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Data-Driven Ai-and Bi-Soliton of the Cylindrical Korteweg-de Vries Equation via Prior-Information Physics-Informed Neural Networks
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作者 田十方 李彪 张钊 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第3期1-6,共6页
By the modifying loss function MSE and training area of physics-informed neural networks(PINNs),we propose a neural networks model,namely prior-information PINNs(PIPINNs).We demonstrate the advantages of PIPINNs by si... By the modifying loss function MSE and training area of physics-informed neural networks(PINNs),we propose a neural networks model,namely prior-information PINNs(PIPINNs).We demonstrate the advantages of PIPINNs by simulating Ai-and Bi-soliton solutions of the cylindrical Korteweg-de Vries(cKdV)equation. 展开更多
关键词 equation SOLITON CYLINDRICAL
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Two-dimensional materials-decorated microfiber devices for pulse generation and shaping in fiber lasers 被引量:3
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作者 Zhi-Chao Luo* Meng Liu +1 位作者 Ai-Ping Luo and Wen-Cheng Xu 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第9期63-72,共10页
Two-dimensional(2D) materials have been regarded as a promising nonlinear optical medium for fabricating versatile optical and optoelectronic devices. Among the various photonic applications, the employment of 2D ma... Two-dimensional(2D) materials have been regarded as a promising nonlinear optical medium for fabricating versatile optical and optoelectronic devices. Among the various photonic applications, the employment of 2D materials as nonlinear optical devices such as saturable absorbers for ultrashort pulse generation and shaping in ultrafast lasers is one of the most striking aspects in recent years. In this paper, we review the recent progress of 2D materials based pulse generation and soliton shaping in ultrafast fiber lasers, and particularly in the context of 2D materials-decorated microfiber photonic devices. The fabrication of 2D materials-decorated microfiber photonic devices, high performance mode-locked pulse generation, and the nonlinear soliton dynamics based on pulse shaping method are discussed. Finally, the challenges and the perspective of the 2D materials-based photonic devices as well as their applications are also discussed. 展开更多
关键词 two-dimensional materials MICROFIBER soliton dynamics fiber lasers
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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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Recent progress on mechanisms,principles,and strategies for high-activity and high-stability non-PGM fuel cell catalyst design
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作者 Yuping Yuan Yun Zheng +4 位作者 Dan Luo Weibin Qiu Jiantao Wang Xin Wang Zhongwei Chen 《Carbon Energy》 SCIE EI CAS CSCD 2024年第5期25-52,共28页
The commercialization of a polymer membrane H2-O2 fuel cell and its widespread use call for the development of cost-effective oxygen reduction reaction(ORR)nonplatinum group metal(NPGM)catalysts.Nevertheless,to meet t... The commercialization of a polymer membrane H2-O2 fuel cell and its widespread use call for the development of cost-effective oxygen reduction reaction(ORR)nonplatinum group metal(NPGM)catalysts.Nevertheless,to meet the requests for the real-world fuel cell application and replacing platinum catalysts,it still needs to address some challenges for NPGM catalysts regarding the sluggish ORR kinetics in the cathode and their poor durability in acidic environment.In response to these issues,numerous efforts have been made to study NPGM catalysts both theoretically and experimentally,developed these into the atomically dispersed coordinated metal-nitrogen-carbon(M-N-C)form over the past decades.In this review,we present a comprehensive summary of recent advancements on NPGM catalysts with high activity and durability.Catalyst design strategies in terms of optimizing active-site density and enhancing catalyst stability against demetalization and carbon corrosion are highlighted.It is also emphasized the importance of understanding the mechanisms and principles behind those strategies through a combination of theoretical modeling and experimental work.Especially,further understanding the mechanisms related to the active-site structure and the formation process of the single-atom active site under pyrolysis conditions is critical for active-site engineering.Optimizing the active-site distance is the basic principle for improving catalyst activity through increasing the catalyst active-site density.Theoretical studies for the catalyst deactivation mechanism and modeling stable active-site structures provide both mechanisms and principles to improve the NPGM catalyst durability.Finally,currently remained challenges and perspectives in the future on designing high-performance atomically dispersed NPGM catalysts toward fuel cell application are discussed. 展开更多
关键词 BATTERIES ELECTROCATALYSIS energy storage and conversion fuel cells
