Masato Suzuki, Keisaku Yamane, Kazuhiko Oka, Yasunori Toda, Ryuji Morita
In a recent letter, Milione et al. reported the Pancharatnam-Berry phase (PBP) on a higher-order Poincaré sphere (HOPS) [Phys. Rev. Lett, 108, 190401 (2012)]. They used two spin-orbit converters (SOCs) to make a trajectory along the HOPS. However, the SOCs actually do not make a path on the HOPS. We briefly discuss a way of acquiring a PBP made by SOCs.
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Relying on the local orientation of nanostructures, Pancharatnam-Berry metasurfaces are currently enabling a new generation of polarization-sensitive optical devices. A systematical mesoscopic description of topological metasurfaces is developed, providing a deeper understanding of the physical mechanisms leading to the polarization-dependent breaking of translational symmetry in contrast with propagation phase effects. These theoretical results, along with interferometric experiments, contribute to the development of a solid theoretical framework for arbitrary polarization-dependent metasurfa…
We apply the Pancharatnam-Berry phase approach to plasmonic metasurfaces loaded by highly nonlinear multi-quantum well substrates, establishing a platform to control the nonlinear wavefront at will based on giant localized nonlinear effects. We apply this approach to design flat nonlinear metasurfaces for efficient second-harmonic radiation, including beam steering, focusing, and polarization manipulation. Our findings open a new direction for nonlinear optics, in which phase matching issues are relaxed, and an unprecedented level of local wavefront control is achieved over thin devices with g…
The Pancharatnam-Berry (PB) phase in metasurfaces obeys the symmetry restriction, according to which the PB phases of two orthogonal circularly polarized waves are the same but with opposite signs. Here, we reveal a general mechanism to break the axisymmetry of meta-atoms in order to break the PB-phase symmetry restriction. As a proof of concept, we designed a novel meta-atom with a QR-code structure and successfully demonstrated circular-polarization multiplexing metasurface holography. This study provides a fundamentally new understanding of the PB phase and opens a path for arbitrary wavefr…
Since its introduction by Sir Michael Berry in 1984, geometric phase became of fundamental importance in physics, with applications ranging from solid state physics to optics. In optics, Pancharatnam-Berry phase allows the tailoring of optical beams by a local control of their polarization. Here we discuss light propagation in the presence of an intensity-dependent local modulation of the Pancharatnam-Berry phase. The corresponding self-modulation of the wavefront counteracts the natural spreading due to diffraction, i.e., self-focusing takes place. No refractive index variation is associated …
In polarization optics unitary and non-unitary operations can be carried out by the Jones matrix. $\mathbf{Z}$ matrix is the $4\times 4$ analogue of the Jones matrix and the Mueller matrix of a nondepolarizing optical medium can be written as $\mathbf{M}=\mathbf{Z}\mathbf{Z}^*$. Jones matrix acts on the two component complex Jones vector, while the $\mathbf{Z}$ matrix acts on the four component real Stokes vector. Polarizer and retarder $\mathbf{Z}$ matrices can be written in compact forms in terms of the components of the position vector on the Poincaré sphere. In this note it is shown that t…
Active control of phase matching in nonlinear metasurfaces using Pancharatnam--Berry phase
通过利用非线性潘查拉坦-伯瑞相，研究非线性超材料的相匹配控制，实现900-970nm波长范围内二次谐波生成相匹配峰的连续调谐。
We derived the Berry connection of vector vortex states (VVSs) from the "true" Hamiltonian obtained through the Maxwell--Schrödinger equation for an inhomogeneous anisotropic (IA) medium, and we experimentally demonstrated measurement of the corresponding Pancharatnam--Berry (PB) geometrical phase of VVSs. The PB phase (PBP) of VVSs can be divided into two phases: homogeneous and inhomogeneous PBPs. Homogeneous and inhomogeneous PBPs are related to the conventional PBP and the spatially-dependent geometric phase given by an IA medium such as a polarization converter, respectively. We theoretic…
We theoretically and numerically investigate the properties of waveguides based on the Pancharatnam-Berry phase, obtained by a longitudinally periodic rotation of the optic axis in a transversely-twisted birefringent medium. In this paper we study the case where the period of the longitudinal modulation is chosen so that a net accumulation of geometric phase in propagation occurs. First, the interplay between different contributions to the optical potential is addressed. Second, a continuous evolution of the polarization structure of the quasi-modes is observed in the numerical simulations. We…
