Reciprocal Vectors Research Articles

Full-duplex cylindrical vector beam multiplexing communication using spin-dependent phase modulation metasurfaces

Cylindrical vector beam (CVB) has recently gained attention as a promising carrier for signal multiplexing owing to its mode orthogonality. However, the full-duplex multiplexing communication has not been previously explored for the lack of effective technologies to parallelly couple and separate CVB modes. Herein, we present a full-duplex solution for CVB multiplexing communication that utilizes spin-dependent phase modulation metasurfaces. By independently phase-modulating the two spin eigenstates of CVBs with the metasurface via spin-dependent orbital interactions, and loading two binary Dammann vortex gratings, we enabled an independent and reciprocal wave vector manipulation of CVBs for full-duplex (de)multiplexing operation. To demonstrate this concept, we constructed a 16-channel (including 4 CVB modes and 4 wavelengths) full-duplex CVB multiplexing communication system and achieved the bidirectional transmission of 800 Gbit/s quadrature-phase shift-keying (QPSK) signals over a 5 km few-mode fiber. Our results demonstrate the successful multiplexing and demultiplexing of 2 radial CVB modes and 2 azimuthal CVB modes in full-duplex communication with the bit-error-rates approaching 1.87 × 10−5.

Hysteretic Responses of Skyrmion Lattices to Electric Fields in Magnetoelectric Cu2OSeO3.

Electric field control of topologically nontrivial magnetic textures, such as skyrmions, provides a paradigm shift for future spintronics beyond the current silicon-based technology. While significant progress has been made by X-ray and neutron scattering studies, direct observation of such nanoscale spin structures and their dynamics driven by external electric fields remains a challenge in understanding the underlying mechanisms and harness functionalities. Here, using Lorentz transmission electron microscopy combined with in situ electric and magnetic fields at liquid helium temperatures, we report the crystallographic orientation-dependent skyrmion responses to electric fields in thin slabs of magnetoelectric Cu2OSeO3. We show that electric fields not only stabilize the hexagonally packed skyrmion lattices in the entire sample in a hysteretic manner but also induce the rotation of their reciprocal vector discretely by 30°. The nonvolatile and energy-efficient skyrmion lattice control by electric fields demonstrated in this work provides an important foundation for designing skyrmion-based qubits and memory devices.

Magnetic Weyl Semimetal in BaCrSe2 with Long-Distance Distribution of Weyl Points.

Weyl semimetals (WSMs) have attracted great attentions that provide intriguing platforms for exploring fundamental physical phenomena and future topotronics applications. Despite the fact that numerous WSMs are achieved, WSMs with long-distance distribution of Weyl points (WPs) in given material candidates remain elusive. Here, the emergence of intrinsic ferromagnetic WSMs in BaCrSe2 with the nontrivial nature explicitly confirmed by the Chern number and Fermi arc surface states analysis is theoretically demonstrated. Remarkably, unlike previous WSMs for which opposite chirality WPs are located very close to each other, the WPs of BaCrSe2 host a long-distance distribution, as much as half of the reciprocal space vector, suggesting that the WPs are highly robust and difficult to be annihilated by perturbations. The presented results not only advance the general understanding of magnetic WSMs but also put forward potential applications intopotronics.

Ab initio quantum approach to electron-hole exchange for semiconductors hosting Wannier excitons

We propose a quantum approach to ``electron-hole exchange,'' better named electron-hole pair exchange, that makes use of the second quantization formalism to describe the problem in terms of Bloch-state electron operators. This approach renders transparent the fact that such singular effect comes from interband Coulomb processes. We first show that, due to the sign change when turning from valence-electron destruction operator to hole creation operator, the interband Coulomb interaction only acts on spin-singlet electron-hole pairs, just like the interband electron-photon interaction, thereby making these spin-singlet pairs optically bright. We then show that, when written in terms of reciprocal lattice vectors ${\mathbf{G}}_{m}$, the singularity of the interband Coulomb scattering in the small wave-vector transfer limit entirely comes from the ${\mathbf{G}}_{m}=\mathbf{0}$ term, which renders its singular behavior easy to calculate. Comparison with the usual real-space formulation in which the singularity appears through a sum of ``long-range processes'' over all ${\mathbf{R}}_{\ensuremath{\ell}}\ensuremath{\ne}\mathbf{0}$ lattice vectors once more proves that periodic systems are easier to handle in terms of reciprocal vectors ${\mathbf{G}}_{m}$ than in terms of lattice vectors ${\mathbf{R}}_{\ensuremath{\ell}}$. Well-accepted consequences of the electron-hole exchange on excitons and polaritons are reconsidered and refuted for different major reasons.