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Singular optical propagation properties of two types of one-dimensional anti-PT-symmetric periodic ring optical waveguide networks
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作者 樊阳龙 杨湘波 +5 位作者 练华达 陈润楷 朱蓬勃 邓冬梅 刘宏展 韦中超 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第3期355-362,共8页
Two types of one-dimensional(1D)anti-PT-symmetric periodic ring optical waveguide networks,consisting of gain and loss materials,are constructed.The singular optical propagation properties of these networks are invest... Two types of one-dimensional(1D)anti-PT-symmetric periodic ring optical waveguide networks,consisting of gain and loss materials,are constructed.The singular optical propagation properties of these networks are investigated.The results show that the system composed of gain materials exhibits characteristics of ultra-strong transmission and bidirectional reflection.Conversely,the system composed of loss materials demonstrates equal transmittance and reflectance at some frequencies.In both the systems,a new type of total reflection phenomenon is observed.When the imaginary part of the refractive indices of waveguide segments is smaller than 10-5,the system shows bidirectional transparency with the transmittance tending to be 1 and reflectivity to be smaller than 10-8 at some bands.When the refractive indices of the waveguide segments are real,the system will be bidirectional transparent at the full band.These findings may deepen the understanding of anti-PT-symmetric optical systems and optical waveguide networks,and possess potential applications in efficient optical energy storage,ultra-sensitive optical filters,ultra-sensitive all-optical switches,integrated optical chips,stealth physics,and so on. 展开更多
关键词 anti-PT-symmetric waveguide networks bidirectional transparent
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Multifunctional disk device for optical switch and temperature sensor 被引量:1
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作者 卞振宇 梁瑞生 +3 位作者 张郁靖 易丽璇 赖根 赵瑞通 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第10期518-521,共4页
A multifunctional surface plasmon polariton disk device coupled by two metal-insulator-metal(MIM) waveguides is proposed and investigated numerically with finite-difference time-domain simulation. It can be used as ... A multifunctional surface plasmon polariton disk device coupled by two metal-insulator-metal(MIM) waveguides is proposed and investigated numerically with finite-difference time-domain simulation. It can be used as optical switch and temperature sensor by filling disk with liquid crystal and ethanol, respectively. The simulation results demonstrate that the transmission characteristics of an optical switch can be manipulated by adjusting the radius of disk and the slit width between disk and MIM waveguides. The transmittance and modulation depth of optical switch at 1550 nm are up to 64.82% and 17.70 d B, respectively. As a temperature sensor, its figure of merit can reach 30.46. In this paper, an optical switch with better efficiency and a temperature sensor with better sensitivity can be achieved. 展开更多
关键词 surface plasmon polaritons optical switch modulation depth temperature sensor figure of merit
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Propagation properties and radiation force of circular Airy Gaussian vortex beams in strongly nonlocal nonlinear medium 被引量:1
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作者 Xinyu Liu Chao Sun Dongmei Deng 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第2期285-292,共8页
We study the abruptly autofocusing and autodefocusing properties of the circular Airy Gaussian vortex(CAi GV)beams in strongly nonlocal nonlinear medium for the first time through numerical simulations.The magnitude o... We study the abruptly autofocusing and autodefocusing properties of the circular Airy Gaussian vortex(CAi GV)beams in strongly nonlocal nonlinear medium for the first time through numerical simulations.The magnitude of topological charges and the position of the vortex could change not only the light spot pattern but also the intensity contrast.Meanwhile,we can change the position of the autofocusing and autodefocusing planes by changing the parameter of the incident beam.Furthermore,we can control the peak intensity contrast through choosing properly the truncation factor.As for the radiation force,we study the gradient and the scattering forces of CAi GV beams on Rayleigh dielectric sphere.Our analyses demonstrate that the radiation force can be enhanced by choosing proper parameters of CAi GV beams. 展开更多
关键词 optical vortices abruptly autofocusing radiation force strongly nonlocal nonlinear
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Negativity of Wigner function and phase sensitivity of an SU(1,1) interferometer
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作者 Chun-Li Liu Li-Li Guo +1 位作者 Zhi-Ming Zhang Ya-Fei Yu 《Chinese Physics B》 SCIE EI CAS CSCD 2019年第6期121-125,共5页
