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Scattering of Circularly Polarized Terahertz Waves on a Graphene Nanoantenna 被引量:1
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作者 刘志坤 谢亚楠 +2 位作者 耿莉 潘登科 宋盼 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第2期129-132,共4页
We present a surface current method to model the graphene rectangular nanoantenna scattering in the terahertz band with Comsol. Compared with the equivalent thin slab method, the results obtained by the surface curren... We present a surface current method to model the graphene rectangular nanoantenna scattering in the terahertz band with Comsol. Compared with the equivalent thin slab method, the results obtained by the surface current method are more accurate and efficient. Then the electromagnetic scattering of circularly polarized terahertz waves on graphene nanoantennas is numerically analyzed by utilizing the surface current method. The depen- dences of the antenna resonant frequency with the circularly polarized wave on width and length are consistent with those for the linear polarized waves. These results are proved to be useful to design et^cient nanoantennas in terahertz wireless communications. 展开更多
关键词 of in Scattering of Circularly polarized Terahertz waves on a Graphene Nanoantenna IS SCM THZ on for
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A planar chiral nanostructure with asymmetric transmission of linearly polarized wave and huge optical activity in near-infrared band 被引量:2
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作者 刘道亚 罗孝阳 +1 位作者 刘锦景 董建峰 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第12期256-261,共6页
Just like an electronic diode that allows the electrical current to flow in one direction only, a kind of chiral metamaterial structure with a similar functionality for the electromagnetic wave is proposed. The design... Just like an electronic diode that allows the electrical current to flow in one direction only, a kind of chiral metamaterial structure with a similar functionality for the electromagnetic wave is proposed. The designed nanostructure that consists of twisted metallic split-ring resonators on both sides of a dielectric substrate achieves asymmetric transmission for a forward and backward propagating linearly polarized wave by numerical simulation in near-infrared band. Difference in transmission efficiency of the optimized structure between the same polarized waves incident from opposite directions can reach a maximum at the communication wavelength (1.55 μm). Moreover, the simulation results of this structure also exhibit strong optical activity and circular dichroism. 展开更多
关键词 asymmetric transmission optical activity linearly polarized wave circular dichroism
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Faraday Angle of Linearly Polarized Waves Along Magnetic Field in Magnetized Collisional Plasmas
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作者 袁忠才 时家明 +1 位作者 黄勇 许波 《Plasma Science and Technology》 SCIE EI CAS CSCD 2010年第5期519-522,共4页
In magnetized collisional plasmas, owing to the differences between attenuations of left- and right-handed polarized waves, the Faraday rotation angle differs from that in collision- aless plasmas. In this paper, the ... In magnetized collisional plasmas, owing to the differences between attenuations of left- and right-handed polarized waves, the Faraday rotation angle differs from that in collision- aless plasmas. In this paper, the attenuation rates of left- and right-handed polarized waves are analyzed, and the Faraday angle is expressed by the real and imaginary parts of refractive index of the magnetized plasma, with clear physics meaning. Furthermore, the dependence of Faraday angle on collision frequency is calculated and discussed. 展开更多
关键词 linearly polarized wave magnetized collisional plasmas Faraday angle ATTENUATION
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Inversion of an Atomic Wave Packet in a Circularly Polarized Electromagnetic Wave
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作者 ZENGGao-Jian 《Communications in Theoretical Physics》 SCIE CAS CSCD 2001年第1期83-86,共4页
We study behavior of an atomic wave packet in a circularly polarized electromagnetic wave, and particularly calculate the atomic inversion of the wave packet. A general method of calculation is presented. The results ... We study behavior of an atomic wave packet in a circularly polarized electromagnetic wave, and particularly calculate the atomic inversion of the wave packet. A general method of calculation is presented. The results are interesting. For example, if the wave packet is very narrow or/and the interaction is very strong, no matter the atom is initially in its ground state or excited state, the atomic inversion approaches zero as time approaches infinity. If the atom is initially in its ground state and excited state with the probability 1/2 respectively, and if the momentum density is an even function, then the atomic inversion equals zero at any time. 展开更多
