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Photon Structure and Wave Function from the Vector Potential Quantization
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作者 Constantin Meis 《Journal of Modern Physics》 CAS 2023年第3期311-329,共19页
A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behave... A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy  and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized. 展开更多
关键词 photonS photon Wave Function Vector Potential Quantization photon Electric and Magnetic Fields photon structure Wave-Corpuscle Representation photon “Energy-Vector Potential” Equation
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Double Helix Particle Models of Photon/Torsion Field and Their Relationships with Chirality of Life on Earth
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作者 Jiang Jianzhong Chen Xi-Qi 《Journal of Environmental Science and Engineering(B)》 2025年第2期81-90,共10页
In light of the double helix structure hypothesis for photon,we attempt to elucidate the generation mechanism underlying TF(Torsion Field)from both wave and particle perspectives and the enigma surrounding chiral life... In light of the double helix structure hypothesis for photon,we attempt to elucidate the generation mechanism underlying TF(Torsion Field)from both wave and particle perspectives and the enigma surrounding chiral life on Earth by proposing a neutrino-propagation model for TF,which will serve as a crucial key in unraveling the enigma of life’s origins and is promising to trigger a paradigm transformation in future medical and healthcare technologies. 展开更多
关键词 Chirality of life TF SW(Scalar Wave) neutrino-propagation model of TF photon structure
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Photonic band structures of quadrangular multiconnected networks 被引量:1
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作者 宋欢欢 杨湘波 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第7期313-321,共9页
By means of the network equation and generalized dimensionless Floquet-Bloch theorem, this paper investigates the properties of the band number and width for quadrangular multiconnected networks (QMNs) with a differ... By means of the network equation and generalized dimensionless Floquet-Bloch theorem, this paper investigates the properties of the band number and width for quadrangular multiconnected networks (QMNs) with a different number of connected waveguide segments (NCWSs) and various matching ratio of waveguide length (MRWL). It is found that all photonic bands are wide bands when the MRWL is integer. If the integer attribute of MRWL is broken, narrow bands will be created from the wide band near the centre of band structure. For two-segment-connected networks and three-segment-connected networks, it obtains a series of formulae of the band number and width. On the other hand, it proposes a so-called concept of two-segment-connected quantum subsystem and uses it to discuss the complexity of the band structures of QMNs. Based on these formulae, one can dominate the number, width and position of photonic bands within designed frequencies by adjusting the NCWS and MRWL. There would be potential applications for designing optical switches, optical narrow-band filters, dense wavelength-division-multiplexing devices and other correlative waveguide network devices. 展开更多
关键词 multiconnected network WAVEGUIDE photonic band structure
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Theoretical investigation of hierarchical sub-wavelength photonic structures fabricated using high-order waveguide-mode interference lithograph 被引量:1
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作者 Ru Wang Xiangxian Wang +1 位作者 Hua Yang Yunping Qi 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第2期213-217,共5页
This paper presents the theoretical investigation of hierarchical sub-wavelength photonic structures with various periods and numbers of layers, which were fabricated using a high-order waveguide-mode interference fie... This paper presents the theoretical investigation of hierarchical sub-wavelength photonic structures with various periods and numbers of layers, which were fabricated using a high-order waveguide-mode interference field. A 442-nm laser was used to excite high-order waveguide modes in an asymmetric metal-cladding dielectric waveguide structure. The dispersion curve of the waveguide modes was theoretically analyzed, and the distribution of the interference field of high-order waveguide modes was numerically simulated using the finite-element method. The various dependences of the characteristics of hierarchical sub-wavelength photonic structures on the thickness and refractive index of the photoresist and the waveguide mode were investigated in detail. These hierarchical sub-wavelength photonic structures have various periods and numbers of layers and can be fabricated by a simple and low-cost method. 展开更多
关键词 sub-wavelength photonic structure finite-element method waveguide modes lithography
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Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals 被引量:1
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作者 Si-Qi Zhang Jing-Bin Lu +6 位作者 Yu Liang Ji Ma Hong Li Xue Li Xiao-Jing Liu Xiang-Yao Wu Xiang-Dong Meng 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第2期242-249,共8页
Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic c... Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals. 展开更多
关键词 two-dimensional photonic crystals function dielectric constants band gaps structures
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Au Microdisk-Size Dependence of Quantum Dot Emission from the Hybrid Metal-Distributed Bragg Reflector Structures Employed for Single Photon Sources 被引量:1
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作者 王海艳 苏丹 +7 位作者 杨爽 窦秀明 朱海军 江德生 倪海桥 牛智川 赵翠兰 孙宝权 《Chinese Physics Letters》 SCIE CAS CSCD 2015年第10期134-137,共4页
We investigate metallic microdisk-size dependence of quantum dot (QD) spontaneous emission rate and micro- antenna directional emission effect for the hybrid metM-distributed Bragg reflector structures based on a pa... We investigate metallic microdisk-size dependence of quantum dot (QD) spontaneous emission rate and micro- antenna directional emission effect for the hybrid metM-distributed Bragg reflector structures based on a particular single QD emission. It is found that the measured photolumineseence (PL) intensity is very sensitive to the size of metMlic disk, showing an enhancement factor of 11 when the optimal disk diameter is 2μm and the numerical aperture of microscope objective NA=0.5. It is found that for large metal disks, the Purcell effect is dominant for enhanced PL intensity, whereas for small size disks the main contribution comes from plasmon scattering at the disk edge within the light cone collected by the microscope objective. 展开更多
关键词 Au Microdisk-Size Dependence of Quantum Dot Emission from the Hybrid Metal-Distributed Bragg Reflector structures Employed for Single photon Sources DBR QDs
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Bio‑inspired Tough Metafiber with Hierarchical Photonic Structures for Durable Passive Radiative Thermal Management
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作者 Xiaoyan Li Zhiguang Guo +6 位作者 Yating Ji Peibo Du Jun Wang Bi Xu Fengyan Ge Yaping Zhao Zaisheng Cai 《Advanced Fiber Materials》 2025年第2期607-619,共13页
Passive radiative thermal management holds substantial potential for enhancing energy efficiency and sustainability.However,few research efforts have addressed the integration of mechanical robustness and durability w... Passive radiative thermal management holds substantial potential for enhancing energy efficiency and sustainability.However,few research efforts have addressed the integration of mechanical robustness and durability with the distribution and composition of photonic structures within materials.Silk fibers,known for their distinctive hierarchical morphological structure,offer a solution to these challenges by providing exceptional optical and mechanical properties.Inspired by this,we developed a silk-like tough metafiber(PMABF)that incorporated multiple scatterers through a multi-scale structural construction of nanofiber aggregates and molecular interface engineering.We show that fabrics woven with PMABF can provide high midinfrared(MIR)emissivity(98.6%)within the atmospheric window and 86.7%reflectivity in the solar spectrum,attributed to its ellipsoidal photonic structure featuring by surface micro-/nano-particles and numerous internal voids.Through mature and scalable industrial manufacturing routes,our metafibers show excellent mechanical strength,hydrophobicity and thermal stability while maintaining effective passive radiative cooling.Practical application tests demonstrated that molecules introduced during the heterogeneous composite process significantly enhanced the metafiber’s tensile strength(125%)and compressive stress(261.5%)by forming junction welds among the nanofiber backbones to efficiently distribute the external forces.Furthermore,the superior thermal stability and flexibility of PMABF open abundant opportunities for diverse applications with demanding thermal management requirements,such as thermal protection and multi-scenario thermal camouflage. 展开更多
关键词 SILK-LIKE Metafiber photonic structure Molecular engineering Radiative thermal management Multimode thermal regulation
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A New Theory of the Essence and Mass of Photon
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作者 Nader Butto 《Journal of High Energy Physics, Gravitation and Cosmology》 CAS 2022年第4期1084-1101,共18页
Many properties of a single photon, such as density, rest mass, and orbital angular momentum, are still unknown. In a previous study, the photon was presented as a superfluid prolate spheroid structure, with a long-ax... Many properties of a single photon, such as density, rest mass, and orbital angular momentum, are still unknown. In a previous study, the photon was presented as a superfluid prolate spheroid structure, with a long-axis radius, short-axis radius, and volume, embodied with two spins—transversal and longitudinal—which are responsible for the three-dimensional helical trajectory of the electromagnetic wave. In this study, the rest mass, density, and energy of photon are mathematically derived, and the relationship between the radius of photon and its frequency is demonstrated. In