Both the negativity of Wigner function and the phase sensitivity of an SU(1,1) interferometer are investigated in this paper. In the case that the even coherent state and squeezed vacuum state are input into the inter... Both the negativity of Wigner function and the phase sensitivity of an SU(1,1) interferometer are investigated in this paper. In the case that the even coherent state and squeezed vacuum state are input into the interferometer, the Heisenberg limit can be approached with parity detection. At the same time, the negativity volume of Wigner function of detection mode comes entirely from the input state and varies periodically with the encoding phase. In addition, the negativity volume of Wigner function is positively correlated with the phase sensitivity of the SU(1,1) interferometer. The positive correlation may mean that the non-classicality indicated by negative Wigner function is a kind of resource that can verify some related research results of phase estimation. 展开更多
关键词 SU(1 1) INTERFEROMETER WIGNER FUNCTION PHASE sensitivity
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Solar broadband metamaterial perfect absorber based on dielectric resonant structure of Ge cone array and InAs film
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作者 Kuang-Ling Guo Hou-Hong Chen +2 位作者 Xiao-Ming Huang Tian-Hui Hu Hai-Ying Liu 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第11期325-330,共6页
The broadband metamaterial perfect absorber has been extensively studied due to its excellent characteristics and promising application prospect.In this work a solar broadband metamaterial perfect absorber is proposed... The broadband metamaterial perfect absorber has been extensively studied due to its excellent characteristics and promising application prospect.In this work a solar broadband metamaterial perfect absorber is proposed based on the structure of the germanium(Ge)cone array and the indium arsenide(InAs)dielectric film on the gold(Au)substrate.The results show that the absorption covers the whole ultraviolet-visible and near-infrared range.For the case of A>99%,the absorption bandwidth reaches up to 1230 nm with a wavelength range varied from 200 nm to 1430 nm.The proposed absorber is able to absorb more than 98.7%of the solar energy in a solar spectrum from 200 nm to 3000 nm.The electromagnetic dipole resonance and the high-order modes of the Ge cone couple strongly to the incident optical field,which introduces a strong coupling with the solar radiation and produces an ultra-broadband absorption.The absorption spectrum can be feasibly manipulated via tuning the structural parameters,and the polarization insensitivity performance is particularly excellent.The proposed absorber can possess wide applications in active photoelectric effects,thermion modulators,and photoelectric detectors. 展开更多
关键词 METAMATERIAL electromagnetic resonance perfect absorber solar broadband absorption`
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Alleviating hysteresis and improving device stability of perovskite solar cells via alternate voltage sweeps
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作者 Chao Xia Wei-Dong Song +8 位作者 Chong-Zhen Zhang Song-Yang Yuan Wen-Xiao Hu Ping Qin Ru-Peng Wang Liang-Liang Zhao Xing-Fu Wang Miao He Shu-Ti Li 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第1期537-541,共5页
The anomalous hysteresis in a perovskite solar cell induced by an asymmetric field is confirmed by a capacitance–voltage measurement. By applying several cycles of alternating reverse and forward scans, this hysteres... The anomalous hysteresis in a perovskite solar cell induced by an asymmetric field is confirmed by a capacitance–voltage measurement. By applying several cycles of alternating reverse and forward scans, this hysteresis phenomenon is obviously alleviated, resulting in a hysteresis-less state in the perovskite solar cell. Meanwhile, the open-circuit voltage and power conversion efficiency of the perovskite solar cell are enhanced by 55.74% and 61.30%, respectively, while the current density and fill factor keep almost invariable. The operation of alleviating hysteresis is essential for further research and is likely to bring in performance gains. 展开更多
关键词 perovskite solar cells hysteresis behavior alternate voltage sweeps built-in electric field
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Micro-light-emitting-diode array with dual functions of visible light communication and illumination
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作者 黄涌 郭志友 +1 位作者 孙慧卿 黄鸿勇 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第10期490-495,共6页
We demonstrate high-speed blue 4 ×4 micro-light-emitting-diode (LED) arrays with 14 light-emitting units (two light-emitting units are used as the positive and negative electrodes for power supply, respectivel... We demonstrate high-speed blue 4 ×4 micro-light-emitting-diode (LED) arrays with 14 light-emitting units (two light-emitting units are used as the positive and negative electrodes for power supply, respectively) comprising multiple quantum wells formed of GaN epitaxial layers grown on a sapphire substrate, and experimentally test their applicability for being used as VLC transmitters and illuminations. The micro-LED arrays provide a maximum -3-dB frequency response of 60.5 MHz with a smooth frequency curve from 1 MHz to 500 MHz for an optical output power of 165 mW at an injection current of 30 mA, which, to our knowledge, is the highest response frequency ever reported for blue GaN-based LEDs operating at that level of optical output power. The relationship between the frequency and size of the device single pixel diameter reveals the relationship between the response frequency and diffusion capacitance of the device. 展开更多