关键词 atomic inversion atomic wave packet circularly polarized electromagnetic wave
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Parametric Instabilities of Parallel Propagating Circularly Polarized Alfven Waves:One-Dimensional Hybrid Simulations
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作者 何鹏 高新亮 +1 位作者 陆全明 赵金松 《Chinese Physics Letters》 SCIE CAS CSCD 2015年第11期85-91,共7页
By performing one-dimensional (l-D) hybrid simulations, we analyze in detail the parametric instabilities of the Alfv^n waves with a spectrum in a low beta plasma. The parametric instabilities experience two stages.... By performing one-dimensional (l-D) hybrid simulations, we analyze in detail the parametric instabilities of the Alfv^n waves with a spectrum in a low beta plasma. The parametric instabilities experience two stages. In the first stage, the density modes are excited and immediately couple with the pump Alfv6n waves. In the second stage, each pump Alfv^n wave decays into a density mode and a daughter Alfv6n mode similar to the monochromatic cases. Ftlrthermore, the proton velocity beam will also be formed after the saturation of the parametric instabilities. When the plasma beta is high, the parametric decay in the second stage will be strongly suppressed. 展开更多
关键词 Parametric Instabilities of Parallel Propagating Circularly polarized Alfven waves:One-Dimensional Hybrid Simulations FIGURE
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Theoretical analysis and comparison of OAM waves generated by three kinds of antenna array 被引量:2
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作者 Dandan Liu Liangqi Gui +5 位作者 Ke Chen Liang Lang Zixiao Zhang Han Chen Lixing Liu Tao Jiang 《Digital Communications and Networks》 SCIE CSCD 2021年第1期16-28,共13页
Antenna array is one of the methods which can generate Orbital Angular Momentum(OAM)waves.However,OAM waves generated by different antenna arrays have different characteristics of Electric-field(E-field)com-ponents... Antenna array is one of the methods which can generate Orbital Angular Momentum(OAM)waves.However,OAM waves generated by different antenna arrays have different characteristics of Electric-field(E-field)com-ponents'distribution and radiation patterns.In order to solve this problem,we derive E-feld formulas of OAM waves generated by different kinds of dipole antenna array in this paper.The dipole antenna arrays are arranged by three methods:1)antenna elements are in the same direction of y axis,2)antenna elements are in the radial direction and 3)antenna elements are in the azimuthal direction.Results show that x components,y components and z components carry different OAM modes under the three conditions.Simulation results show that the same direction antenna array produces the best OAM waves because the y component is dominated by OAM mode l and RHCP/LHCP waves are negligible in energy,while the pure OAM waves carried by the z components generated by the other two antenna arrays have little energy.In addition,only the radiation pattern ofl=0 produced by the same direction antenna array does not have a null zone in the propagation direction.Radiation patterns of l=±1 do not have null zones in the propagation direction generated by other two antenna arrays. 展开更多
关键词 Orbital angular momentum Circularly polarized wave Antenna array Theoretical formula
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SIMULTANEOUS MULTIPLE TARGET RECOGNITION USING POLARIZATION AGILE WAVES 被引量:2
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作者 Chen Xinwei Zhao Jianzhong Wu Wen 《Journal of Electronics(China)》 2012年第3期237-241,共5页
A novel matching method for simultaneous multi-target recognition is proposed by jointly considering target's prior scattering knowledge and the polarization parameters of radar echoes. The matching coefficients a... A novel matching method for simultaneous multi-target recognition is proposed by jointly considering target's prior scattering knowledge and the polarization parameters of radar echoes. The matching coefficients are calculated for the judgment. MATLAB simulations show that several targets can be accurately recognized simultaneously, and a high recognition probability can be achieved in Monte Carlo simulations. The total execution time can be remarkably reduced in the Field Programmable Gate Array (FPGA) implementation of the matching procedure. 展开更多
关键词 Matching method Multiple target recognition Polarization agile waves Field Programmable Gate Arrays (FPGA)
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The characteristics of shear wave splitting in the source region of the April 20,2013 Lushan earthquake 被引量:2
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作者 Sha Liu Jiansi Yang +3 位作者 Baofeng Tian Yu Zheng Xudong Jiang Zhiqiang Xu 《Earthquake Science》 2013年第3期223-228,共6页