Second-harmonic and cascaded third-harmonic generation in generalized quasiperiodic poled lithium niobate waveguides.

Lithium niobate (LN) thin film has recently emerged as an important platform for nonlinear optical investigations for its large χ(2) nonlinear coefficients and ability of light localization. In this Letter, we report the first, to the best of our knowledge, fabrication of LN-on-insulator ridge waveguides with generalized quasiperiodic poled superlattices using the electric field polarization technique and microfabrication techniques. Benefiting from the abundant reciprocal vectors, we observed efficient second-harmonic and cascaded third-harmonic signals in the same device, with normalized conversion efficiency of 1735% W-1 cm-2 and 0.41% W-2 cm-4, respectively. This work opens a new direction for nonlinear integrated photonics based on LN thin film.

Evaluation local strain of twisted bilayer graphene via moiré pattern

Twisted bilayer graphene with hexagonal moiré patterns have shown a variety of unusual physical and mechanical phenomena. Unfortunately, some residual strain is introduced during the fabrication process of twisted bilayer graphene, leading to the deformation of moiré pattern. In this work, we employed water assisted transfer approach to build the suspended twisted bilayer graphene over the microscale holes patterned SiO2/Si substrate. Atomic force microscopy is involved to characterize the moiré pattern. Based on reciprocal vectors analysis, a theoretical model was proposed to extract the local strain of twisted bilayer graphene sample. The local strain of twisted bilayer graphene induced by the transfer process as well as the biaxial tensile stretch was evaluated respectively.

The generalized Wiener–Hopf equations for the elastic wave motion in angular regions

In this work, we introduce a general method to deduce spectral functional equations in elasticity and thus, the generalized Wiener–Hopf equations (GWHEs), for the wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity. The work extends the methodology used in electromagnetic applications and proposes for the first time a complete theory to get the GWHEs in elasticity. In particular, we introduce a vector differential equation of first-order characterized by a matrix that depends on the medium filling the angular region. The functional equations are easily obtained by a projection of the reciprocal vectors of this matrix on the elastic field present on the faces of the angular region. The application of the boundary conditions to the functional equations yields GWHEs for practical problems. This paper extends and applies the general theory to the challenging canonical problem of elastic scattering in angular regions.

Wave transport in 1D stealthy hyperuniform phononic materials made of non-resonant and resonant scatterers

Stealthy hyperuniform point patterns are characterized by a vanishing spatial Fourier transform around the origin of the reciprocal vector space. The long-range point density fluctuations are suppressed as well in materials consisting of such distribution of scatterers, opening up opportunities to control waves. Beside wave transport in such structured materials are driven by several elements, such as the acoustic properties of the host material, the scatterer characteristics, i.e., dimensions or resonant features, and the scatterer distribution patterns. The effects of these three basic elements on the wave transport properties are usually hard to discriminate. In this work, we analyze the transport properties of acoustic waves in one-dimensional phononic materials constituted of either non-resonant or resonant scatterers distributed along stealthy hyperuniform patterns in air. The pattern is controlled by the stealthiness, allowing us to continuously vary from random phononic materials to phononic crystals. The properties of the scatterers are controlled by their size and/or the resonant frequencies. The properties of the host material are controlled by the viscothermal losses. Transport properties of stealthy hyperuniform materials are found to be robust to both the scatterer dimensions and inherent viscothermal losses, while strongly affected by the scatterer resonances, which introduce sharp dips in the transmission coefficient.

