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There Is a Way to Comprise Half-Integer Eigenvalues for Photon Spin
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作者 ShaoXu Ren 《Journal of Modern Physics》 2016年第11期1364-1374,共12页
In this article, an attempt based on Spin Topological Space, STS, to give areasonable detailed account of the cause of photonic fermionization phenomena of light photon is made. STS is an unconventional spin space in ... In this article, an attempt based on Spin Topological Space, STS, to give areasonable detailed account of the cause of photonic fermionization phenomena of light photon is made. STS is an unconventional spin space in quantum mechanics, which can be used to account for where the unconventional half-integer spin eigenvalues phenomenon of light photon comes from. We suggest to dectect the possible existence of photonic one-third-spinization phenomenon of light photon, by using three beams of light photon in interference experiment. 展开更多
关键词 spin Topological Space STS Non-Hermitian matrix Casimir operator photonic fermionization phenomena half-integer spin eigenvalues one third one fourth spin eigenvalues of photon spin
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<i>E</i>Infinity, the Zero Set, Absolute Space and the Photon Spin
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作者 Jean-Paul Auffray 《Journal of Modern Physics》 2015年第5期536-545,共10页
As defined and used in General Relativity calculations, spacetime is a strictly classical construct which does not incorporate in any way, shape or form the concept of quantum. While reviewing the efforts that Alexand... As defined and used in General Relativity calculations, spacetime is a strictly classical construct which does not incorporate in any way, shape or form the concept of quantum. While reviewing the efforts that Alexandria theoretician M. S. El Naschie has made to resolve the dichotomy, we discovered that his E infinity theory contains a Cantor set which has characteristics specified by Isaac Newton for Absolute space. We show that this unexpected connection leads to an understanding of the mysterious origin of the one and only attribute that all particles listed in the Standard Model of Elementary Particles possess—including notably the photon—and which has remained unexplained hitherto: spin. This most rewarding result reinforces our belief in the relevance of the E infinity basic concepts in relation to our own Xonic Quantum Physics (XQP) which places dynamical action rather spacetime and energy at the core of the System of the World. 展开更多
关键词 QUANTUM Foam E INFINITY Xonic QUANTUM Physics Newton ABSOLUTE SPACE photon spin
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Engineered photonic spin Hall effect of Gaussian beam in antisymmetric parity-time metamaterials
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作者 刘露遥 冯振校 +1 位作者 邓冬梅 王光辉 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第9期255-260,共6页
A model of the photonic spin Hall effect(PSHE)in antisymmetric parity-time(APT)metamaterials with incidence of Gaussian beams is proposed here.We derive the displacement expression of the PSHE in APT metamaterials bas... A model of the photonic spin Hall effect(PSHE)in antisymmetric parity-time(APT)metamaterials with incidence of Gaussian beams is proposed here.We derive the displacement expression of the PSHE in APT metamaterials based on the transport properties of Gaussian beams in positive and negative refractive index materials.Furthermore,detailed discussions are provided on the APT scattering matrix,eigenstate ratio,and response near exceptional points in the case of loss or gain.In contrast to the unidirectional non-reflection in parity-time(PT)symmetric systems,the transverse shift that arises from both sides of the APT structure is consistent.By effectively adjusting the parameters of APT materials,we achieve giant displacements of the transverse shift.Finally,we present a multi-layer APT structure consisting of alternating left-handed and right-handed materials.By increasing the number of layers,Bragg oscillations can be generated,leading to an increase in resonant peaks in transverse shift.This study presents a new approach to achieving giant transverse shifts in the APT structure.This lays a theoretical foundation for the fabrication of related nano-optical devices. 展开更多
关键词 antisymmetric parity-time photonic spin Hall effect Gaussian beam
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Visualizing the Spin & Radiation of the Extended Electron in Magnetic Field
