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High and low frequency relaxation oscillations in a capacitive discharge plasma

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Chinese Physics B 2008年第10期17卷 3799-3806页

作者：周筑文 Sungjin Kim 吉世印孙光宇邓明森 Department of physics Guizhou Educational College Department of Electrical Engineering and Computer Sciences - 1770 University of California

Both high and low frequency relaxation oscillations have been observed in an argon capacitive discharge connected to a peripheral grounded chamber through a slot with dielectric spacers. The oscillations, observed from time-varying optical emission of the main discharge chamber, show, for example, a high frequency （46 kHz） relaxation oscillation at 100 mTorr, with an absorbed power near the peripheral breakdown, and a low frequency （2.7-3.7 Hz） oscillation, at a higher absorbed power. The high frequency oscillation is found to ignite a plasma in the slot, but usually not in the periphery. The high frequency oscillation is interpreted by using an electromagnetic model of the slot impedance, combined with the circuit analysis of the system including a matching network. The model is further developed by using a parallel connection of variable peripheral capacitance to analyse the low frequency oscillation. The results obtained from the model are in agreement with the experimental observations and indicate that a variety of behaviours are dependent on the matching conditions.

关键词： relaxation oscillation capacitive discharge periphery slot

Review of relaxation oscillations in plasma processing discharges

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Chinese Physics B 2007年第3期16卷 758-765页

作者：周筑文 M. A. Lieberman Sungjin Kimb Department of Physics Guizhou Educational College Guiyang 550003 China Department of Electrical Engineering and Computer Sciences- 1770 University of California Berkeley CA 94720 U.S.A

relaxation oscillations due to plasma instabilities at frequencies ranging from a few Hz to tens of kHz have been observed in various types of plasma processing discharges. relaxation oscillations have been observed in electropositive capacitive discharges between a powered anode and a metallic chamber whose periphery is grounded through a slot with dielectric spacers. The oscillations of time-varying optical emission from the main discharge chamber show, for example, a high-frequency （- 40 kHz） relaxation oscillation at 13.33Pa, with an absorbed power being nearly the peripheral breakdown power, and a low-frequency （- 3 Hz） oscillation, with an even higher absorbed power. The high-frequency oscillation is found to ignite plasma in the slot, but usually not in the peripheral chamber. The kilohertz oscillations are modelled using an electromagnetic model of the slot impedance, coupled to a circuit analysis of the system including the matching network. The model results are in general agreement with the experimental observations, and indicate a variety of behaviours dependent on the matching conditions. In low-pressure inductive discharges, oscillations appear in the transition between low-density capacitively driven and high-density inductively driven discharges when attaching gases such as SF6 and Ar/SF6 mixtures are used. oscillations of charged particles, plasma potential, and light, at frequencies ranging from a few Hz to tens of kHz, are seen for gas pressures between 0.133 Pa and 13.33 Pa and discharge powers in a range of 75 1200 W. The region of instability increases as the plasma becomes more electronegative, and the frequency of plasma oscillation increases as the power, pressure, and gas flow rate increase. A volume-averaged （global） model of the kilohertz instability has been developed; the results obtained from the model agree well with the experimental observations.

关键词： relaxation oscillation capacitive discharges inductive discharges plasma instability

Transient mode competition in directly modulated DFB semiconductor laser

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Science China(Physics,Mechanics & Astronomy) 2015年第12期58卷 187-192页

作者： XIAO RuLei SHI YueChun ZHENG JiLin ZHANG YunShan ZHENG JunShou CHEN XiangFei National Laboratory of Solid State Microstructures Collaborative Innovation Center of Advanced Microstructures and College of Engineering and Applied Sciences Nanjing University Photonics Information Technology Laboratory Institute of Communication Engineering PLA University of Science and Technology

A new effect of transient mode competition in directly modulated DFB laser based on equivalent phase-shift （EPS） technique is presented and studied. Since there are multi-order reflections in EPS structure and if the 0th order subgrating is properly de- signed, the transient lasing of 0th order will occur during the rising time of the injection current. As a result, transient mode competition between -lst order （main mode） and 0th order will occur accordingly. This can consume redundant carrier and suppress the transient relaxation oscillation, which may be applied in some areas like on-off switching modulation of DFB semiconductor lasers. As an example, an equivalent n phase shift （n-EPS） is carefully designed to realize the effect. In such a laser the 0th order wavelength is in the margin of the material gain region and the -1st order wavelength is around the gain peak, while the stable single longitudinal mode （SLM） operation of the -lst order is guaranteed. The simulation investigation is performed. Good results with suppressed relaxation oscillation and 1.25 Gb/s directly on-off modulation （32 dB extinction ratio） are demonstrated. We believe it provides a new kind of method for on-off switching with high extinction ratio and weak relaxation oscillation.