Perfect vortex beams are the orbital angular momentum (OAM)-carrying beams with fixed annular intensities, which provide a better source of OAM than traditional Laguerre- Gaussian beams. However, ordinary schemes to obtain the perfect vortex beams are usually bulky and unstable. We demonstrate here a novel generation scheme by designing planar Pancharatnam-Berry (PB) phase elements to replace all the elements required. Different from the conventional approaches based on reflective or refractive elements, PB phase elements can dramatically reduce the occupying volume of system. Moreover, the PB…
We tested the ability of human observers to discriminate distinct profiles of spatially dependant geometric phases when directly viewing stationary structured light beams. Participants viewed polarization coupled orbital angular momentum (OAM) states, or ``spin-orbit'' states, in which the OAM was induced through Pancharatnam-Berry phases. The coupling between polarization and OAM in these beams manifests as spatially dependant polarization. Regions of uniform polarization are perceived as specifically oriented Haidinger's brushes, and study participants discriminated between two spin-orbit st…
We discuss the propagation of an electromagnetic field in an inhomogeneously anisotropic material where the optic axis is rotated in the transverse plane but is invariant along the propagation direction. In such a configuration, the evolution of an electromagnetic wavepacket is governed by the Pancharatnam-Berry phase (PBP), responsible for the appearance of an effective photonic potential. In a recent paper [A. Alberucci et al., "Electromagnetic confinement via spin-orbit interaction in anisotropic dielectrics", ACS Photonics \textbf{3}, 2249 (2016)] we demonstrated that the effective potenti…
Recent developments in the field of photonic spin Hall effect (SHE) offer new opportunities for advantageous measurement of the optical parameters (refractive index, thickness, etc.) of nanostructures and enable spin-based photonics applications in the future. However, it remains a challenge to develop a tunable photonic SHE with any desired spin-dependent splitting for generation and manipulation of spin-polarized photons. Here, we demonstrate experimentally a scheme to realize the photonic SHE tunably by tailoring the space-variant Pancharatnam-Berry phase (PBP). It is shown that light beams…
Manipulating the polarisation of light is crucial for sensing and imaging applications. One such aspect in particular is selective transmission of one circular polarisation (spin) when light is transmitted through a medium or a device. However, most present methods of achieving this have relatively low efficiency and selectivity, whilst high selectivity examples rely on lossy and complex three-dimensional helical or multilayer structures. Here, we propose a dielectric metamaterial approach for achieving spin-selective transmission of electromagnetic waves, utilizing spin-controlled constructiv…
Pancharatnam Berry Phase as the Origin of Vector Nature Observed in Hermite Gaussian Superposition States
Hermite高斯叠加态中向量性质的起源源于径向不均匀强度分布和偏振依赖的Pancharatnam Berry相位。
On-demand longitudinal transformations of light beams via an amplitude-phase-decoupled Pancharatnam-Berry phase element
本文提出棋盘编码的Pancharatnam-Berry相位元件，实现振幅与相位同时调制，并结合液晶q板和波片首次实现传播变换光学斯格明子及多种光束的按需纵向变换。
In this paper, the implementation of optical elements in the form of Pancharatnam-Berry optics is considered. With respect to 3D bulk and diffractive optics, acting on the dynamic phase of light, Pancharatnam-Berry optical elements transfer a phase which is geometric in nature by locally manipulating the polarization state of the incident beam. They can be realized as space-variant sub-wavelengths gratings that behave like inhomogeneous form-birefringent materials. We present a comprehensive work of simulation, realization, and optical characterization at the telecom wavelength of 1310 nm of t…
The working principle of ordinary refractive lenses can be explained in terms of the space-variant optical phase retardations they introduce, which reshape the optical wavefront curvature and hence affect the subsequent light propagation. These phases, in turn, are due to the varying optical path length seen by light at different transverse positions relative to the lens centre. A similar lensing behavior can however be obtained when the optical phases are introduced by an entirely different mechanism. Here, we consider the "geometric phases" that arise from the polarization transformations oc…
