Geometric Phase Research Articles

Flat optics of nonuniform phase gradient metasurfaces

Abstract Flat optics of uniform phase gradient metasurfaces based on the generalized Snell’s law has been extensively studied. The optics of nonuniform phase gradient metasurfaces (NPGMs) is less clear. Here based on Huygens’ principle and finite-difference time-domain (FDTD) simulation, we explore the optical properties of NPGMs made of nanorods (meta-atoms), which can be tuned by modulation of propagation phase and geometric phase. It is found that the nonuniformity of phase gradient may lead to multichannel anomalous reflection/refraction. The multiple beam splitters with arbitrary intensity ratio can be achieved by using the amplitude/phase modulation. Based on our design principle, we can obtain different anomalous reflection patterns (with channels ±1, ±2, both ±1 and ±2, or no reflection at anomalous angle) by different arrangement of just two types of meta-atoms. In addition, we are able to achieve chiral anomalous reflections for designed NPGMs made of nanorods and L-shaped nanoparticles. Our formulism provides general design guidance for NPGMs and can be used to realize the beam splitting function with adjustable angle and intensity ratio.

Multifunctional Meta-Devices for Full-Polarization Rotation and Focusing in the Near-Infrared

The creation of multi-channel focused beams with arbitrary polarization states and their corresponding optical torques finds effective applications in the field of optical manipulation at the micro-nanoscale. The existing metasurface-based technologies for polarization rotation have made some progress, but they have been limited to single functions and have not yet achieved the generation of full polarization. In this work, we propose a multi-channel and spatial-multiplexing interference strategy for the generation of multi-channel focusing beams with arbitrary polarization rotation based on all-dielectric birefringent metasurfaces via simultaneously regulating the propagation phase and the geometric phase and independently controlling the wavefronts at different circular polarizations. For the proof of concept, we demonstrate highly efficient multi-channel polarization rotation meta-devices. The meta-devices demonstrate ultra-high polarization extinction ratios and high focusing efficiencies at each polarization channel. Our work provides a compact and versatile wavefront-shaping methodology for full-polarization control, paving a new path for planar multifunctional meta-optical devices in optical manipulation at micro–nano dimensions.

Using Rotations to Control Observable Relativistic Effects

This paper examines the possibility of controlling the outcome of measured (flat space-time) relativistic effects, such as time dilation or length contractions, using pure rotations and their nontrivial interactions with Lorentz boosts in the isometry group SO+(3,1). In particular, boost contributions may annihilate leaving only a geometric phase (Wigner rotation), which we see in the complex solutions of the generalized Euler decomposition problem in R3. We consider numerical examples involving specific matrix factorizations, along with possible applications in special relativity, electrodynamics and quantum scattering. For clearer interpretation and simplified calculations we use a convenient projective biquaternion parametrization which emphasizes the geometric phases and for a large class of problems allows for closed-form solutions in terms of only rational functions.

Phase and amplitude reconstruction by weak measurement based on metasurface

Phase distribution is crucial for obtaining the whole information of phase object in imaging. However, due to the transparency of phase objects, the phase distribution cannot be obtained in traditional bright-field imaging. Here, we propose a phase distribution reconstruction based on the imaginary value of weak measurement, which is achieved by a Pancharatnam–Berry phase metasurface. Moreover, by adjusting the weak value to a real weak value, amplitude reconstruction can also be achieved. Different parts of weak values can be obtained by controlling the preselection and postselection states. The weak interaction is achieved by the metasurface, which is convenient to control the weak coupling and reduce the complexity of the experimental setup at the same time. Furthermore, the edge contour of objects can also be acquired by the weak measurement, and the edge sharpness is related to types of the weak values, which plays an important role in image resolution. Our method paves a way for quantitative phase imaging and unlabeled biological imaging.