addition, the difference between the Compton and de Broglie wavelengths is clarified. The calculated density, volume, and rest mass of photon agree with previous experimental results. The photon’s simultaneous longitudinal and transversal spins are moving forces of longitudinal and transversal trajectories, which are the origin of the three-dimensional helix shape of the electromagnetic field. A new mechanism for the photon movement is proposed, and the reason for the zero mass moving photon is revealed;a traveling photon in space exhibits zero mass because its boundaries demonstrate zero relative velocity with the surrounding vacuum. The orbital angular momentum of photon is described using similar macroscopic rotation concepts and applying hydrodynamics laws. A rotating photon is endowed with an angular velocity vector whose magnitude measures the speed with which the radius of the principal axis sweeps an angle, and whose direction indicates the principal axis of rotation and is given by the right-hand rule. The deviation angle is calculated using trigonometric functions, and the origin of the Lorenz factor is revealed. 展开更多
关键词 photon structure Electromagnetic Wave photon Mass photon Energy
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Photonic Band Modulation in a Two-Dimensional Photonic Crystal with a One-Dimensional Periodic Dielectric Background 被引量:1
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作者 ZHANG Yan SHI Jun-Jie 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第3期747-752,共6页
A two-dimensional photonic crystal with a one-dimensional periodic dielectric background is proposed. The photonic band modulation effects due to the periodic background are investigated based on the plane wave expans... A two-dimensional photonic crystal with a one-dimensional periodic dielectric background is proposed. The photonic band modulation effects due to the periodic background are investigated based on the plane wave expansion method. We find that periodic modulation of the dielectric background greatly alters photonic band structures, especially for the E-polarization modes. The number, width and position of the photonic band gaps (PBGs) sensitively depend on the structure parameters (the layer thicknesses and dielectric constants) of the one-dimensional periodic background, 展开更多
关键词 photonic band structures two-dimensional photonic crystal one-dimensional periodic dielectric background
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Observation of trapped light induced by Dwarf Dirac-cone in out-of-plane condition for photonic crystals
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作者 Subir Majumder Tushar Biswas Shaymal K Bhadra 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第10期314-322,共9页
Existence of out-of-plane conical dispersion for a triangular photonic crystal lattice is reported. It is observed that conical dispersion is maintained for a number of out-of-plane wave vectors(k;). We study a case... Existence of out-of-plane conical dispersion for a triangular photonic crystal lattice is reported. It is observed that conical dispersion is maintained for a number of out-of-plane wave vectors(k;). We study a case where Dirac like linear dispersion exists but the photonic density of states is not vanishing, called Dwarf Dirac cone(DDC) which does not support localized modes. We demonstrate the trapping of such modes by introducing defects in the crystal. Interestingly, we find by k-point sampling as well as by tuning trapped frequency that such a conical dispersion has an inherent light confining property and it is governed by neither of the known wave confining mechanisms like total internal reflection, band gap guidance. Our study reveals that such a conical dispersion in a non-vanishing photonic density of states induces unexpected intense trapping of light compared with those at other points in the continuum. Such studies provoke fabrication of new devices with exciting properties and new functionalities. 展开更多
关键词 band structure photonic band gap materials multilayers SUPERLATTICES photonic structures META-MATERIALS
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Slow Light Transmission in Chalcogenide Photonic Crystal Waveguide 被引量:1
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作者 Bhuvneshwer Suthar Ajay Kumar Nagar Anami Bhargava 《Journal of Electronic Science and Technology of China》 2010年第1期39-42,共4页
The slow light propagation in a line defect waveguide in chalcogenide photonic crystal of As2S3 rods in air medium has been investigated. It is found that the filling factor of the chaleogenide photonic crystal and th... The slow light propagation in a line defect waveguide in chalcogenide photonic crystal of As2S3 rods in air medium has been investigated. It is found that the filling factor of the chaleogenide photonic crystal and the size of defect rods decide the propagation of the guided mode. An increase in the filling factor results in a sharp decrease of the group velocity in the photonic crystal waveguide. It has been demonstrated that, by tuning the filling factor and size of defect rods, the group velocity will be reduced up to about 0.22c. 展开更多
关键词 Chalcogenide photonic crystalwaveguide group velocity photonic band structure.