In order to overcome the accommodation and convergence (A-C) conflict that commonly causes visual fatigue in AR display, we propose a Maxwellian-viewing-super-multi-view (MV-SMV) near-eye display system based on a Pancharatnam-Berry optical element (PBOE). The PBOE, which is constituted with an array of high-efficiency polarization gratings, is implemented to direct different views to different directions simultaneously, constructing the 3D light field. Meanwhile, each view is like a Maxwellian view display that possesses a small viewpoint and a large depth of field (DOF). Hence, the MV-SMV di…
We report the realization of a Pancharatnam-Berry phase optical element [Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. \textbf{27}, 1141 (2002)] for wavefront shaping working in the visible spectral domain, based on patterned liquid crystal technology. This device generates helical modes of visible light with the possibility of electro-optically switching between opposite helicities by controlling the handedness of the input circular polarization. By cascading this approach, fast switching among multiple wavefront helicities can be achieved, with potential applications to multi-s…
Deciphering Pancharatnam's discovery of geometric phase
针对Pancharatnam1956年发现的几何相位因论文晦涩常被误读的问题，梳理其原始推导并关联近年研究，助力学界准确理解这篇经典工作。
A simple variation of the traditional Young's double slit experiment can demonstrate several subtleties of interference with polarized light, including Berry and Pancharatnam's phase. Since the position of the fringes depends on the polarization state of the light at the input, the apparatus can also be used to measure the light's polarization without a quarter-wave plate or an accurate measurement of the light's intensity. In principle this technique can be used for any wavelength of photon as long as one can effectively polarize the incoming radiation.
Breaking of reciprocity and the Pancharatnam-Berry phase for light scattered by a disordered cold atom cloud
本文利用偏振操控元件的非对易性，在无序冷原子云散射光中实现互易性破缺，通过条纹对比度降低和位移观测Pancharatnam-Berry相位，为操控无序介质散射光的路径干涉奠定基础。
The nonlinear processes of frequency conversion like second harmonic generation (SHG) usually obey certain selection rules, resulting from the preservation of different kind of physical quantities, e.g., the angular momentum. For SHG created by monolayer of transition-metal dichalcogenides (TMDCs) like WS2, the valley-exciton locked selection rule predicts an SHG signal in the cross-polarization state. By combining plasmonic nanostructures with a monolayer of TMDC, a hybrid metasurface is realized which affects this nonlinear process due to an additional polarization conversion process. Here, …
Parallel sorting of orbital angular momentum (OAM) and polarization has recently acquired paramount importance and interest in a wide range of fields ranging from telecommunications to high-dimensional quantum cryptography. Due to their inherently polarization-sensitive optical response, optical elements acting on the geometric phase prove to be useful for processing structured light beams with orthogonal polarization states by means of a single optical platform. In this work, we present the design, fabrication and test of a Pancharatnam-Berry optical element in silicon implementing a log-pol …
Whenever a quantum system undergoes a cycle governed by a slow change of parameters, it acquires a phase factor: the geometric phase. Its most common formulations are known as the Aharonov-Bohm, Pancharatnam and Berry phases, but both prior and later manifestations exist. Though traditionally attributed to the foundations of quantum mechanics, the geometric phase has been generalized and became increasingly influential in many areas from condensed-matter physics and optics to high energy and particle physics and from fluid mechanics to gravity and cosmology. Interestingly, the geometric phase …
Topological transitions of the generalized Pancharatnam-Berry phase
本文利用光学平台实验演示并研究了单量子比特广义测量所诱导的广义 Pancharatnam-Berry 几何相位随测量强度发生的拓扑转变，证明其对协议推广和部分缺陷具有鲁棒性。
Nonreciprocal Pancharatnam-Berry Metasurface for Unidirectional Wavefront Manipulation
提出利用 YIG 磁光效应与 PB 几何相位协同的亚波长非互易超表面，实现圆偏振光高隔离及单向光束偏转与聚焦。
Dielectric metasurfaces with spatially varying birefringence and high transmission efficiency can exhibit exceptional abilities for controlling the photonic spin states. We present here some of our works on spin photonics and spin-photonic devices with metasurfaces. We develop a hybrid-order Poincare sphere to describe the evolution of spin states of wave propagation in the metasurface. Both the Berry curvature and the Pancharatnam-Berry phase on the hybrid-order Poincare sphere are demonstrated to be proportional to the variation of total angular momentum. Based on the spin-dependent property…