First-principles study on the structural, elastic, electronic, optical and thermophysical properties of NaNO3 and K-doped NaNO3

The current work illustrates the optical, thermophysical, electronic, elastic, and structural characteristics of pure and K-doped NaNO3 obtained using DFT calculations. Electronic characteristics such as band structure, projected and total density of states of pure and doped NaNO3 are analyzed where the calculated band gaps for pure and K-doped NaNO3 were discovered to be 3.05 eV and 2.90 eV, respectively. The Berry–phase calculations carried out on both systems showed the existence of ferroelectric polarization, where an enhanced spontaneous polarization value of 36 μC/cm2 for K-doped NaNO3, as compared to 20 μC/cm2 for intrinsic NaNO3 is obtained. The thermophysical properties such as bulk modulus (B0), Debye temperature (θ D), and specific heat capacity (Cv) were calculated over a wide temperature range from 0 K to 800 K. The linear optical properties namely the dielectric constant, refractive index, electron energy loss function, absorption and extinction coefficient are calculated in wide energy range from 0 to 30 eV and discussed in detail.

Nontrivial evolution and geometric phase for an orbital angular momentum qutrit

Photonic orbital angular momentum (OAM) offers a promising platform for high-dimensional quantum information processing. While geometric phase (GP) is the crucial tool in enabling intrinsically fault-tolerant quantum computation, the measurement of GP using linear optics remains relatively unexplored in the OAM state space. Here, we propose an experimental scheme to detect GP shifts resulting from the cyclic evolution of OAM qutrit states. Distinguished with the conventional evolution along cyclic path on the Poincaré sphere (PS), the nontrivial evolution in our theoretical scheme is along a cyclic path residing within the SU(3)/U(2) parameter space. By employing a combination of X-gates, dove prisms, and double cylindrical lenses, we achieve the cyclic evolution and analyse the resultant GP through our designed Sagnac interferometer. Our theoretical study may find potential in high-dimensional quantum computation using twisted photons and in exploring the geometric structure of such optical systems.

Two-dimensional Sb net generated nontrivial topological states in SmAgSb2 probed by quantum oscillations

Abstract The REAgSb2 (RE = rare earth and Y) family has drawn considerable research interest because the two-dimensional Sb net in their crystal structure hosts topological fermions and hence rich topological properties. We report herein the magnetization and magnetotransport measurements of SmAgSb2 single crystal, which unveil very large magnetoresistance and high carrier mobility up to 6.2×103% and 5.58×103 cm2V-1s-1, respectively. The analysis of both Shubnikov-de Haas and de Haas-van Alphen quantum oscillations indicates nontrivial Berry phases in the paramagnetic state while trivial Berry curvature in the antiferromagnetic state, indicating a topological phase transition induced by the antiferromagnetic order. It is also supported by the first-principles calculations. The results not only provide a new interesting topological material but also offer valuable insights into the correlation between magnetism and nontrivial topological states.

Broadband spin-decoupled metasurface for independent wavefront manipulations of orthogonal circularly-polarized waves

Abstract Metasurfaces endowed with spin-decoupled functionalities offer the capability to meticulously customize the electromagnetic wavefronts of incident dual orthogonal circularly-polarized (CP) waves in a desirable manner, that holds immense potential for broadening their application fields. Nevertheless, a major lack that persists in most spin-decoupled metasurfaces is the limited bandwidth or the intricate design requirements. Herein, we propose a broadband spin-decoupled metasurface, consisted of weak-resonant mirror-symmetry unit structures, that enables independent and distinct wavefront manipulations under the incidence of orthogonal CP waves. As a demonstration, we present a dual-channel metasurface that integrates geometric and propagation phases to generate vortex waves with two distinct modes in a wide frequency range from 10 GHz to 16 GHz. Both simulated and experimental results
are consistent and collectively confirm the validity of our proposed metasurface. The research provides a practical and efficient avenue for constructing spin-decoupled metasurface within a broad frequency band.

Polarization evolution on higher and hybrid-order Poincaré spheres with coaxial polarization holograms

Based on the tensor polarization holography theory, we propose a simple and convenient method in the recording material, phenanthrenequinone-doped polymethylmethacrylate, to generate beams on higher and hybrid-order Poincaré spheres, and realize their polarization evolution on the spheres by combining the recorded phase with the Pancharatnam–Berry phase. By simultaneously adjusting the polarization azimuth angle and relative phase of the recorded waves, independent phase-shifts can be imparted onto two orthogonal circular polarization states in reconstruction process of polarization holography. The beams on basic Poincaré sphere are transformed into that on arbitrary higher or hybrid-order Poincaré spheres. We get the Poincaré spheres’ type and polarization distribution of the reconstructed wave by interferometry and polarizer, and the results match well with the theoretical predictions.

