolutions of shock frontal structures and chemical explosive mode. The chemical explosive mode analysis confirms that a detonation re-initiation event is caused by a re-initiation point with high pressure and explosive propensity, resulting from transverse shock focusing. The influence of particle dimeter/concentration, and curtain thickness on the DW are also examined with peak pressure trajectories, shock speed, and interphase exchange rates of energy and momentum. In addition, small variations of the curtain thickness will affect the short-term behaviors of detonation development, but the long-term DW behaviors are negligibly affected. Furthermore, the evolutions of curtain morphologies are analyzed by the particle velocity, volume fraction, Stokes drag and Archimedes force. This analysis confirms the importance of drag force in influencing the curtain morphologies. Different curtain evolution regimes are found: quasi-stationary regime, shrinkage regime, constant-thickness regime, and expansion regime. Finally, the influences of the curtain thickness on the characteristic time of curtain evolutions are studied. It is found that all characteristic time become smaller when the curtain thickness increases.

Ultrashort X-ray Free Electron Laser Pulse Manipulation by Optical Matrix

Free electron laser (FEL) is capable of producing ultra-short X-ray pulses. The estimation of X-ray pulse propagation is the key process of X-ray FEL beamline design. By using the Kostenbauder matrix approach, the evolution of an ultra-short pulse in a beamline system can be calculated. Therefore, it is of significant importance to investigate the Kostenbauder matrices of different kinds of X-ray optics. In this work, we derive a unified 6 × 6 optical matrix to describe various kinds of X-ray optical elements, including varied-line-spacing (VLS) toroidal grating, VLS spherical grating, VLS cylindrical grating, VLS plane grating, toroidal grating, spherical grating, cylindrical grating, plane grating, toroidal mirror, spherical mirror, cylindrical mirror, and plane mirror. These optics are usually adopted in soft X-ray regime. We apply this method to describe the transverse focusing, pulse front tilt, and pulse stretching after an X-ray pulse going through a VLS plane grating monochromator (VLS-PGM). We also use this approach to simulate a grating compressor which can be used to compress chirped soft X-ray pulse. This work is helpful in the design and optimization of X-ray beamline systems.

Spin polarization and spin-dependent scattering of holes observed in transverse magnetic focusing

In two-dimensional hole systems, the Rashba spin-orbit interaction leads to a spin dependent momentum. A perpendicular magnetic field spatially separates holes with different spins, creating a mass spectrometer for spin. Spin-resolved magnetic focussing has been used to measure spin polarization from the amplitude of magnetic focussing peaks. In this work, the authors show that the ${k}^{3}$ form of the Rashba spin-orbit interaction term for semiconductor holes changes the scattering rate, which has an exponential effect on the focussing peak amplitude. This result further demonstrates the impact of the Rashba spin-orbit interaction in the field of semiconductor hole spin physics.