This paper presents the design and experimental demonstration of an impedance-matched circular polarization selective surface which also offers spin-selective phase modulations at microwave frequencies. We achieve this by leveraging the theory of Pancharatnam-Berry phase and cascading four tensor impedance layers, each comprising an array of crossed meander lines. These meander lines are precisely tuned and rotated to implement particular tensor surface impedance values to satisfy the impedance-matching condition for the transmitted right-handed circularly-polarized field while inducing Pancha…
Gateway to all-optical spin switching in Heusler ferrimagnets: Pancharatnam-Berry tensor and magnetic moment ratio
本研究提出以费米能级附近平带作为AOS门户态，引入三阶PB张量并结合亚晶格磁矩比，揭示Mn基Heusler亚铁磁体实现全光自旋翻转的判据。
In this work, we develop a hybrid-order Poincaré sphere to describe the evolution of polarization states of wave propagation in inhomogeneous anisotropic media. We extend the orbital Poincaré sphere and high-order Poincaré sphere to a more general form. Polarization evolution in inhomogeneous anisotropic media with special geometry can be conveniently described by state evolution along the longitude line on the hybrid-order Poincaré sphere. Similar to that in previously proposed Poincaré spheres, the Berry curvature can be regarded as an effective magnetic field with monopole centered at the o…
On-chip optical wavefront shaping by transverse spin induced Pancharatanam-Berry phase
本文提出一种基于导波光固有横向自旋的新型Pancharatnam-Berry几何相位，通过旋转金属纳米棒实现表面等离激元波前调控，用于片上光操纵和超紧凑光学器件设计。
Geometric phase, owing to its topological nature and properties of fault tolerance, plays an important role in devising real world applications in both classical and quantum domain. For classical systems, geometric phase has been observed and studied so far for fully polarized light only. Using an interferometric experiment we demonstrate, for the first time, the existence of Pancharatnam-Berry phase for states covering all empty space inside the Poincaré sphere namely the unpolarized and partially polarized light fields. The observed geometric phase is found identical to its fully polarized c…
We examine the spin-orbit coupling effects that appear when a wave carrying intrinsic angular momentum interacts with a medium. The Berry phase is shown to be a manifestation of the Coriolis effect in a non-inertial reference frame attached to the wave. In the most general case, when both the direction of propagation and the state of the wave are varied, the phase is given by a simple expression that unifies the spin redirection Berry phase and the Pancharatnam--Berry phase. The theory is supported by the experiment demonstrating the spin-orbit coupling of electromagnetic waves via a surface p…
We realize a robust and compact cylindrical vector beam generator which consists of a simple two-element interferometer composed of a beam displacer and a cube beamsplitter. The interferometer operates on the higher-order Poincare sphere transforming a homogeneously polarized vortex into a cylindrical vector (CV) beam. We experimentally demonstrate the transformation of a single vortex beam into all the well-known CV beams and show the operations on the higher-order Poincare sphere according to the control parameters. Our method offers an alternative to the Pancharatnam-Berry phase optical ele…
Converting spin angular momentum to orbital angular momentum has been shown to be a practical and efficient method for generating optical beams carrying orbital angular momentum and possessing a space-varying polarized field. Here, we present novel liquid crystal devices for tailoring the wavefront of optical beams through the Pancharatnam-Berry phase concept. We demonstrate the versatility of these devices by generating an extensive range of optical beams such as beams carrying $\pm200$ units of orbital angular momentum along with Bessel, Airy and Ince-Gauss beams. We characterize both the ph…
Polarization vectors of light traveling in a coiled optical fiber rotate around its propagating axis even in the absence of birefringence. This rotation was usually explained due to the Pancharatnam-Berry phase of spin-1 photons. Here, we use a purely geometric method to understand this rotation. We show that similar geometric rotations also exist for twisted light carrying orbital angular momentum (OAM). The corresponding geometric phase can be applied in photonic OAM-state-based quantum computation and quantum sensing.