Strong Angular Oscillation of Rotationally Resolved Differential Cross Section in the H + HD → H2 + D Reaction at the Collision Energy of 2.07 eV: Evidence of Geometric Phase Effects.

Geometric phase (GP) effects in chemical reactions are subtle quantum phenomena that are challenging to identify. In this work, we report a joint experimental and theoretical study of the H + HD → H2 + D reaction at a collision energy of 2.07 eV, which is far below the energy of the conical intersection of 2.53 eV. The rotationally state-resolved differential cross sections were measured by a crossed-beam experiment with the scheme of D-atom Rydberg tagging time-of-flight detection. Experimental angular distributions of three rotational states of H2 products exhibit notable variation near the backward scattering direction. Time-dependent quantum mechanics calculations (TDQMs) were carried out at the same collision energy, with and without the inclusion of GP. The experimental angular distributions are in good agreement with TDQM results with the inclusion of GP but do not agree with TDQM results without the inclusion of GP. This work demonstrates the existence of GP effects at energy far below the conical intersection.

The type-I, III nodal ring, type-I, III quadratic nodal point, and Dirac valley phonons in 2D kagome lattices M2C3 (M = As, Bi, Cd, Hg, P, Sb, Zn)

Topological phases in kagome systems have garnered considerable interest since the introduction of the colloidal kagome lattice. Our study employs first-principle calculations and symmetry analysis to predict the existence of ideal type-I, III nodal rings (NRs), type-I, III quadratic nodal points (QNPs), and Dirac valley phonons (DVPs) in a collection of two-dimensional (2D) kagome lattices M2C3 (M = As, Bi, Cd, Hg, P, Sb, Zn). Specifically, the Dirac valley points (DVPs) can be observed at two inequivalent valleys with Berry phases of +π and −π , connected by edge arcs along the zigzag and armchair directions. Additionally, the QNP is pinned at the Γ point, and two edge states emerge from its projections. Notably, these kagome lattices also exhibit ideal type-I and III nodal rings protected by time inversion and spatial inversion symmetries. Our work examines the various categories of nodal points and nodal ring phonons within the 2D kagome systems and presents a selection of ideal candidates for investigating topological phonons in bosonic systems.

Independent Phase Control in Gap‐Tuned Metasurfaces for Dual‐Function Switching

AbstractSeeking new ways to actively control the phase using metasurfaces has gained significant attention in recent years, which is the key to achieve controllable wavefronts under external stimuli. Among various active phase control mechanisms, a mechanical method based on gap tuning, termed as gap‐tuned metasurface here, has shown promise in continuous phase adjustment. However, previous studies face limitations in independent and complete phase control at different gap distances, which is crucial in dual‐function switching applications. In this study, a novel type of gap‐tuned metasurfaces are proposed, which can overcome the above limitations through simultaneously manipulating the Pancharatnam–Berry phase and gap‐induced dynamic phase under circularly polarized incidences. Two exemplary gap‐tuned metasurfaces capable of orbital angular momentum (OAM) switching and focusing‐polarity switching are experimentally demonstrated. Furthermore, the special dynamic phase design also exhibits phase conjugate property similar to the Pancharatnam–Berry phase, making circular polarization handedness an alternative route for dual‐function switching. This method provides a straightforward and effective means for the development of active wavefront control devices.