Using seismic data of the aftershocks sequence of the April 20, 2013 Lushan earthquake recorded by seismic temporary and permanent stations in the source region, with the visual inspection of particle motion diagrams,... Using seismic data of the aftershocks sequence of the April 20, 2013 Lushan earthquake recorded by seismic temporary and permanent stations in the source region, with the visual inspection of particle motion diagrams, this paper preliminarily contains the polarization directions of fast shear wave and the time-delays of split shear waves at every station, and analyzes the crustal anisotropic characteristics in the source region. In the study area, the polarization direc- tions at stations BAX, TQU, L 132, L 133, L 134, and L 135 are northeast, which is consistent with the strike of Dachuan- Shuangshi fault. There are two polarization directions at MDS and L131, which are northeast and southeast. The scatter of polarization directions suggests the complex stress field around these two stations where two faults intersect. For the normalized time-delays at every station, the range is 1.02-8.64 ms/km. The largest time-delay is from L134 which is closest to the mainshock, and the smallest one is from L133. The variations in time-delays show the decreasing at stations BAX, L134, and L135 because of the stress-relaxation after earthquake. 展开更多
关键词 Lushan earthquake Shear wavesplitting Polarization direction of fast shear wave Time-delay of split shear wave
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A Transmission-Type Electrically Tunable Polarizer Based on Graphene Ribbons at Terahertz Wave Band 被引量:1
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作者 唐祎程 朱志宏 +4 位作者 张检发 郭楚才 刘肯 袁晓东 秦石乔 《Chinese Physics Letters》 SCIE CAS CSCD 2015年第2期91-94,共4页
We theoretically and numerically demonstrate that a transmission-type electrically tunable polarizer can be realized by using graphene ribbons supported on a dielectric film with a graphene sheet behind. The polarizat... We theoretically and numerically demonstrate that a transmission-type electrically tunable polarizer can be realized by using graphene ribbons supported on a dielectric film with a graphene sheet behind. The polarization mechanism originates from the antenna plasmon resonance of graphene stripes. The results of full-wave numerical simulations reveal that transmittance of 0.70 for one polarization and 0.0073 for another polarization can be obtained at normal incidence. The transmission-type electrically tunable polarizer provides and facilitates a variety of applications, including filtering, detecting, and imaging. 展开更多
关键词 THz A Transmission-Type Electrically Tunable Polarizer Based on Graphene Ribbons at Terahertz wave Band
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Shear wave splitting analysis of local earthquakes from dense arrays in Shimian,Sichuan 被引量:2
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作者 Sha Liu Baofeng Tian 《Earthquake Science》 2023年第1期52-63,共12页
The Shimian area of Sichuan sits at the junction of the Bayan Har block.Sichuan-Yunnan rhombic block,and Yangtze block,where several faults intersect.This region features intense tectonic activity and frequent earthqu... The Shimian area of Sichuan sits at the junction of the Bayan Har block.Sichuan-Yunnan rhombic block,and Yangtze block,where several faults intersect.This region features intense tectonic activity and frequent earthquakes.In this study,we used local seismic waveform data recorded using dense arrays deployed in the Shimian area to obtain the shear wave splitting parameters at 55 seismic stations and thereby determine the crustal anisotropic characteristics of the region.We then analyzed the crustal stress pattern and tectonic setting and explored their relationship in the study area.Although some stations returned a polarization direction of NNW-SSE.a dominant polarization direction of NW-SE was obtained for the fast shear wave at most seismic stations in the study area.The polarization directions of the fast shear wave were highly consistent throughout the study-area.This orientation was in accordance with the direction of the regional principal compressive stress and parallel to the trend of the Xianshuihe and Daliangshan faults.The distribution of crustal anisotropy in this area was affected by the regional tectonic stress field and the fault structures.The mean delay time between fast and slow shear waves was 3.83 ms/km.slightly greater than the values obtained in other regions of Sichuan.This indicates that the crustal media in our study area had a high anisotropic strength and also reveals the influence of tectonic complexity resulting from the intersection of multiple faults on the strength of seismic anisotropy. 展开更多
关键词 shear wave splitting polarization direction of the fast shear wave regional principal compressive stress dense array Citation:Liu S and Tian BF(2023).Shear wave splitting analysis of local earthquakes from dense arrays in Shimian Sichuan.