Comment on ``Near-field spin Chern number quantized by real-space topology of optical structures''
该评论指出，作者提出的实空间自旋陈数本质上是欧拉特征数，未定义新不变量，其结果是Chern-Gauss-Bonnet定理的特例。
Visualized Geometric Phase of Caustic Geometric Beams
针对光的Pancharatnam-Berry几何相位检测需干涉或特殊截断的问题，提出一种无需干涉仪或光束截断的直接可视化方法，利用SU(2)结构光束中焦散轨迹波包的演化，实现几何相位与Gouy相位的可视化，为复杂光场几何相位研究及光学系统设计提供新途径。
We propose and experimentally demonstrate that a metasurface consisting of Pancharatnam-Berry phase optical elements can enable the full control of optical spin-to-orbital angular momentum conversion. Our approach relies on the critical interference between the transmission and reflection upon the metasurfaceto create actively tunable and controllable conversion with a high output via coherent control of the two incident beams. The introduced control methodology is general and could be an important step toward the development of functional optical devices for practical applications.
We demonstrate experimentally an optical process in which the spin angular momentum carried by a circularly polarized light beam is converted into orbital angular momentum, leading to the generation of helical modes with a wavefront helicity controlled by the input polarization. This phenomenon requires the interaction of light with matter that is both optically inhomogeneous and anisotropic. The underlying physics is also associated with the so-called Pancharatnam-Berry geometrical phases involved in any inhomogeneous transformation of the optical polarization.
Torsional selection rule for the spin--orbit conversion of light
研究光自旋 - 轨道转换，指出标准介质通过各向异性指向矢转换，而有几何扭转的介质通过材料连接的扭曲转换，得出不同选择规则，模拟证实并提出鉴别器区分两种机制。
Light beam carrying spatially varying state of polarization generates space varying Pancharatnam-Berry geometric phase while propagating through homogeneous anisotropic medium. We show that determination of such space varying geometric phase provides a unique way to quantify the space varying polarization state of light using a single-shot interferometric measurement. We demonstrate this concept in a Mach-Zehnder interferometric arrangement using a linearly polarized reference light beam, where full information on the spatially varying polarization state is successfully recovered by quantifyin…
Exploiting hidden singularity on the surface of the Poincaré sphere
针对共偏振系统波前整形难题，提出一种利用 Poincaré 球表面隐藏奇点实现近单位效率全 2π 相移的拓扑保护相位调制机制，并在微波频段多层超表面中验证，扩展了平面光学设计工具箱。
An optical vortex (OV) is a beam with spiral wave front and screw phase dislocation. This kind of beams is attracting rising interest in various fields. Here we theoretically proposed and experimentally realized a novel but easy approach to generate optical vortices. We leverage the inherent topological vortex structures of polarization around bound states in the continuum (BIC) in the momentum space of two dimensional periodic structures, e.g. photonic crystal slabs, to induce Pancharatnam-Berry phases to the beams. This new class of OV generators operates in the momentum space, meaning that …
Phase, polarization, amplitude and frequency represent the basic dimensions of light, playing crucial roles for both fundamental light-mater interactions and all major optical applications. Metasurface emerges as a compact platform to manipulate these knobs, but previous metasurfaces have limited flexibility to simultaneous control them. Here, we introduce a multi-freedom metasurface that can simultaneously and independently modulate phase, polarization and amplitude in an analytical form, and further realize frequency multiplexing by a k-space engineering technique. The multi-freedom metasurf…
Reconstruction of light profiles with amplitude and phase information, called holography, is an attractive optical technique to display three-dimensional images. Due to essential requirements for an ideal hologram, subwavelength control of both amplitude and phase is crucial. Nevertheless, traditional holographic devices have suffered from their limited capabilities of incomplete modulation in both amplitude and phase of visible light. Here, we propose a novel metasurface that is capable of completely controlling both amplitude and phase profiles of visible light independently with subwaveleng…