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作者 Hoa Van Nguyen 《Journal of High Energy Physics, Gravitation and Cosmology》 CAS 2024年第1期277-291,共15页
This article presents illustrations of an extended model of the electron to visualize how it spins and radiates in the external magnetic field. A time-varying magnetic field B produces a rotational induced electric fi... This article presents illustrations of an extended model of the electron to visualize how it spins and radiates in the external magnetic field. A time-varying magnetic field B produces a rotational induced electric field E which rotates (spins) the electron about its axis. In time-constant magnetic field: the electron radiates the cyclotron radiation. In time-varying magnetic field: synchrotron radiation is generated. The couplings between spin, acceleration and radiation will be discussed. 展开更多
关键词 spinning Forces spin by Inertia Radiating Forces photon or Static Electric Dipole Cloud of photons spin - Radiation Coupling
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Visualizing Spin & Radiation of the Extended Electron in Electric Field (Emission & Absorption of Photons)
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作者 Hoa van Nguyen 《Journal of High Energy Physics, Gravitation and Cosmology》 2023年第3期897-911,共15页
In this article the electron is conceived as an extended particle, consisting of a negatively charged core (-q<sub>0</sub>) which is surrounded by a cloud of electric dipoles (-q, +q). The article presents... In this article the electron is conceived as an extended particle, consisting of a negatively charged core (-q<sub>0</sub>) which is surrounded by a cloud of electric dipoles (-q, +q). The article presents the illustrations that show how and why the electron spins and radiates in an external electric field. In the appendices, Bremsstrahlung & Cerenkov radiations, and the processes of Emission & Absorption of photons will be discussed. 展开更多
关键词 spinning Forces (fs) spin By Inertia Radiating Forces (fr) Pulsating Forces (fp) photons or Electric Dipoles spin-Orbit Coupling
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Photonic spin Hall effect:fundamentals and emergent applications 被引量:2
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作者 Shuoqing Liu Shizhen Chen +1 位作者 Shuangchun Wen Hailu Luo 《Opto-Electronic Science》 2022年第7期1-32,共32页
The photonic spin Hall effect(SHE)refers to the transverse spin separation of photons with opposite spin angular momentum,after the beam passes through an optical interface or inhomogeneous medium,manifested as the sp... The photonic spin Hall effect(SHE)refers to the transverse spin separation of photons with opposite spin angular momentum,after the beam passes through an optical interface or inhomogeneous medium,manifested as the spin-dependent splitting.It can be considered as an analogue of the SHE in electronic systems:the light’s right-circularly polarized and left-circularly polarized components play the role of the spin-up and spin-down electrons,and the refractive index gradient replaces the electronic potential gradient.Remarkably,the photonic SHE originates from the spin-orbit interaction of the photons and is mainly attributed to two different geometric phases,i.e.,the spin-redirection Rytov-Vlasimirskii-Berry in momentum space and the Pancharatnam-Berry phase in Stokes parameter space.The unique properties of the photonic SHE and its powerful ability to manipulate the photon spin,gradually,make it a useful tool in precision metrology,analog optical computing and quantum imaging,etc.In this review,we provide a brief framework to describe the fundamentals and advances of photonic SHE,and give an overview on the emergent applications of this phenomenon in different scenes. 展开更多
关键词 photonic spin Hall effect spin-orbit interaction of light geometric phase weak measurement analog optical computing
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Quantum statistical properties of photon-added spin coherent states 被引量:1
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作者 G Honarasa 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第11期206-209,共4页
The photon-added spin coherent state as a new kind of coherent state has been defined by iterated actions of the proper raising operator on the ordinary spin coherent state. In this paper, the quantum statistical prop... The photon-added spin coherent state as a new kind of coherent state has been defined by iterated actions of the proper raising operator on the ordinary spin coherent state. In this paper, the quantum statistical properties of photon-added spin coherent states such as photon number distribution, second-order correlation function and Wigner function are studied. It is found that the Wigner function shows the negativity in some regions and the second-order correlation function is less than unity. Therefore, the photon-added spin coherent state is a nonclassical state. 展开更多