关键词： DFB semiconductor laser mode competition relaxation oscillation sampled grating

A Four-Element Sensor Array Consisting of Asymmetric Distributed-Feedback Fiber Lasers

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Photonic Sensors 2014年第2期4卷 180-187页

作者： Pengpeng WANG Jun CHANG Cunguang ZHU Boning SUN Guangping LV Sasa ZHANG Yanjie ZHAO Zhihui SUN Xiaolei ZHANG Gangding PENG School of Information Science and Engineering and Shandong Provincial Key Laboratory of Laser Technology andApplication Shandong University Jinan 250100 China Laser Institute of Shandong Academy of Science Jinan 250014 China photonics & Optical Communications Group School of Electrical Engineering & Telecommunications the Universityof New South Wales Sydney 2052 Australia

A sensor array system formed by arranging four asymmetric distributed-feedback fiber lasers （DFB-FL） in ascending order according to their slope efficiencies was proposed. The output flatness could be effectively improved with the application of asymmetric DFB-FLs. The last element had almost the same output with the others although it obtained the smallest pump power. The relative intensity noise （RIN） and relaxation oscillation frequency of the sensor array were also analyzed. It is found that the relaxation oscillation frequency of a certain DFB-FL was relevant to its relative position in the array. And the RIN of a certain DFB-FL was always affected by the other elements in the array, which was not dependent on the order of their arrangement.

关键词： Asymmetric DFB fiber laser sensor array intensity noise relaxation oscillation

Canard explosion,homoclinic and heteroclinic orbits in singularly perturbed generalist predator-prey systems

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International Journal of Biomathematics 2021年第1期14卷 151-174页

作者： Ali Atabaigi Department of Mathematics Razi UniversityKermanshahIran

This paper studies the dynamics of the generalist predator–prey systems modeled in[***,*** and ***,Bistability and limit cycles in generalist predator–prey dynamics,***.14(2013)48–55].When prey reproduces much faster than predator,by combining the normal form theory of slow-fast systems,the geometric singular perturbation theory and the results near non-hyperbolic points developed by Krupa and Szmolyan[relaxation oscillation and canard explosion,*** Equations174(2)(2001)312–368;Extending geometric singular perturbation theory to nonhyperbolic points—fold and canard points in two dimensions,SIAM ***.33(2)(2001)286–314],we provide a detailed mathematical analysis to show the existence of homoclinic orbits,heteroclinic orbits and canard limit cycles and relaxation oscillations bifurcating from the singular homoclinic ***,on global stability of the unique positive equilibrium,we provide some new *** simulations are also carried out to support the theoretical results.

关键词： Canard cycle relaxation oscillation generalist predator prey singular perturbation homoclinic heteroclinic

Revealing the behavior of soliton buildup in a mode-locked laser

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Advanced Photonics 2019年第1期1卷 58-71页

作者： Xueming Liu Yudong Cui Zhejiang University College of Optical Science and EngineeringState Key Laboratory of Modern Optical InstrumentationHangzhouChina Nanjing University of Aeronautics and Astronautics Institute for Advanced Interdisciplinary ResearchNanjingChina Hunan University of Science and Technology School of Physics and Electronic ScienceXiangtanChina

Real-time spectroscopy based on an emerging time-stretch technique can map the spectral information of optical waves into the time domain,opening several fascinating explorations of nonlinear dynamics in mode-locked ***,the self-starting process of mode-locked lasers is quite sensitive to environmental perturbation,which causes the transient behaviors of lasers to deviate from the true buildup process of *** optimize the laser system to improve its stability,which suppresses the Q-switched lasing induced by environmental ***,therefore,demonstrate the first observation of the entire buildup process of solitons in a mode-locked laser,revealing two possible pathways to generate the temporal *** pathway includes the dynamics of raised relaxation oscillation,quasimode-locking stage,spectral beating behavior,and finally the stable single-soliton *** other pathway contains,however,an extra transient bound-state stage before the final single-pulse modelocking ***,we propose a theoretical model to predict the buildup time of solitons,which agrees well with the experimental *** findings can bring real-time insights into ultrafast fiber laser design and optimization,as well as promote the application of fiber laser.

关键词： fiber laser mode-locking self-starting process relaxation oscillation real-time spectroscopy

Canard Solutions in a Predator-Prey Model

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Journal of Applied Mathematics and Physics 2022年第5期10卷 1678-1693页

作者： Guojian Lin School of Mathematics Renmin University of China Beijing China

The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical point, pitchfork point, canard point, are identified;then Hopf bifurcation, relaxation oscillation, together with the canard transition from Hopf bifurcation to relaxation oscillation are discussed.

关键词： Canard Explosion relaxation oscillation Predator-Prey Model Geometric Singular Perturbation Theory

The Study on the Performance of the Wavelength Conversion Based on a Tunable External Cavity Semiconductor Laser

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Chinese Journal of Lasers 2001年第1期 41-47页

作者： YE Yabin ZHANG Hanyi ZHENG Xiaoping DAI Wuju GUO Yili (Department of Electronic Engineering, Tsinghua University, Beijing 100084, China) Received March 14, 2000 Revised manuscript received May 15, 2000

In this paper, the performance of the wavelength conversion based on a tunable external cavity semiconductor laser (ECL) was studied. The static wavelength conversion was achieved in the tunable wavelength range of the ECL. The dynamic wavelength conversions of 155 Mb/s and 622 Mb/s nonreturn to zero (NRZ) signals were realized. The simulation of the ECL output characteristics using modified compound cavity rate equation shows that the higher bit rate wavelength conversion can be realized by increasing the relaxation oscillation frequency of the ECL. When the modulated bit rate is much lower than the relaxation oscillation frequency, under a fixed input signal power, there is an optimal bias current for the wavelength converter based on ECL.

关键词： Tunable external cavity semiconductor laser wavelength conversion relaxation oscillation