In-situ SAXS study on pore structure change of PAN-based carbon fiber during graphitization

Graphitization (1400 °C–2200 °C) of polyacrylonitrile (PAN)-based carbon fiber in a small furnace with direct electric heating by Joule effect was studied in situ by small angle X-ray scattering (SAXS) with X-ray synchrotron radiation. The two-dimensional SAXS images display an anisotropic shape indicating the existence of needle-like or elongated ellipsoid-shaped pores oriented along the fiber axis. The one-dimensional scattering curves display obvious positive deviation from Porod's law indicating the existence of micro-fluctuation of electron density in the skeleton of the fiber which give rise to additional scattering. After correcting the deviation from Porod's law, the pure pore scattering was derived, and the pore structure parameters were computed. The results show that with increasing temperature the orientation angle decreases whereas the orientation degree increases. The long axis decreases whereas the short axis increases leading to a lower axial ratio. The size distribution becomes broader and there is a maximum value of porosity and specific surface area at 1900 °C. The change of pore structure in the fiber with temperatures can be approximately divided into two stages corresponding to denitrification condensation (1400 °C–1900 °C) and structure rearrangement (1900 °C–2200 °C) during graphitization, respectively. The corresponding mechanism was analyzed. Reciprocal relationship between the orientation of the needle-like or elongated ellipsoid-shaped pores in carbon fiber and the scattering images (inspired from Macromolecules, 2000, 33, 1848–1852; Polymer, 2001, 42, 1601–1612; Journal of Light Scattering (In Chinese), 2021, 33, 328–334). The left is schematic diagram and the right is actual sample and SAXS images. Where φ is the orientation angle of pore, L is the long axis of pore, r is the short axis of pore, q 12 and q 3 are the components of the reciprocal space vector q (q = 4π·sinθ/λ, 2θ is the scattering angle, λ is the incident X-ray wavelength) in the directions perpendicular and parallel to the principal axis of the pore, respectively. • In-situ SAXS study on PAN-based carbon fiber during graphitization (1400 °C–2200 °C). • Obvious positive deviation from Porod's law for all measured SAXS curves. • Change of pore structure of fiber in two stages dividing by 1900 °C.

Quasi-phase-matching-division multiplexing holography in a three-dimensional nonlinear photonic crystal

Nonlinear holography has recently emerged as a novel tool to reconstruct the encoded information at a new wavelength, which has important applications in optical display and optical encryption. However, this scheme still struggles with low conversion efficiency and ineffective multiplexing. In this work, we demonstrate a quasi-phase-matching (QPM) -division multiplexing holography in a three-dimensional (3D) nonlinear photonic crystal (NPC). 3D NPC works as a nonlinear hologram, in which multiple images are distributed into different Ewald spheres in reciprocal space. The reciprocal vectors locating in a given Ewald sphere are capable of fulfilling the complete QPM conditions for the high-efficiency reconstruction of the target image at the second-harmonic (SH) wave. One can easily switch the reconstructed SH images by changing the QPM condition. The multiplexing capacity is scalable with the period number of 3D NPC. Our work provides a promising strategy to achieve highly efficient nonlinear multiplexing holography for high-security and high-density storage of optical information.

Multiple charge density wave phases of monolayer VSe2 manifested by graphene substrates

A combined study of scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES) is conducted to understand the multiple charge density wave (CDW) phases of monolayer (ML) VSe2 films manifested by graphene substrates. Submonolayer (∼0.8 ML) VSe2 films are prepared on two different substrates of single-layer graphene (SLG) and bi-layer graphene (BLG) on a 6H-SiC(0001). We find that ML VSe2 films are less coupled to the SLG substrate compared to that of ML VSe2/BLG. Then, ML VSe2 grown on SLG and BLG substrates reveals a very different topography in STM. While ML VSe2/BLG shows one unidirectional modulation of √3 × 2 and √3 × √7 CDW in topography, ML VSe2/SLG presents a clear modulation of 4 × 1 CDW interfering with √3 × 2 and √3 × √7 CDW which has not been previously observed. We explicitly show that the reciprocal vector of 4 × 1 CDW fits perfectly into the long parallel sections of cigar-shaped Fermi surfaces near the M point in ML VSe2, satisfying Fermi surface nesting. Since bulk VSe2 is also well-known for the 4 × 4 × 3 CDW formed by Fermi surface nesting, the 4 × 1 CDW in ML VSe2/SLG is attributed to the planar projection of 4 × 4 × 3 CDW in bulk. Our result clarifies the nature of the 4 × 1 CDW in ML VSe2 system and is a good example demonstrating the essential role of substrates in two-dimensional transition metal dichalcogenides.