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Radio Disturbance Suppression for Ground Wave Radar
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作者 Qiao, Xiaolin Liu, Yongtan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1994年第2期1-11,共11页
A new method of single sample polarization filtering is proposed. The algorithm is fast and suitable for the polarization processing of stationary or nonstationary polarized disturbed signals with one or more independ... A new method of single sample polarization filtering is proposed. The algorithm is fast and suitable for the polarization processing of stationary or nonstationary polarized disturbed signals with one or more independent disturbances. A ground wave polarimetric radar with the ability of radio disturbance suppression is then introduced. Some numerical results demonstrate the effectiveness of single sample polarization filtering method for ground wave polarimetric radar. 展开更多
关键词 ALGORITHMS ATTENUATION Electromagnetic wave polarization Interference suppression POLARIMETERS Radar countermeasures Radar interference Radar transmitters Signal filtering and prediction Telecommunication equipment
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Controlling of the Polarization States of Electromagnetic Waves Using Epsilon-near-Zero Metamaterials
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作者 张晓静 吴玺 徐亚东 《Chinese Physics Letters》 SCIE CAS CSCD 2017年第8期51-54,共4页
We demonstrate theoretically that the epsilon-near-zero materials can be utilized to control effectively the polarization conversion of an electromagnetic wave through reflection. The significant feature differing fro... We demonstrate theoretically that the epsilon-near-zero materials can be utilized to control effectively the polarization conversion of an electromagnetic wave through reflection. The significant feature differing from all other means based on whatever natural materials or metamaterials is that for TM incident wave, the reflected phase is a constant, while for TE wave, the reflected phase is a linear function of the incident angle. The phase difference between them covers the range from -180°to 0°, and the polarization conversions from linear states to elliptical or circular states can be obtained by only adjusting the incident angle. Because no complex structures are employed, our proposal promises a simple approach for manipulating polarization conversion at both terahertz and optical frequencies. 展开更多
关键词 Controlling of the Polarization States of Electromagnetic waves Using Epsilon-near-Zero Metamaterials TE TM
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Analysis of Mechanically Tunable Frequency Selective Surfaces 被引量:6
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作者 Zhang, Wenxun Song, Hongxin 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1997年第4期7-16,共10页
The frequency selective surface (FSS) has been widely applied by means of its spatial frequency-filter characteristic, but it is always designed and used as a device with fixed frequency response. In order to tune the... The frequency selective surface (FSS) has been widely applied by means of its spatial frequency-filter characteristic, but it is always designed and used as a device with fixed frequency response. In order to tune the resonant frequency and switch the frequency channel, a scheme of mechanically tunable FSS is theoretically analyzed by using the method of Floquet's vector modes expansion and fields matching. A double-layer tunable FSS with dipole element can perform a dynamic range of resonant frequency covering whole X-band. 展开更多
关键词 Antenna accessories Electric filters Electromagnetic field theory Electromagnetic wave polarization Electromagnetic wave reflection Frequency response Mathematical models Natural frequencies Semiconductor device structures
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Two Types of Arctic Oscillation and Their Associated Dynamic Features 被引量:1
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作者 SHI Ning BUEH Cholaw 《Atmospheric and Oceanic Science Letters》 2011年第5期287-292,共6页
In this paper,the dynamical evolutions of two types of Arctic Oscillation (AO),the stratospheric (S) and tropospheric (T) types,have been investigated on an intermediate time scale in terms of transient eddy feedback ... In this paper,the dynamical evolutions of two types of Arctic Oscillation (AO),the stratospheric (S) and tropospheric (T) types,have been investigated on an intermediate time scale in terms of transient eddy feedback forcing and three-dimensional Rossby wave propagation.S-Type (T-type) events are characterized by an anomalous stratospheric polar vortex that is in phase (out of phase) with its tropospheric counterpart.Approximately onethird of AO events,both positive and negative,are T-type events.For the positive phase of a T-type event,the formation and maintenance of stratospheric positive anomalies over the polar cap are associated with an upward propagation of Rossby wave packets originating from the near-tropopause altitude over northeastern Asia.However,such upward propagating features are not found for S-type events.In the troposphere,transient eddy feedback forcing is primarily responsible for the meridional seesaw structure of both the S-and T-type events,with an additional contribution from Rossby wave propagation. 展开更多