关键词 photon-added spin coherent states photon number distribution Wigner function
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Enhancing terahertz photonic spin Hall effect via optical Tamm state and the sensing application
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作者 程杰 徐家豪 +4 位作者 项寅杰 刘胜利 迟逢逢 李斌 董鹏 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第12期229-234,共6页
The photonic spin Hall effect(PSHE),characterized by two splitting beams with opposite spins,has great potential applications in nano-photonic devices,optical sensing fields,and precision metrology.We present the sign... The photonic spin Hall effect(PSHE),characterized by two splitting beams with opposite spins,has great potential applications in nano-photonic devices,optical sensing fields,and precision metrology.We present the significant enhancement of terahertz(THz)PSHE by taking advantage of the optical Tamm state(OTS)in In Sb-distributed Bragg reflector(DBR)structure.The spin shift of reflected light can be dynamically tuned by the structural parameters(e.g.the thickness)of the InSb-DBR structure as well as the temperature,and the maximum spin shift for a horizontally polarized incident beam at 1.1 THz can reach up to 11.15 mm.Moreover,we propose a THz gas sensing device based on the enhanced PSHE via the strong excitation of OTS for the InSb-DBR structure with a superior intensity sensitivity of 5.873×10^(4)mm/RIU and good stability.This sensor exhibits two orders of magnitude improvement compared with the similar PSHE sensor based on In Sb-supported THz long-range surface plasmon resonance.These findings may provide an alternative way for the enhanced PSHE and offer the opportunity for developing new optical sensing devices. 展开更多
关键词 photonic spin Hall effect optical Tamm state INSB gas sensor
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Modulation and enhancement of photonic spin Hall effect with graphene in broadband regions
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作者 董鹏 王高俊 程杰 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第3期260-265,共6页
The photonic spin Hall effect(SHE)holds great potential applications in manipulating spin-polarized photons.However,the SHE is generally very weak,and previous studies of amplifying photonic SHE were limited to the in... The photonic spin Hall effect(SHE)holds great potential applications in manipulating spin-polarized photons.However,the SHE is generally very weak,and previous studies of amplifying photonic SHE were limited to the incident light in a specific wavelength range.In this paper,we propose a four-layered nanostructure of prism-graphene-air-substrate,and the enhanced photonic SHE of reflected light in broadband range of 0 THz–500 THz is investigated theoretically.The spin shift can be dynamically modulated by adjusting the thickness of air gap,Fermi energy of graphene,and also the incident angle.By optimizing the structural parameter of this structure,the giant spin shift(almost equal to its upper limit,half of the incident beam waist)in broadband range is achieved,covering the terahertz,infrared,and visible range.The difference is that in the terahertz region,the Brewster angle corresponding to the giant spin shift is larger than that of infrared range and visible range.These findings provide us with a convenient and effective way to tune the photonic SHE,and may offer an opportunity for developing new tunable photonic devices in broadband range. 展开更多
关键词 photonic spin Hall effect GRAPHENE spin shift
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Asymmetrical photonic spin Hall effect based on dielectric metasurfaces
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作者 耿广州 潘如豪 +1 位作者 朱维 李俊杰 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第12期267-271,共5页
