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 l...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 lasers.However,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 solitons.We optimize the laser system to improve its stability,which suppresses the Q-switched lasing induced by environmental perturbation.We,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 solitons.One pathway includes the dynamics of raised relaxation oscillation,quasimode-locking stage,spectral beating behavior,and finally the stable single-soliton mode-locking.The other pathway contains,however,an extra transient bound-state stage before the final single-pulse modelocking operation.Moreover,we propose a theoretical model to predict the buildup time of solitons,which agrees well with the experimental results.Our findings can bring real-time insights into ultrafast fiber laser design and optimization,as well as promote the application of fiber laser.展开更多
We establish a new Kamenev-type theorem for a class of second-order nonlinear damped delay dynamic equations on a time scale by using the generalized Riccati transformation technique. The criterion obtained improves r...We establish a new Kamenev-type theorem for a class of second-order nonlinear damped delay dynamic equations on a time scale by using the generalized Riccati transformation technique. The criterion obtained improves related contributions to the subject. An example is provided to illustrate assumptions in our theorem are less restrictive.展开更多
基金We thank X.Yao,X.Han,G.Chen,W.Li,G.Wang,and Y.Zhang for fruitful discussions.The work was supported by the National Natural Science Foundation of China under Grant Nos.61525505,11774310, 61705193by the Key Scientific and Technological Innovation Team Project in Shaanxi Province(2015KCT-06)and by China Postdoctoral Science Foundation(2017M610367).
文摘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 lasers.However,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 solitons.We optimize the laser system to improve its stability,which suppresses the Q-switched lasing induced by environmental perturbation.We,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 solitons.One pathway includes the dynamics of raised relaxation oscillation,quasimode-locking stage,spectral beating behavior,and finally the stable single-soliton mode-locking.The other pathway contains,however,an extra transient bound-state stage before the final single-pulse modelocking operation.Moreover,we propose a theoretical model to predict the buildup time of solitons,which agrees well with the experimental results.Our findings can bring real-time insights into ultrafast fiber laser design and optimization,as well as promote the application of fiber laser.
基金supported by the Applied Mathematics Enhancement Program of Linyi University
文摘We establish a new Kamenev-type theorem for a class of second-order nonlinear damped delay dynamic equations on a time scale by using the generalized Riccati transformation technique. The criterion obtained improves related contributions to the subject. An example is provided to illustrate assumptions in our theorem are less restrictive.
基金the Natural Science Foundation of Hunan Province(12JJ6006)the Hunan Province Science and Technology Project(2012FJ3107)+1 种基金the National Natural Science Foundation ofChina(11071222)the Scientific Research Fund of Education Department of Guangxi Zhuang Autonomous Region(2013YB223)