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Tunability of One-Dimensional Plasma Photonic Crystals with an External Magnetic Field
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作者 郭斌 彭莉 邱孝明 《Plasma Science and Technology》 SCIE EI CAS CSCD 2013年第7期609-613,共5页
We investigated in detail how photonic band structures (PBSs) of one dimensional plasma photonic crystals (PPCs) are tuned after being exposed to an external magnetic field. We showed that the properties of PBSs o... We investigated in detail how photonic band structures (PBSs) of one dimensional plasma photonic crystals (PPCs) are tuned after being exposed to an external magnetic field. We showed that the properties of PBSs of PPCs are tuned correspondingly because the dielectric constant of the micro plasma layer is modified differently in different frequency ranges due to magneto-optical effects. Two numerical cases are calculated and discussed to study the magneto-optical effects on the properties of PBSs, including the Faraday and Voigt effects. 展开更多
关键词 photonic band structures magneto-optical effects Faraday effect Voigt effect
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Noncommutative metasurfaces enabled diverse quantum path entanglement of structured photons
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作者 Yan Wang Yichang Shou +5 位作者 Jiawei Liu Qiang Yang Shizhen Chen Weixing Shu Shuangchun Wen Hailu Luo 《Opto-Electronic Science》 2025年第10期1-12,共12页
Quantum entanglement, a fundamental concept in quantum mechanics, lies at the heart of many current and futurequantum technologies. A pivotal task is the generation and control of diverse quantum entangled states in a... Quantum entanglement, a fundamental concept in quantum mechanics, lies at the heart of many current and futurequantum technologies. A pivotal task is the generation and control of diverse quantum entangled states in a more compactand flexible manner. Here, we introduce an approach to achieve diverse path entanglement by exploiting the interactionbetween noncommutative metasurfaces and entangled photons. Different from other path entanglements, ourquantum path entanglement is evolution path entanglement of photons on Poincaré sphere. Due to quantum entanglementbetween idler photons and structured signal photons, evolution path of idler photons on the fundamental Poincarésphere can be nonlocally mirrored by structured signal photons on any higher-order Poincaré sphere, resulting in quantumpath entanglement. Benefiting from noncommutative metasurfaces, diverse quantum path entanglement can beswitched across different higher-order Poincaré spheres using distinct combination sequences of metasurfaces. Ourmethod allows for the tuning of diverse quantum path entanglement across a broad spectrum of quantum states, offeringa significant advancement in the manipulation of quantum entanglement. 展开更多
关键词 noncommutative metasurfaces structured photons diverse path entanglement
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Photonic Metafabric with Biomimetic Triangular Light Track for Passive Radiative Cooling 被引量:1
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作者 Hongyu Guo Bomou Ma +2 位作者 Jianyong Yu Xueli Wang Yang Si 《Advanced Fiber Materials》 2025年第1期106-116,共11页
Integrating passive radiative cooling techniques with wearable fabrics provides a zero-energy strategy for preventing people from heat stress and reducing cooling demand.However,developing wearable passive radiative c... Integrating passive radiative cooling techniques with wearable fabrics provides a zero-energy strategy for preventing people from heat stress and reducing cooling demand.However,developing wearable passive radiative cooling fabrics with ideal optical characteristics,wearability,and scalability has consistently presented a challenge.Here,we developed a metafabric with high sunlight reflectivity(88.07%)according to the design of an individual photonic structure,which demonstrates total internal reflection with the tailored triangular light track.A skin simulator covered by metafabric exhibits a temperature drop of 7.17℃ in the daytime compared with regular polyester fabric in an outdoor cooling test.Consequently,it was theoretically proven to exert a substantial influence on achieving a significant cooling demand reduction of 52.69–185.79 W·m^(-2).These characteristics,coupled with structural stability,air-moisture permeability,sufficient wearability,and scalability,allowed the metafabric to provide a solution for introducing zero-energy passive radiative cooling technique into human body cooling. 展开更多