The photonic spin Hall effect has attracted considerable research interest due to its potential applications in spincontrolled nanophotonic devices.However,realization of the asymmetrical photonic spin Hall effect wit... The photonic spin Hall effect has attracted considerable research interest due to its potential applications in spincontrolled nanophotonic devices.However,realization of the asymmetrical photonic spin Hall effect with a single optical element is still a challenge due to the conjugation of the Pancharatnam-Berry phase,which reduces the flexibility in various applications.Here,we demonstrate an asymmetrical spin-dependent beam splitter based on a single-layer dielectric metasurface exhibiting strong and controllable optical response.The metasurface consists of an array of dielectric nanofins,where both varying rotation angles and feature sizes of the unit cells are utilized to create high-efficiency dielectric metasurfaces,which enables to break the conjugated characteristic of phase gradient.Thanks to the superiority of the phase modulation ability,when the fabricated metasurface is under normal incidence with a wavelength of 1550 nm,the lefthanded circular polarization(LCP)light exhibits an anomalous refraction angle of 28.9°,while the right-handed circular polarization(RCP)light transmits directly.The method we proposed can be used for the flexible manipulation of spin photons and has potentials in high efficiency metasurfaces with versatile functionalities,especially with metasurfaces in a compact space. 展开更多
关键词 dielectric metasurface photonic spin Hall effect asymmetrical optical response
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Two-Photon Exchange Corrections to Single Spin Asymmetry of Neutron and 3He
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作者 CHEN Dian-Yong DONG Yu-Bing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第3期489-494,共6页
在一个简单 hadronic 模型,对为核子和 3He 的单个旋转不对称现象的二光子的交换贡献被估计。当为 3He 的那些相对大时,结果证明到为核子的单个旋转不对称现象的二光子的交换的有弹性的贡献是相当小的。除强壮的尖依赖以外,对为 3He... 在一个简单 hadronic 模型,对为核子和 3He 的单个旋转不对称现象的二光子的交换贡献被估计。当为 3He 的那些相对大时,结果证明到为核子的单个旋转不对称现象的二光子的交换的有弹性的贡献是相当小的。除强壮的尖依赖以外,对为 3He 的单个旋转不对称现象的二光子的贡献对动量转移很敏感。 展开更多
关键词 不对称性 核子自旋 光子交换 中子 更正 氦-3 e模型 双光子
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The Spin-Spin Interaction and the New Concept of Photon
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作者 Quang Quy Ho 《Journal of Electromagnetic Analysis and Applications》 2012年第11期447-451,共5页
After researching carefully the well known M. Planck’s law of the black-body radiation, the quantum theory of field and the Einstein’s postulates about interaction of the photon with the atoms, there are a lot of un... After researching carefully the well known M. Planck’s law of the black-body radiation, the quantum theory of field and the Einstein’s postulates about interaction of the photon with the atoms, there are a lot of unclear questions about photon and its interaction with atom. From all the above questions, there are three main following questions: Why does the energy of a light mode include zero-point energy? Where does the first photon come from in universe? and What is the first fact as a reason of absorption, emission in the photon-atom interaction? To find out the acceptable answers, here we propose postulates about the zero-photon and then about the new concepts of photon. Using them, we have tried to describe the basic characters of the photon and explain the photon-atom interaction in other way: the spin-spin interaction. Our results showed out the different picture of mechanism of the photon-atom interaction, the existence of the zero-photon energy, the absorption as well as the emission rule and its probabilities. 展开更多
关键词 Zero-Point of Energy photon-Atom Interaction BIG Bang spin UNIVERSE Wave
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Photon-mediated spin-polarized current in a quantum dot under thermal bias
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作者 迟锋 刘黎明 孙连亮 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第3期489-494,共6页
Spin-polarized current generated by thermal bias across a system composed of a quantum dot (QD) connected to metallic leads is studied in the presence of magnetic and photon fields. The current of a certain spin ori... Spin-polarized current generated by thermal bias across a system composed of a quantum dot (QD) connected to metallic leads is studied in the presence of magnetic and photon fields. The current of a certain spin orientation vanishes when the dot level is aligned to the lead's chemical potential, resulting in a 100% spin-polarized current. The spin-resolved current also changes its sign at the two sides of the zero points. By tuning the system's parameters, spin-up and spin-down currents with equal strength may flow in opposite directions, which induces a pure spin current without the accompany of charge current. With the help of the thermal bias, both the strength and the direction of the spin-polarized current can be manipulated by tuning either the frequency or the intensity of the photon field, which is beyond the reach of the usual electric bias voltage. 展开更多