关键词 Arctic Oscillation stratospheric polar vortex Rossby wave transient eddy feedback forcing
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Threshold of parametric instability in the ionospheric heating experiments
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作者 Xiang WANG Chen ZHOU +3 位作者 Moran LIU Farideh HONARY Binbin NI Zhengyu ZHAO 《Plasma Science and Technology》 SCIE EI CAS CSCD 2018年第11期53-60,共8页
Many observations in the ionospheric heating experiment, by a powerful high frequency electromagnetic wave with ordinary polarization launched from a ground-based facility, is attributed to parametric instability (PI... Many observations in the ionospheric heating experiment, by a powerful high frequency electromagnetic wave with ordinary polarization launched from a ground-based facility, is attributed to parametric instability (PI). In this paper, the general dispersion relation and the threshold of the PI excitation in the heating experiment are derived by considering the inhomogeneous spatial distribution of pump wave field. It is shown that the threshold of PI is influenced by the effective electron and ion collision frequencies and the pump wave frequency. Both collision and Landau damping should be considered in the PI calculation. The derived threshold expression has been used to calculate the required threshold for excitation of PI for several ionospheric conditions during heating experiments conducted employing EISCAT high frequency transmitter in TromsФ, Norway, on 2nd October 1998, 8th November 2001, 19th October 2012 and 7th July 2014. The results indicate that the calculated threshold is in good agreement with the experimental observations. 展开更多
关键词 ionospheric plasma ionospheric modification parametric instability ordinary polarized EM wave
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Design and studies on the traveling wave transverse RF deflecting structure 被引量:1
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作者 张敬如 侯汨 +2 位作者 戴建枰 裴士伦 裴国玺 《Chinese Physics C》 SCIE CAS CSCD 北大核心 2008年第3期232-235,共4页
With the development of free electron laser (FEL) and the international linear collider (ILC), the electron bunch length is getting smaller and smaller, The traveling-wave transverse RF deflecting structure is an ... With the development of free electron laser (FEL) and the international linear collider (ILC), the electron bunch length is getting smaller and smaller, The traveling-wave transverse RF deflecting structure is an important part of the RF deflecting method for bunch length measurement and phase space diagnostics. The operation mode in RF deflector is the "TM11-like" mode. Since the TM11-like mode in this structure has a pair of degenerate dipole modes, two additional holes are provided on either side of each iris to stabilize the mode. The simulation and optimization have been done. A prototype has been fabricated and tested. The cold test results have been compared with the simulations of the first three modes. 展开更多
关键词 TM11-like mode RF deflector mode stabilizer vertical polarized wave parallel polarized wave
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Linear polarization conversion of transmitted terahertz wave with double-layer meta-grating surfaces 被引量:1
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作者 Han Sun Yaxin Zhang +4 位作者 Kailong Wang Yuncheng Zhao Wei Kou Shixiong Liang Siaguang Han Ziqiang Yang 《Chinese Optics Letters》 SCIE EI CAS CSCD 2018年第8期54-57,共4页
In this Letter, we demonstrate a linear polarization conversion of transmitted terahertz wave with double-layer meta-grating surfaces, which integrated the frequency selectivity of a split ring resonator metasurface a... In this Letter, we demonstrate a linear polarization conversion of transmitted terahertz wave with double-layer meta-grating surfaces, which integrated the frequency selectivity of a split ring resonator metasurface and the polarization selectivity of a metallic grating surface. Since the double-layer can reduce the loss, and the Fabry- Perot like resonant effect between the two layers can improve the conversion efficiency, this converter can rotate the incident y-polarized terahertz wave into an x-polarized transmitted wave with relatively low loss and high efficiency. Experimental results show that an average conversion efficiency exceeding 75% from 0.25 to 0.65 THz with the highest efficiency of 90% at 0.43 THz with onlv -2 dB loss has been achieved. 展开更多
关键词 Linear polarization conversion of transmitted terahertz wave with double-layer meta-grating surfaces THZ
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Graded-index ridge surface plasmon polaritons waveguide