关键词 light-emitting devices optical communications diffusion capacitance
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Propagation of rotating elliptical Gaussian beams from right-handed material to left-handed material
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作者 彭喜 陈迟到 +1 位作者 陈波 邓冬梅 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第12期313-318,共6页
By applying the ABCD matrix method, we report the propagating properties of the rotating elliptical Gaussian beams(REGBs) from the right-handed material(RHM) to the left-handed material(LHM). Based on the propag... By applying the ABCD matrix method, we report the propagating properties of the rotating elliptical Gaussian beams(REGBs) from the right-handed material(RHM) to the left-handed material(LHM). Based on the propagation equation, we obtain the intensity distributions of the REGBs during the propagation. It is found that the rotating direction of the REGBs is opposite in the RHM and the LHM, and the rotation angles tend to be π /2 as the propagation distance is long enough.Then we analyze the relationship between the refractive index and the rotating velocity. Furthermore, the energy flow and the angular momentum(AM) of the REGBs which can rotate are also obtained. 展开更多
关键词 ABCD matrix rotating elliptical Gaussian beams left-handed material
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Flexible planar micro supercapacitor diode
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作者 Yihui Ma Pei Tang +7 位作者 Zhenyuan Miao Wuyang Tan Qijun Wang Yuecong Chen Guosheng Li Qingyun Dou Xingbin Yan Lingling Shui 《Journal of Energy Chemistry》 SCIE EI CAS CSCD 2024年第6期429-435,I0011,共8页
Supercapacitor diode is a novel ion device that performs both supercapacitor energy storage and ion diode rectification functions.However,previously reported devices are limited by their large size and complex process... Supercapacitor diode is a novel ion device that performs both supercapacitor energy storage and ion diode rectification functions.However,previously reported devices are limited by their large size and complex processes.In this work,we demonstrate a screen-printed micro supercapacitor diode(MCAPode)that based on the insertion of a finger mode with spinel ZnCo_(2)O_(4) as cathode and activated carbon as anode for the first time,and featuring an excellent area specific capacitance(1.21 mF cm^(-2)at 10 mV s^(-1))and high rectification characteristics(rectification ratioⅠof 11.99 at 40 mV s^(-1)).Taking advantage of the ionic gel electrolyte,which provides excellent stability during repeated flexing and at high temperatures.In addition,MCAPode exhibits excellent electrochemical performance and rectification capability in"AND"and"OR"logic gates.These findings provide practical solutions for future expansion of micro supercapacitor diode applications. 展开更多
关键词 Micro devices Supercapacitor diodes Screen-printing RECTIFICATION Logic gates
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Propagation of an Airy–Gaussian beam in uniaxial crystals 被引量:6
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作者 周美玲 陈迟到 +3 位作者 陈波 彭喜 彭玉莲 邓冬梅 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第12期309-312,共4页
Under the paraxial approximation, the analytical propagation expression of an Airy–Gaussian beam(Ai GB) in uniaxial crystals orthogonal to the optical axis is investigated. The propagation dynamics of the Ai GB is ... Under the paraxial approximation, the analytical propagation expression of an Airy–Gaussian beam(Ai GB) in uniaxial crystals orthogonal to the optical axis is investigated. The propagation dynamics of the Ai GB is given for different ratios of the extraordinary index to the ordinary refractive index. It has been found that the continuity and the self-bending effect of Ai GB become weaker when the ratio increases. From the figure of the maximum intensity of Ai GB, one can see that the maximum intensity is not monotone decreasing due to the anisotropic effect of the crystals. The intensity distribution of Ai GB in different distribution factors is shown. The Ai GB converges toward a Gaussian beam as the distribution factor increases. 展开更多
关键词 Airy–Gaussian beam extraordinary and ordinary refractive index anisotropic effect
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Propagation of Airy Gaussian vortex beams in uniaxial crystals 被引量:5
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作者 余伟浩 赵瑞璜 +5 位作者 邓富 黄加耀 陈迟到 杨湘波 赵燕平 邓冬梅 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第4期121-126,共6页
The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtai... The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtained. The propagation features of the Airy Gaussian vortex beams are shown with changes of the distribution factor and the ratio of the extraordinary refractive index to the ordinary refractive index. The correlations between the ratio and the maximum intensity value during the propagation, and its appearing distance have been investigated. 展开更多
