28<\/strong>, 17424-17433 (2020)<\/a>.<\/p>\n\n\n\nFigure-of-9 fiber laser is a type of nonlinear amplified loop mirror (NALM) mode-locked fiber laser. The reported Yb-doped figure-of-9 laser cavity was constructed by entirely polarization maintaining (PM) fibers and PM fiber-pigtailed components. A nonreciprocal phase shifter providing a linear \u03c0\/2 phase bias was inserted into the NALM loop to promote self-starting of the mode-locked operation.<\/p>\n\n\n\n
By adjusting pump power, the working state of the laser could be switched between fundamental mode-locking and period-quadrupling mode-locking. In contrast with the fundamental mode-locked state, the pulse intensity of the period-quadrupling was no longer uniform, but alternated between four different values, which indicated that steady-state period switched from 1 to 4 round trip times. Other periods can be observed if one slightly modifies the configuration, a small change in passive fiber length, for example.<\/p>\n\n\n\n
Based on the experimental observation, we proposed a simplified iteration model to prove that pulse multiplication is a result of overdriving the artificial saturable absorber regardless of pulse formation mechanism. The reliability of the iteration model was also verified experimentally.<\/p>\n\n\n\n
Further theoretical insight was obtained by numerical simulations based on the cubic Ginzburg\u2013Landau equation and the split-step Fourier method, which clearly showed that the ratio between the distances of each bifurcation point was approaching the Feigenbaum constant.<\/p>\n\n\n\n
The results agree with the classical chaos theory and strongly suggest that the laser design presented here could be a stable and reliable ultrafast optical platform to study bifurcation and chaos.<\/p>\n","protected":false},"excerpt":{"rendered":"
Period multiplication is a bifurcation phenomenon, which depicts a typical roadmap from periodic steady-state to chaos. Nonlinear system, whose output is periodic, may go through period bifurcation before its output becomes chaos. Examples could be as simple as droplets\u2019 patterns of a water tap or as complex as discrete-time neural networks. There has been particular […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[26,25,7,28,27],"class_list":["post-239","post","type-post","status-publish","format-standard","hentry","category-research-news","tag-bifurcation","tag-chaos","tag-mode-locked-fiber-laser","tag-nonlinear-dynamics","tag-period-multiplication"],"_links":{"self":[{"href":"https:\/\/laser.im\/possible\/wp-json\/wp\/v2\/posts\/239","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/laser.im\/possible\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/laser.im\/possible\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/laser.im\/possible\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/laser.im\/possible\/wp-json\/wp\/v2\/comments?post=239"}],"version-history":[{"count":2,"href":"https:\/\/laser.im\/possible\/wp-json\/wp\/v2\/posts\/239\/revisions"}],"predecessor-version":[{"id":241,"href":"https:\/\/laser.im\/possible\/wp-json\/wp\/v2\/posts\/239\/revisions\/241"}],"wp:attachment":[{"href":"https:\/\/laser.im\/possible\/wp-json\/wp\/v2\/media?parent=239"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/laser.im\/possible\/wp-json\/wp\/v2\/categories?post=239"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/laser.im\/possible\/wp-json\/wp\/v2\/tags?post=239"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}