Identifying rotational symmetry axes in Kikuchi patterns by reciprocal vectors.

Symmetry analysis of the Kikuchi pattern is helpful to determine the crystal structure, and can significantly reduce the screening range of phase identification, thereby improving the accuracy and reliability of phase identification in electron backscatter diffraction (EBSD). Accurately identifying the symmetry axis from the Kikuchi pattern is the primary task of symmetry analysis. In this study, a new method was proposed to identify symmetry axes in Kikuchi patterns with the aid of reciprocal vectors. Taking the Kikuchi patterns of single-crystal silicon as a typical example, a method for drawing reciprocal vectors after strict projection correction is introduced. The complex task of identifying the symmetry axis is transformed into an intuitive judgment of the geometric relationship between reciprocal vectors, thus greatly simplifying the process. This method successfully elucidated information on six Kikuchi poles in three single-crystal silicon Kikuchi patterns, including 3-fold axes, 4-fold axes and asymmetric axes. The method can also distinguish between a 3-fold axis and an analogous 3-fold axis despite their only slight differences.

Broadband second harmonic generation in aperiodic nonlinear photonic crystals: 1D projection from 2D Vogel sunflower spiral array

The structure of the sunflower head can be used to realize broadband applications in optics. However, this 2D structure, with a ring-shaped reciprocal space, only has a normalized Fourier coefficient peak around 0.033, which leads to a relatively low conversion efficiency and may restrict its applications. We tried to maintain its broadband features while with larger Fourier coefficients by structure dimension reduction. We obtained an aperiodic 1D structure from a 2D Vogel sunflower spiral array by a cut-and-projection method. Workable reciprocal vector bands were found with this 1D structure in the vicinity of a pre-set central wavelength λ0 = 1.4 µm, and its peak Fourier coefficients can be 5–7 times as large as the original 2D structure. With this, we investigated broadband quasi-phase matching (QPM) second harmonic generation (SHG) in samples with different reversed ratios D. To illustrate in more detail, three samples were closely examined with D = 0.4, 0.5, and 0.6. Bandwidths of these three samples for first-order QPM SHG are 90, 70, and 30 nm, respectively, with a fundamental wave in the vicinity of λ0 = 1.4 µm. The exact SHG solution of coupled-wave equations was used in the evaluation of conversion efficiencies. Calculations showed broadband high conversion efficiency.

MAXIM: Metasurfaces-oriented electromagnetic wave simulation software with intuitive graphical user interfaces