Multichannel focused higher-order Poincaré sphere beam generation based on a dielectric geometric metasurface

Focused vector beams (VBs) are important topic in the areas of light field manipulation. Geometric metasurfaces provide a convenient platform to facilitate the generation of focused VBs. In this study, we propose a dielectric geometric metasurface to generate multichannel focused higher-order Poincaré sphere (HOP) beams. With identical meta-atoms of half-wave plate, the metasurface comprises two sub-metasurfaces, and each of them includes two sets of rings related to Fresnel zones. For meta-atoms on each set of rings, the hyperbolic geometric phase profile is configured so that the mirror-symmetrical position-flip of the off-axis focal point is enabled under the chirality switch of the illuminating circular polarization. With the design of helical geometric phase profiles for the two sets of rings, a sub-metasurface generate two HOP beams at the symmetrical two focal points. The performance of the two sub-metasurfaces enables the metasurface with four sets of rings to generate the array of four HOP beams. The proposed method was validated by theoretical analyses, numerical simulation and experimental conduction. This research would be significant in miniaturizing and integrating optical systems involving applications of VB generations and applications.

Delusive chirality and periodic strain pattern in moiré systems

Geometric phase analysis (GPA) is a widely used technique for extracting displacement and strain fields from scanning probe images. Here, we demonstrate that GPA should be implemented with caution when several fundamental lattices contribute to the image, in particular in twisted heterostructures featuring moiré patterns. We find that in this case, GPA is likely to suggest the presence of chiral displacement and periodic strain fields, even if the structure is completely relaxed and without distortions. These delusive fields are subject to change with varying twist angles, which could mislead the interpretation of twist angle-dependent properties.

Design, fabrication, and test of bi-functional metalenses for the spin-dependent OAM shift of optical vortices

The ability to encode different operations into a single miniaturized optical device is required to reduce the complexity and size of optical paths for light manipulation, which usually employs dynamic optical components, interferometric setups, and/or multiple bulky elements in cascade. A very efficient solution is provided by metalenses, which are flat optical elements able to generate and manipulate structured light beams in a compact and efficient way, offering a powerful and attractive tool in many fields, such as life science and telecommunications. In this work, we present the design and test of transmission dielectric bi-functional metalenses that exploit both the dynamic and the geometric phases, to enable the spin-controlled manipulation of different focused orbital angular momentum (OAM) beams, depending on the circularly polarized state in input. In detail, we provide numerical algorithms for the design and simulation of the meta-optics in the telecom infrared, the fabrication processes, and the optical characterization under different impinging polarized optical vortices. This solution provides new integrated flat optics for applications in imaging, optical tweezing and trapping, optical computation, and high-capacity telecommunication and encryption.

Quantum oscillations and electronic features in V1− δ Sb2 single crystals

Nonsymmorphic compounds have attracted much interest owing to their potential nontrivial electronic states. Here, we grew V1−δSb2 single crystal with a nonsymmorphic space group I4/mcm and studied their de Haas–van Alphen oscillations. Orientation-dependent magnetization showed quantum oscillations, allowing determination of the three-dimensional Fermi surface and Berry phase. Our theoretical calculation implied that VSb2's band structures manifest flat bands along the Γ–X path, Dirac band crossings near the P and N points, and in the Γ–Z direction, and nontrivial surface states along the Γ¯–Z¯ line. However, the inconsistencies in observed and calculated quantum oscillation frequencies suggest that VSb2's band structures cannot nicely account for these electronic properties of our samples. This study reveals the profound impact of V vacancies on VSb2's electronic states, implying the possible topological quantum phase transition via defect engineering.

Cascaded chiral birefringent media enabled planar lens with programable chromatic aberration

Wavefront control is the fundamental requirement in optical informatics. Planar optics have drawn intensive attention due to the merits of compactness and light weight. However, it remains a challenge to freely manipulate the dispersion, hindering practical applications, especially in imaging. Here, we propose the concept of frequency-synthesized phase engineering to solve this problem. A phasefront-frequency matrix is properly designed to encode different spatial phases to separate frequencies, thus makes arbitrary dispersion tailoring and even frequency-separated functionalization possible. The periodically rotated director endows cholesteric liquid crystal with a spin and frequency selective reflection. Moreover, via presetting the local initial orientation of liquid crystal, geometric phase is encoded to the reflected light. We verify the proposed strategy by cascading the chiral anisotropic optical media of specifically designed helical pitches and initial director orientations. By this means, planar lenses with RGB achromatic, enhanced chromatic aberration and color routing properties are demonstrated. Inch-sized and high-efficient lenses are fabricated with low crosstalk among colors. It releases the freedom of dispersion control of planar optics, and even enables frequency decoupled phase modulations. This work brings new insights to functional planar optics and may upgrade the performance of existing optical apparatuses.