关键词 quantum dot spin-polarized current thermal bias photon field
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Photon-assisted electronic and spin transport through two T-shaped three-quantum-dot molecules embedded in an Aharonov-Bohm interferometer
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作者 白继元 李立 +4 位作者 贺泽龙 叶树江 赵树军 党随虎 孙伟民 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第11期460-468,共9页
We investigate the time-modulated electronic and spin transport properties through two T-shaped three-quantum-dot molecules embedded in an Aharonov-Bohm(A-B) interferometer. By using the Keldysh non-equilibrium Gree... We investigate the time-modulated electronic and spin transport properties through two T-shaped three-quantum-dot molecules embedded in an Aharonov-Bohm(A-B) interferometer. By using the Keldysh non-equilibrium Green's function technique, the photon-assisted spin-dependent average current is analyzed. The T-shaped three-quantum-dot molecule A-B interferometer exhibits excellent controllability in the average current resonance spectra by adjusting the interdot coupling strength, Rashba spin-orbit coupling strength, magnetic flux, and amplitude of the time-dependent external field.Efficient spin filtering and multiple electron-photon pump functions are exploited in the multi-quantum-dot molecule A-B interferometer by a time-modulated external field. 展开更多
关键词 non-equilibrium Green's function photon-assisted electron transport Aharonov-Bohm interferometer Rashba spin-orbit coupling
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基于光子自旋霍尔效应的甲烷检测理论研究
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作者 侯自如 王哲飞 武永 《激光技术》 CAS CSCD 北大核心 2024年第3期345-351,共7页
为了实现对甲烷体积分数的高精度检测,采用多层结构激发了具有高品质因素的光子自旋霍尔效应现象。利用非对称的排列方式,将甲烷敏感膜引入结构中,通过敏感膜的折射率变化,实现对甲烷体积分数的检测;研究了气体孔隙率、周期数、金属厚... 为了实现对甲烷体积分数的高精度检测,采用多层结构激发了具有高品质因素的光子自旋霍尔效应现象。利用非对称的排列方式,将甲烷敏感膜引入结构中,通过敏感膜的折射率变化,实现对甲烷体积分数的检测;研究了气体孔隙率、周期数、金属厚度和敏感膜厚度对光子自旋霍尔效应的影响,并采用传输矩阵法进行了数值分析。结果表明,该传感器可对体积分数为0~3%、折射率变化为1.4364~1.4478的甲烷气体进行检测,灵敏度为29.6°,最高质量因素和最低检测下限分别为395和0.00012。该传感器结构简单、检测能力强,为光学传感器的研究提供了新思路。 展开更多
关键词 传感器技术 甲烷体积分数 甲烷敏感膜 非互易 光子自旋霍尔效应
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Distributed quantum information processing via quantum dot spins
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作者 刘军 王琼 +1 位作者 匡乐满 曾浩生 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第3期76-82,共7页
We propose a scheme to engineer a non-local two-qubit phase gate between two remote quantum-dot spins. Along with one-qubit local operations, one can in principal perform various types of distributed quantum informati... We propose a scheme to engineer a non-local two-qubit phase gate between two remote quantum-dot spins. Along with one-qubit local operations, one can in principal perform various types of distributed quantum information processing. The scheme employs a photon with linearly polarisation interacting one after the other with two remote quantum-dot spins in cavities. Due to the optical spin selection rule, the photon obtains a Faraday rotation after the interaction process. By measuring the polarisation of the final output photon, a non-local two-qubit phase gate between the two remote quantum-dot spins is constituted. Our scheme may has very important applications in the distributed quantum information processing. 展开更多
关键词 quantum-dot spins nonlocal quantum gates polarised photon
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A Xon Signature in the Electron Spin
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作者 Jean-Paul Auffray 《Journal of Modern Physics》 2013年第11期9-13,共5页
The elementary particles listed in the Standard Model of particle physics have all in common a quantum mechanical attribute which has the dimension of the xon, suggesting that the xon might be a structural ingredient ... The elementary particles listed in the Standard Model of particle physics have all in common a quantum mechanical attribute which has the dimension of the xon, suggesting that the xon might be a structural ingredient of matter. The xon should therefore be included as a full-fledged member in the SM catalog of elementary particles. 展开更多
关键词 OBSERVABLE UNIVERSE DARK MATTER Standard Model Ordinary MATTER Electron spin Xon photon GRAVITOMAGNETISM Smolin Haroche Arbab
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Are Photons Massless or Massive?