关键词 Airy Gaussian vortex beams uniaxial crystals anisotropic effect
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Propagation of a Pearcey beam in uniaxial crystals 被引量:2
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作者 Chuangjie Xu Ludong Lin +2 位作者 Zhengzhong Huang Donglong He Dongmei Deng 《Chinese Physics B》 SCIE EI CAS CSCD 2019年第2期210-214,共5页
An analytical propagation expression of a Pearcey beam in uniaxial crystals orthogonal to the optical axis is derived.The propagations of the Pearcey beam in the tourmaline and the quartz are investigated. The phase d... An analytical propagation expression of a Pearcey beam in uniaxial crystals orthogonal to the optical axis is derived.The propagations of the Pearcey beam in the tourmaline and the quartz are investigated. The phase distribution and the angular momentum of the Pearcey beam in the tourmaline are also performed. The result shows that the positions of the auto-focusing and the inversion simply relate to the extraordinary refractive index of the crystals. In other words, we can choose the suitable crystals to adjust the positions of auto-focusing and inversion of the Pearcey beam to meet the actual needs. 展开更多
关键词 CRYSTAL OPTICS DIFFRACTION THEORY PROPAGATION
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Interaction of Airy–Gaussian beams in saturable media 被引量:2
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作者 周美玲 彭玉莲 +3 位作者 陈迟到 陈波 彭喜 邓冬梅 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第8期146-150,共5页
Based on the nonlinear Schr o¨dinger equation, the interactions of the two Airy–Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different a... Based on the nonlinear Schr o¨dinger equation, the interactions of the two Airy–Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy–Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy–Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure. 展开更多
关键词 Airy-Gaussian beam INTERACTION saturable media
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Improved performance of near UV light-emitting diodes with a composition-graded p-AlGaN irregular sawtooth electron-blocking layer 被引量:1
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作者 秦萍 宋伟东 +9 位作者 胡文晓 张苑文 张崇臻 王汝鹏 赵亮亮 夏超 袁松洋 尹以安 李述体 宿世臣 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第8期463-467,共5页
We investigate the performances of the near-ultraviolet(about 350 nm-360 nm) light-emitting diodes(LEDs) each with specifically designed irregular sawtooth electron blocking layer(EBL) by using the APSYS simulat... We investigate the performances of the near-ultraviolet(about 350 nm-360 nm) light-emitting diodes(LEDs) each with specifically designed irregular sawtooth electron blocking layer(EBL) by using the APSYS simulation program.The internal quantum efficiencies(IQEs),light output powers,carrier concentrations in the quantum wells,energy-band diagrams,and electrostatic fields are analyzed carefully.The results indicate that the LEDs with composition-graded pAlxGa1-xN irregular sawtooth EBLs have better performances than their counterparts with stationary component p-AlGaN EBLs.The improvements can be attributed to the improved polarization field in EBL and active region as well as the alleviation of band bending in the EBL/p-AlGaN interface,which results in less electron leakage and better hole injection efficiency,thus reducing efficiency droop and enhancing the radiative recombination rate. 展开更多
关键词 AIGaN-based ultraviolet LEDs irregular sawtooth EBL APSYS simulation program output power
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Nonparaxial propagation properties of the chirped Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis 被引量:1
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作者 Yizuo Chen Guanwen Zhao +2 位作者 Feng Ye Chuangjie Xu Dongmei Deng 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第10期315-321,共7页
In this article, we investigate the nonparaxial propagation properties of the chirped Airy Gaussian vortex(CAiGV)beams in uniaxial crystals orthogonal to the optical axis analytically and numerically. We discuss how... In this article, we investigate the nonparaxial propagation properties of the chirped Airy Gaussian vortex(CAiGV)beams in uniaxial crystals orthogonal to the optical axis analytically and numerically. We discuss how the linear chirp parameters, the quadratic chirp parameters, and the Gaussian factors influence the nonparaxial propagation dynamics of the CAiGV beams. The intensity, the energy flow, the beam center, and the angular momentum of the CAiGV beams are deeply investigated. It is shown that the Gaussian factors have a great effect on the intensity and the centroid positions of the CAiGV beams. With the Gaussian factors increasing, the intensity of CAiGV beams decreases rapidly. The main lobes of the transverse intensity distribution of the CAiGV beams are similar to triangles. 展开更多
关键词 Chirped Airy Gaussian vortex beams energy flow angular momentum nonparaxial propagation
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