We develop MAXIM which is electromagnetic wave simulation software based on rigorous coupled-wave analysis. The principal advantage of MAXIM is an intuitive graphical user interface drastically improving the accessibility of the software to who are not familiar with computer programming. Here, we present the basic formulation and computation methods that are incorporated in MAXIM. The computation performance is also evaluated for several didactic examples of dielectric metasurfaces which are the main application of MAXIM. The comparison of the calculation results with commercial software based on a finite-difference time-domain method confirms that the computation results of two programs coincide closely with each other within 1% difference. Considering the easy accessibility, wide availability and high reliability, MAXIM will serve the development of related research fields of metasurfaces and nanophotonics. Program summaryProgram Title: MAXIMCPC Library link to program files:https://doi.org/10.17632/352jpd593h.1Licensing provisions: LGPLProgramming language: Python 3.8Supplementary material: User guide and tutorial movieNature of problem: Time-harmonic electromagnetic wave simulations on multilayered periodic structures composed of isotropic materials. Diffraction occurs as a propagating electromagnetic wave meets periodically-structured arrays of materials that have different refractive indices. Wave parameters such as amplitude and phase of diffracted waves are modulated depending on the structure configuration. The main purpose of this software is to calculate complex transmission and reflection coefficients of diffracted waves from dielectric metasurfaces that are composed of arrays of subwavelength antennas.Solution method: Rigorous coupled-wave analysis associated with an extended scattering matrix method. According to Bloch’s theorem, diffracted waves from periodic structures can be represented as a truncated Fourier series in which the primitive reciprocal vector is the same as that of periodic structures. Appropriate boundary conditions at the interface of a single structure layer enable development of an eigenvalue equation for which the solution gives a scattering matrix of the layer, and the coupling coefficients within it. In the case of a multilayered structure, a total scattering matrix can be obtained using the Redheffer star product, which interconnects scattering matrices of each layer. Total coupling coefficients can be also calculated using the extended Redheffer star product; this ability is a major advantage of the extended scattering matrix method. Diffraction from periodic structures can be fully described by the total scattering matrix and total coupling coefficients.Additional comments including restrictions and unusual features: MAXIM builds on several open-source Python packages including PySide2 [1], Numpy [2], Scipy [3], Pandas [4], Matplotlib [5] and Pyinstaller [6].

Raman Spectroscopy of Twisted Bilayer Graphene

When two periodic two-dimensional structures are superposed, any mismatch rotation angle between the layers generates a Moiré pattern superlattice, whose size depends on the twisting angle θ. If the layers are composed by different materials, this effect is also dependent on the lattice parameters of each layer. Moiré superlattices are commonly observed in bilayer graphene, where the mismatch angle between layers can be produced by growing twisted bilayer graphene (TBG) samples by CVD or folding the monolayer back upon itself. In TBG, it was shown that the coupling between the Dirac cones of the two layers gives rise to van Hove singularities (vHs) in the density of electronic states, whose energies vary with θ. The understanding of the behavior of electrons and their interactions with phonons in atomically thin heterostructures is crucial for the engineering of novel 2D devices. Raman spectroscopy has been often used to characterize twisted bilayer graphene and graphene heterostructures. Here, we review the main important effects in the Raman spectra of TBG discussing firstly the appearance of new peaks in the spectra associated with phonons with wavevectors within the interior of the Brillouin zone of graphene corresponding to the reciprocal unit vectors of the Moiré superlattice, and that are folded to the center of the reduced Brillouin Zone (BZ) becoming Raman active. Another important effect is the giant enhancement of G band intensity of TBG that occurs only in a narrow range of laser excitation energies and for a given twisting angle. Results show that the vHs in the density of states is not only related to the folding of the commensurate BZ, but mainly associated with the Moiré pattern that does not necessarily have a translational symmetry. Finally, we show that there are two different resonance mechanisms that activate the appearance of the extra peaks: the intralayer and interlayer electron–phonon processes, involving electrons of the same layer or from different layers, respectively. Both effects are observed for twisted bilayer graphene, but Raman spectroscopy can also be used to probe the intralayer process in any kind of graphene-based heterostructure, like in the graphene/h-BN junctions.

Three-dimensional nonlinear photonic crystal in naturally grown potassium\u2013tantalate\u2013niobate perovskite ferroelectrics

Since quasi-phase-matching of nonlinear optics was proposed in 1962, nonlinear photonic crystals were rapidly developed by ferroelectric domain inversion induced by electric or light poling. The three-dimensional (3D) periodical rotation of ferroelectric domains may add feasible modulation to the nonlinear coefficients and break the rigid requirements for the incident light and polarization direction in traditional quasi-phase-matching media. However, 3D rotating ferroelectric domains are difficult to fabricate by the direct external poling technique. Here, we show a natural potassium–tantalate–niobate (KTN) perovskite nonlinear photonic crystal with spontaneous Rubik’s cube-like domain structures near the Curie temperature of 40 °C. The KTN crystal contains 3D ferroelectric polarization distributions corresponding to the reconfigured second-order susceptibilities, which can provide rich reciprocal vectors to compensate for the phase mismatch along an arbitrary direction and polarization of incident light. Bragg diffraction and broadband second-harmonic generation are also presented. This natural nonlinear photonic crystal directly meets the 3D quasi-phase-matching condition without external poling and establishes a promising platform for all-optical nonlinear beam shaping and enables new optoelectronic applications for perovskite ferroelectrics.