关键词 Biomimetic materials photonic structures FABRICS Passive radiative cooling
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Supersymmetry of In-group and “Out-group” Particles and Some Strange Phenomena
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作者 焦善庆 龚自正 +1 位作者 许弟余 江光佐 《Journal of Southwest Jiaotong University(English Edition)》 2006年第1期47-51,共5页
The symmetry of the in-group particles, which are of three-generation fermions, and the “out-group” ones, which are not admitted by three-generation fermions, is discussed. It was found that the “out-group” antipa... The symmetry of the in-group particles, which are of three-generation fermions, and the “out-group” ones, which are not admitted by three-generation fermions, is discussed. It was found that the “out-group” antiparticles of Bose type, which came into being because of CP ( charge Conjugation-Parity conservation) violation in the early universe and became heavier due to the phase transformation from low temperature to high temperature, are the supersymmetric companions of the in-group particles of Fermi type. The ratio of the number density of photons to that of protons calculated with Planck distribution method is about 0.61× 10^10, which is close to the observed value ( about 10^10) available in literature. A theoretical analysis of the structure of a photon suggests that the photon has a quark-gluon structure, which is consistent with the experimental result reported in literature. As the lightest particle in the supersymmetric companions, the calculated mass of a neutralino is 320 GeV. The so-called “vast area of desert” in mass scale appears to be the supersymmetry area of the three-generation particles, and “neutralinos” are the source of the moving of galaxies and the dark matter of non-baryons. 展开更多
关键词 “Out-group” particles Supersymmctry photon structure Antilcpton-quark resonance Dark matter
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Recent progress in terahertz modulation using photonic structures based on two-dimensional materials 被引量:4
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作者 Ziming Wang Jie Qiao +4 位作者 Shuqi Zhao Shilei Wang Chuan He Xutang Tao Shanpeng Wang 《InfoMat》 SCIE CAS 2021年第10期1110-1133,共24页
Terahertz(THz)technology has attracted great attention in the past few decades for its unique applications in various fields,including spectroscopy,noninvasive detection,wireless communications,and imaging.In parallel... Terahertz(THz)technology has attracted great attention in the past few decades for its unique applications in various fields,including spectroscopy,noninvasive detection,wireless communications,and imaging.In parallel to this,the practical,fast,and broadband modulation of THz waves is becoming indispensable.Two-dimensional(2D)materials exhibit unusual optical and electrical properties,which has prompted tremendous interest and significant advances in THz modulation.This review provides the recent progress in 2D materials-based THz modulators,outlining the operating principles,including all-optical,electro-optic,magneto-optic,and other exotic mechanisms.We focus on the recent advances in THz modulation by the designed photonic structures,such as heterostructure,metamaterial,capacitor,optical cavity,and waveguide integration.Lastly,we discussed the challenges and opportunities for 2D materials-based THz modulators and presented our prospects for the future development. 展开更多
关键词 2D material optoelectronic device photonic structure terahertz modulation
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Functional photonic structures for external interaction with flexible/ wearable devices 被引量:2
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作者 Young Jin Yoo Se-Yeon Heo +3 位作者 Yeong Jae Kim Joo Hwan Ko Zafrin Ferdous Mira Young Min Song 《Nano Research》 SCIE EI CSCD 2021年第9期2904-2918,共15页