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作者 叶春伟 刘玉敏 +2 位作者 汪洁 吕宏博 俞重远 《Chinese Optics Letters》 SCIE EI CAS CSCD 2014年第9期79-82,共4页
We propose and analyze a long-range dielectric-loaded surface plasmon polariton (SPP) waveguide based on graded-index ridge over server millimeter distances. Then the influence of the dielectric thickness and the ri... We propose and analyze a long-range dielectric-loaded surface plasmon polariton (SPP) waveguide based on graded-index ridge over server millimeter distances. Then the influence of the dielectric thickness and the ridge refractive index on propagation length and mode width is discussed and simulated with the finite ele- ment raethod. The result shows that the SPP can propagate as long as 3.42 mm, as well as the mode width keeping as 1.64μm, a better one compared with the fixed refractive index. Considering its nanoscale dimension and outstanding performance, the structure is easily realized when connected with electrodes. 展开更多
关键词 Electromagnetic wave polarization Finite element method Particle optics PHONONS PHOTONS PLASMONS Quantum theory Refractive index Surface plasmon resonance Traveling wave tubes waveguides
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Morphology controllable urchin-shaped bimetallic nickel-cobalt oxide/carbon composites with enhanced electromagnetic wave absorption performance
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作者 Fushan Li Qiuyu Li +13 位作者 Hideo Kimura Xiubo Xie Xiaoyu Zhang Nannan Wu Xueqin Sun Ben Bin Xu Hassan Algadi Rami Adel Pashameah Abdullah K.Alanazi Eman Alzahrani Handong Li Wei Du Zhanhu Guo Chuanxin Hou 《Journal of Materials Science & Technology》 SCIE EI CAS CSCD 2023年第17期250-259,共10页
The microscopic morphology of electromagnetic wave absorbers influences the multiple reflections of electromagnetic waves and impedance matching,determining the absorption properties.Herein,the urchin-shaped bimetalli... The microscopic morphology of electromagnetic wave absorbers influences the multiple reflections of electromagnetic waves and impedance matching,determining the absorption properties.Herein,the urchin-shaped bimetallic nickel-cobalt oxide/carbon(NiCo_(2)O_(4)/C)composites are prepared via a hy-drothermal route,whose absorption properties are investigated by different morphologies regulated by changing calcination temperature.A minimum reflection loss(RL_(min))of-75.26 dB is achieved at a match-ing thickness of 1.5 mm,and the effective absorption bandwidth(EAB)of 8.96 GHz is achieved at 2 mm.Multi-advantages of the synthesized NiCo_(2)O_(4)/C composites contribute to satisfactory absorption proper-ties.First,the interweaving of the needle-like structures increases the opportunities for scattering and multiple reflections of incident electromagnetic waves,and builds up a conductive network to facilitate the enhancement of conductive losses.Second,the carbon component in the NiCo_(2)O_(4)/C composites en-hances the interfacial polarization and reduces the density of the absorber.Besides,generous oxygen va-cancy defects are introduced into the NiCo_(2)O_(4)/C composites,which induces defect polarization and dipole polarization.In summary,the ternary coordination of components,defects and morphology led to out-standing electromagnetic wave absorption,which lightened the path for improving the electromagnetic wave absorption property and enriching the family of NiCo_(2)O_(4) absorbers with excellent performance. 展开更多
关键词 NiCo_(2)O_(4)/C Oxygen vacancies Interfacial polarization Electromagnetic wave absorber
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HIGH ACCURACY ARITHMETIC AVERAGE TYPE DISCRETIZATION FOR THE SOLUTION OF TWO-SPACE DIMENSIONAL NONLINEAR WAVE EQUATIONS
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作者 R.K.MOHANTY VENU GOPAL 《International Journal of Modeling, Simulation, and Scientific Computing》 EI 2012年第2期1-18,共18页
In this paper,we propose a new high accuracy discretization based on the ideas given by Chawla and Shivakumar for the solution of two-space dimensional nonlinear hyper-bolic partial differential equation of the form u... In this paper,we propose a new high accuracy discretization based on the ideas given by Chawla and Shivakumar for the solution of two-space dimensional nonlinear hyper-bolic partial differential equation of the form utt=A(x,y,t)uxx+B(x,y,t)uyy+g(x,y,t,u,ux,uy,ut),0<x,y<1,t>0 subject to appropriate initial and Dirichlet boundary conditions.We use only five evaluations of the function g and do not require any fictitious points to discretize the differential equation.The proposed method is directly applicable to wave equation in polar coordinates and when applied to a linear telegraphic hyperbolic equation is shown to be unconditionally stable.Numerical results are provided to illustrate the usefulness of the proposed method. 展开更多
关键词 Nonlinear hyperbolic equation variable coefficients arithmetic average type approximation wave equation in polar coordinates van der Pol equation telegraphic equation maximum absolute errors.
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