Instrument-model refinement in normalized reciprocal-vector space for X-ray Laue diffraction.

A simple yet efficient instrument-model refinement method for X-ray diffraction data is presented and discussed. The method is based on least-squares minimization of differences between respective normalized (i.e. unit length) reciprocal vectors computed for adjacent frames. The approach was primarily designed to work with synchrotron X-ray Laue diffraction data collected for small-molecule single-crystal samples. The method has been shown to work well on both simulated and experimental data. Tests performed on simulated data sets for small-molecule and protein crystals confirmed the validity of the proposed instrument-model refinement approach. Finally, examination of data sets collected at both BioCARS 14-ID-B (Advanced Photon Source) and ID09 (European Synchrotron Radiation Facility) beamlines indicated that the approach is capable of retrieving goniometer parameters (e.g. detector distance or primary X-ray beam centre) reliably, even when their initial estimates are rather inaccurate.

Generation of narrowband counterpropagating polarization-entangled photon pairs based on thin-film lithium niobate on insulator

We propose a scheme for the generation of counterpropagating polarization-entangled photon pairs from a periodically poled lithium niobate on insulator waveguide. The waveguide is designed to enable a special dispersion relationship between the T M 00 and T E 00 modes that allows two concurrent counterpropagating quasi-phase-matching type-II spontaneous parametric downconversion processes with a single reciprocal wave vector. Due to the counterpropagating phase-matching geometry, the source has a narrow bandwidth in the order of several gigahertz. The compact source opens up a new method for integrated photonic technologies.

Dual-periodically poled lithium niobate microcavities supporting multiple coupled parametric processes.

Periodically poled lithium niobate (PPLN) microcavities with additional reciprocal vectors attract attention as a platform for efficient parametric nonlinear optical processes with wavelength and polarization flexibility. Here, we report the simultaneous realization of multiple coupled parametric processes in PPLN microdisk cavities with dual periods as a result of the significantly increased number of reciprocal vectors to fulfill quasi-phase matchings for a series of nonlinear processes. PPLN microdisks with up to 1.43×105 quality factors and unit domain size of 90 nm in width were fabricated using CMOS compatible microfabrication techniques and electrically poled with the help of piezoresponse force microscopy. The conversion efficiency of second-harmonic signal was measured to be 51%W-1. Our work paves the way towards efficient cascaded parametric effects including third- and fourth-harmonic generations.

An efficient method for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films.

Crystal structure identification of thin organic films entails a number of technical and methodological challenges. In particular, if molecular crystals are epitaxially grown on single-crystalline substrates a complex scenario of multiple preferred orientations of the adsorbate, several symmetry-related in-plane alignments and the occurrence of unknown polymorphs is frequently observed. In theory, the parameters of the reduced unit cell and its orientation can simply be obtained from the matrix of three linearly independent reciprocal-space vectors. However, if the sample exhibits unit cells in various orientations and/or with different lattice parameters, it is necessary to assign all experimentally obtained reflections to their associated individual origin. In the present work, an effective algorithm is described to accomplish this task in order to determine the unit-cell parameters of complex systems comprising different orientations and polymorphs. This method is applied to a polycrystalline thin film of the conjugated organic material 6,13-pentacenequinone (PQ) epitaxially grown on an Ag(111) surface. All reciprocal vectors can be allocated to unit cells of the same lattice constants but grown in various orientations [sixfold rotational symmetry for the contact planes (102) and (102)]. The as-determined unit cell is identical to that reported in a previous study determined for a fibre-textured PQ film. Preliminary results further indicate that the algorithm is especially effective in analysing epitaxially grown crystallites not only for various orientations, but also if different polymorphs are present in the film.