In addition to vital functions,more subsidiary functions are being expected from wearable devices.The wearable technology thus far has achieved the ability to maintain homeostasis by continuously monitoring physiologi... In addition to vital functions,more subsidiary functions are being expected from wearable devices.The wearable technology thus far has achieved the ability to maintain homeostasis by continuously monitoring physiological signals.The quality of life improves if,through further developments of wearable devices to detect,announce,and even control unperceptive or noxious signals from the environment.Soft materials based on photonic engineering can fulfil the abovementioned functions.Due to the flexibility and zero-power operation of such materials,they can be applied to conventional wearables without affecting existing functions.The achievements to freely tailoring a broad range of electromagnetic waves have encouraged the development of wearable systems for independent recognition/manipulation of light,pollution,chemicals,viruses and heat.Herein,the role that photonic engineering on a flexible platform plays in detecting or reacting to environmental changes is reviewed in terms of material selection,structural design,and regulation mechanisms from the ultraviolet to infrared spectral regions.Moreover,issues emerging with the evolution of the wearable technology,such as Joule heating,battery durability,and user privacy,and the potential solution strategies are discussed.This article provides a systematic review of current progress in wearable devices based on photonic structures as well as an overview of possible ubiquitous advances and their applications,providing diachronic perspectives and future outlook on the rapidly growing research field of wearable technology. 展开更多
关键词 photonic structure wearable device health care device colorimetric sensor radiative cooling infrared camouflage
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High efficiency filtering using two-dimensional photonic crystal coupled cavity structures 被引量:2
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作者 王会波 王金生 +1 位作者 李文慧 丁卫强 《Chinese Optics Letters》 SCIE EI CAS CSCD 2008年第6期431-433,共3页
Transmission spectra of coupled cavity structures (CCSs) in two-dimensional (2D) photonic crystals (PCs) are investigated using a coupled mode theory, and an optical filter based on CCS is proposed. The performa... Transmission spectra of coupled cavity structures (CCSs) in two-dimensional (2D) photonic crystals (PCs) are investigated using a coupled mode theory, and an optical filter based on CCS is proposed. The performance of the filter is investigated using finite-difference time-domain (FDTD) method, and the results show that within a very short coupling distance of about 3λ, where ), is the wavelength of signal in vacuum, the incident signals with different frequencies are separated into different channels with a contrast ratio of 20 dB. The advantages of this kind of filter are small size and easily tunable operation frequencies. 展开更多
关键词 CCSs PC CS mode High efficiency filtering using two-dimensional photonic crystal coupled cavity structures LINE
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Nonlinear optical and optical limiting properties of new structures of organic nonlinear optical materials for photonic applications 被引量:5
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作者 A. Jawad Almosawe H. L. Saadon 《Chinese Optics Letters》 SCIE EI CAS CSCD 2013年第4期68-72,共5页
The nonlinear optical (NLO) and optical limiting (OL) properties of three new structures of organic NLO vip host Poly(N-vinylcarbozole)/disperse orange 3 (PVK/DO3), PVK/disperse orange 13 (PVK/DO13). and P... The nonlinear optical (NLO) and optical limiting (OL) properties of three new structures of organic NLO vip host Poly(N-vinylcarbozole)/disperse orange 3 (PVK/DO3), PVK/disperse orange 13 (PVK/DO13). and PVK/disperse orange 25 (PVK/DO25) as a solution at different concentrations and as a thin-film sample are studied using continuous wave z-scan system at 532 nm. The open-aperture z-scan data of the NLO materials in the solution and thin-film samples displayed two-photon and saturable absorptions, respectively. The PVK/DO13 exhibites the largest and best values of the nonlinearities, such as n2, β, X(3) compared with those of PVK/DO3 and PVK/DO25. This nonlinearity increases as the concentration increases. Tile results indicate that these NLO materials are good candidates for optical switching and OL devices. 展开更多
关键词 NLO Nonlinear optical and optical limiting properties of new structures of organic nonlinear optical materials for photonic applications DO PVK
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