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作者 Golden Gadzirayi Nyambuya 《Journal of Modern Physics》 2014年第18期2111-2124,共14页
Prevailing and conventional wisdom as drawn from both Professor Albert Einstein’s Special Theory of Relativity (STR) and our palatable experience, holds that photons are massless particles and that, every particle th... Prevailing and conventional wisdom as drawn from both Professor Albert Einstein’s Special Theory of Relativity (STR) and our palatable experience, holds that photons are massless particles and that, every particle that travels at the speed of light must—accordingly, be massless. Amongst other important but now resolved problems in physics, this assumption led to the Neutrino Mass Problem—namely, “Do neutrinos have mass?” Neutrinos appear very strongly to travel at the speed of light and according to the afore-stated, they must be massless. Massless neutrinos have a problem in that one is unable to explain the phenomenon of neutrino oscillations because this requires massive neutrinos. Experiments appear to strongly suggest that indeed, neutrinos most certainly are massive particles. While this solves the problem of neutrino oscillation, it directly leads to another problem, namely that of “How can a massive particle travel at the speed of light? Is not this speed a preserve and prerogative of only massless particles?” We argue herein that in principle, it is possible for massive particles to travel at the speed of light. In presenting the present letter, our hope is that this may aid or contribute significantly in solving the said problem of “How can massive particles travel at the speed of light?” 展开更多
关键词 Curved SPACETIME DIRAC EQUATION General spin DIRAC EQUATION MASSIVE photon Unified Field Theory
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块状和超薄磁性材料中巨大且可调控的面内自旋角位移
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作者 李乾阳 袁帅杰 +4 位作者 杨锦 王勇 马祖海 陈宇 周新星 《物理学报》 SCIE EI CAS CSCD 北大核心 2023年第1期105-114,共10页
磁光克尔效应是指处于磁场中的光束在磁体表面发生反射时,反射光的偏振面相对入射光发生旋转的物理现象,它反映了磁化强度对磁性材料光学性质的影响.磁性介质的磁光克尔效应则由含磁光常数的介电张量表征,因此对磁光常数进行精确测量具... 磁光克尔效应是指处于磁场中的光束在磁体表面发生反射时,反射光的偏振面相对入射光发生旋转的物理现象,它反映了磁化强度对磁性材料光学性质的影响.磁性介质的磁光克尔效应则由含磁光常数的介电张量表征,因此对磁光常数进行精确测量具有重要的科学意义.光子自旋霍尔效应表现为光束在折射率不同的介质界面上传输时由于自旋-轨道相互作用而产生的光子自旋分裂现象.过去大多数研究利用光子自旋霍尔效应的横向空间位移来表征磁光常数.然而,现有工作只考虑了单个磁场方向的磁光克尔效应,并且由于微小的自旋空间位移而需要引入复杂的弱测量技术.本文从理论上全面探究了3种磁光克尔效应条件下的面内自旋角位移,发现通过改变磁场方向和磁性材料的厚度(考虑块状和超薄)可以实现对光子自旋霍尔效应的有效操纵.同时,该研究提出了一种直接测量磁光常数的新方法,即通过直接观测巨大的面内自旋角位移来表征磁光常数的振幅与相位.该方法不需要引入弱测量系统,不仅为磁光常数的测量提供了直接有效的探针,并且扩展了自旋光子学的相关研究. 展开更多
关键词 光子自旋霍尔效应 磁光克尔效应 光学自旋-轨道相互作用
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Breakdown of effective-medium theory by a photonic spin Hall effect
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作者 Shuaijie Yuan Xinxing Zhou +6 位作者 Yu Chen Yuhan Zhong Lijuan Sheng Hao Hu Hongsheng Chen Ido Kaminer Xiao Lin 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS CSCD 2023年第11期145-154,共10页
Effective-medium theory pertains to the theoretical modelling of homogenization,which aims to replace an inhomogeneous structure of subwavelength-scale constituents with a homogeneous effective medium.The effective-me... Effective-medium theory pertains to the theoretical modelling of homogenization,which aims to replace an inhomogeneous structure of subwavelength-scale constituents with a homogeneous effective medium.The effective-medium theory is fundamental to various realms,including electromagnetics and material science,since it can largely decrease the complexity in the exploration of light-matter interactions by providing simple acceptable approximation.Generally,the effective-medium theory is thought to be applicable to any all-dielectric system with deep-subwavelength constituents,under the condition that the effective medium does not have a critical angle,at which the total internal reflection occurs.Here we reveal a fundamental breakdown of the effective-medium theory that can be applied in very general conditions:showing it for deep-subwavelength all-dielectric multilayers even without a critical angle.Our finding relies on an exotic photonic spin Hall effect,which is shown to be ultrasensitive to the stacking order of deep-subwavelength dielectric layers,since the spin-orbit interaction of light is dependent on slight phase accumulations during the wave propagation.Our results indicate that the photonic spin Hall effect could provide a promising and powerful tool for measuring structural defects for all-dielectric systems even in the extreme nanometer scale. 展开更多
关键词 photonic spin Hall effect effective-medium theory spin-orbit interaction of light
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