Tensile Strain‐Mediated Bimetallene Nanozyme for Enhanced Photothermal Tumor Catalytic Therapy

AbstractNanozymes have demonstrated significant potential in combating malignant tumor proliferation through catalytic therapy. However, the therapeutic effect is often limited by insufficient catalytic performance. In this study, we propose the utilization of strain engineering in metallenes to fully expose the active regions due to their ultrathin nature. Here, we present the first report on a novel tensile strain‐mediated local amorphous RhRu (la‐RhRu) bimetallene with exceptional intrinsic photothermal effect and photo‐enhanced multiple enzyme‐like activities. Through geometric phase analysis, electron diffraction profile, and X‐ray diffraction, it is revealed that crystalline‐amorphous heterophase boundaries can generate approximately 2 % tensile strain in the bimetallene. The ultrathin structure and in‐plane strain of the bimetallene induce an amplified strain effect. Both experimental and theoretical evidence support the notion that tensile strain promotes multiple enzyme‐like activities. Functioning as a tumor microenvironment (TME)‐responsive nanozyme, la‐RhRu exhibits remarkable therapeutic efficacy both in vitro and in vivo. This work highlights the tremendous potential of atomic‐scale tensile strain engineering strategy in enhancing tumor catalytic therapy.

Tensile Strain-Mediated Bimetallene Nanozyme for Enhanced Photothermal Tumor Catalytic Therapy.

Nanozymes have demonstrated significant potential in combating malignant tumor proliferation through catalytic therapy. However, the therapeutic effect is often limited by insufficient catalytic performance. In this study, we propose the utilization of strain engineering in metallenes to fully expose the active regions due to their ultrathin nature. Here, we present the first report on a novel tensile strain-mediated local amorphous RhRu (la-RhRu) bimetallene with exceptional intrinsic photothermal effect and photo-enhanced multiple enzyme-like activities. Through geometric phase analysis, electron diffraction profile, and X-ray diffraction, it is revealed that crystalline-amorphous heterophase boundaries can generate approximately 2 % tensile strain in the bimetallene. The ultrathin structure and in-plane strain of the bimetallene induce an amplified strain effect. Both experimental and theoretical evidence support the notion that tensile strain promotes multiple enzyme-like activities. Functioning as a tumor microenvironment (TME)-responsive nanozyme, la-RhRu exhibits remarkable therapeutic efficacy both in vitro and in vivo. This work highlights the tremendous potential of atomic-scale tensile strain engineering strategy in enhancing tumor catalytic therapy.

Universal scaling law for chiral antiferromagnetism

The chiral antiferromagnetic (AFM) materials, which have been widely investigated due to their rich physics, such as non-zero Berry phase and topology, provide a platform for the development of antiferromagnetic spintronics. Here, we find two distinctive anomalous Hall effect (AHE) contributions in the chiral AFM Mn3Pt, originating from a time-reversal symmetry breaking induced intrinsic mechanism and a skew scattering induced topological AHE due to an out-of-plane spin canting with respect to the Kagome plane. We propose a universal AHE scaling law to explain the AHE resistivity (ρAH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\rho }}_{AH}$$\\end{document}) in this chiral magnet, with both a scalar spin chirality (SSC)-induced skew scattering topological AHE term, ask\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${a}_{sk}$$\\end{document} and non-collinear spin-texture induced intrinsic anomalous Hall term, bin\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{b}}_{{in}}$$\\end{document}. We found that ask\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{a}}}_{{{sk}}}$$\\end{document} and bin\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{b}}}_{{{in}}}$$\\end{document} can be effectively modulated by the interfacial electron scattering, exhibiting a linear relation with the inverse film thickness. Moreover, the scaling law can explain the anomalous Hall effect in various chiral magnets and has far-reaching implications for chiral-based spintronics devices.