Optical metasurfaces are perfect candidates for the phase and amplitude modulation of light, featuring an excellent basis for holographic applications. In this work, we present a dual amplitude holographic scheme based on the photon sieve principle, which is then combined with a phase hologram by utilizing the Pancharatnam-Berry phase. We demonstrate that two types of apertures, rectangular and square shapes in a gold film filled with silicon nanoantennas are sufficient to create two amplitude holograms at two different wavelengths in the visible, multiplexed with an additional phase-only holo…
Geometric phases are ubiquitous in physics; they act as memories of the transformation of a physical system. In optics, the most prominent examples are the Pancharatnam-Berry phase and the spin-redirection phase. Recent technological advances in phase and polarization structuring have led to the discovery of additional geometric phases of light. The underlying mechanism for all of these is provided by fibre bundle theory. In this colloquium, we review how fibre bundle theory does not only shed light on the origin of geometric phases of light, but also lays the foundations for the exploration o…
Surfaces covered with layers of ultrathin nanoantenna structures, so-called metasurfaces, have recently been proven capable of completely controlling phase of light. Metalenses have emerged from the advance in the development of metasurfaces providing a new basis for recasting traditional lenses into thin, planar optical components capable of focusing light. The lens made of arrays of plasmonic gold nanorods were fabricated on a glass substrate by using electron beam lithography. A 1064 nm laser was used to create a high intensity circularly polarized light focal spot through metalens of focal…
Metasurface optical characterization using quadriwave lateral shearing interferometry
针对现有超表面表征多依赖光强测量的局限，提出采用四波横向剪切干涉法（QLSI），以高灵敏度和空间分辨率实现各类超表面的完整光学表征，并通过两类超表面的多种器件验证了该技术的通用性。
Riemann-Silberstein geometric phase in 4D polarization space
针对PB相位局限于二维偏振空间的问题，将几何相位推广至四维RS空间，提出可在任意偏振光中产生的RS相位，实验验证该框架并实现高维波前调控，为光与物质相互作用研究提供新视角。
Dynamic and Geometric Shifts in Wave Scattering
本文提出将几何-动力学分解从波演化相位推广至波散射问题，利用广义Wigner-Smith算子统一描述频率、动量等可观测量位移，并展示其规范不变的分解及广泛应用。
Vortex beams carrying orbital angular momentum (OAM) have been widely applied in various electromagnetic, optical, and quantum systems. A tailored OAM spectrum composed of several specific modes as expected holds a promise for expanding the degrees of freedom of the systems. However, such a broadband high-purity tailored spectrum is difficult to be achieved by the present devices, where the broadband amplitude manipulation has not been explored yet. In this work, inspired by the envelope-modulation theory, an elegant and universal way to manipulate the OAM spectrum in wide bandwidth is propose…
Optical metasurfaces have emerged as a new generation of building blocks for multi-functional optics. Design and realization of metasurface elements place ever-increasing demands on accurate assessment of phase alterations introduced by complex nanoantenna arrays, a process referred to as quantitative phase imaging. Despite considerable effort, the widefield (non-scanning) phase imaging that would approach resolution limits of optical microscopy and indicate the response of a single nanoantenna still remains a challenge. Here, we report on a new strategy in incoherent holographic imaging of me…
Orbital angular momentum (OAM) is a promising degree of freedom for fundamental studies in electromagnetics and quantum mechanics. The unlimited state space of OAM shows a great potential to enhance channel capacities of classical and quantum communications. By exploring the Pancharatnam-Berry phase concept and engineering anisotropic scatterers in a metasurface with spatially varying orientations, a plane wave with zero OAM can be converted to a vortex beam carrying nonzero OAM. In this paper, we proposed two types of novel PEC (perfect electric conductor)-PMC (perfect magnetic conductor) ani…
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