Soliton Molecules With <inline-formula><tex-math notation="LaTeX">$\pm \pi {{/ 2, 0}}$</tex-math> </inline-formula>, and <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math></inline-formula> Phase Differences in a Graphene-Based Mode-Locked Erbium-Doped Fiber Laser
A complete collection of two-soliton bound states exhibiting <inline-formula><tex-math notation="LaTeX">$\pm \pi {{/ 2, 0}}$</tex-math></inline-formula>, and <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math> </inl...
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IEEE
2018-01-01
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| Series: | IEEE Photonics Journal |
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| Online Access: | https://ieeexplore.ieee.org/document/8360765/ |
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| author | Lili Gui Changxi Yang |
| author_facet | Lili Gui Changxi Yang |
| author_sort | Lili Gui |
| collection | DOAJ |
| description | A complete collection of two-soliton bound states exhibiting <inline-formula><tex-math notation="LaTeX">$\pm \pi {{/ 2, 0}}$</tex-math></inline-formula>, and <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math> </inline-formula> phase differences was realized in experiment in a mode-locked erbium-doped fiber laser with a graphene saturable absorber for the first time. The graphene mode-locker possesses modulation depth of about 6% and saturation fluency of about 300 <italic>μ</italic>J/cm<sup>2</sup>. By carefully adjusting the polarization controller in the laser cavity under appropriate pumping power, diverse soliton molecules with distinct temporal separations and different phase relationships were obtained. Our experimental findings provide clear evidence that stable soliton pairs with <inline-formula><tex-math notation="LaTeX">$\pm \pi {{/ 2, 0}}$</tex-math></inline-formula> , and <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math></inline-formula> phase differences can be tightly bounded in fiber lasers as intrinsic attractors, which is independent of cavity details such as the mode-locker we choose. In addition, our numerical simulations unravel the influence of nonlinear properties of a saturable absorber on bound states. It is found that mode-lockers with different modulation depth and/or saturation intensity play a role in interpulse separation and individual pulsewidth of generated soliton molecules while keeping the relative phases between bound solitons unchanged. This paper is instructive to explain current research works on bound states in fiber lasers with sorts of saturable absorbers and is of importance to understand the dissipative dynamics of soliton molecules. |
| format | Article |
| id | doaj-art-39d8c03431cc4ec5adb897ddb4ea2388 |
| institution | DOAJ |
| issn | 1943-0655 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Photonics Journal |
| spelling | doaj-art-39d8c03431cc4ec5adb897ddb4ea23882025-08-20T02:41:49ZengIEEEIEEE Photonics Journal1943-06552018-01-011031910.1109/JPHOT.2018.28322498360765Soliton Molecules With <inline-formula><tex-math notation="LaTeX">$\pm \pi {{/ 2, 0}}$</tex-math> </inline-formula>, and <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math></inline-formula> Phase Differences in a Graphene-Based Mode-Locked Erbium-Doped Fiber LaserLili Gui0https://orcid.org/0000-0002-3710-6330Changxi Yang1https://orcid.org/0000-0002-9972-6965State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing, ChinaState Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing, ChinaA complete collection of two-soliton bound states exhibiting <inline-formula><tex-math notation="LaTeX">$\pm \pi {{/ 2, 0}}$</tex-math></inline-formula>, and <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math> </inline-formula> phase differences was realized in experiment in a mode-locked erbium-doped fiber laser with a graphene saturable absorber for the first time. The graphene mode-locker possesses modulation depth of about 6% and saturation fluency of about 300 <italic>μ</italic>J/cm<sup>2</sup>. By carefully adjusting the polarization controller in the laser cavity under appropriate pumping power, diverse soliton molecules with distinct temporal separations and different phase relationships were obtained. Our experimental findings provide clear evidence that stable soliton pairs with <inline-formula><tex-math notation="LaTeX">$\pm \pi {{/ 2, 0}}$</tex-math></inline-formula> , and <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math></inline-formula> phase differences can be tightly bounded in fiber lasers as intrinsic attractors, which is independent of cavity details such as the mode-locker we choose. In addition, our numerical simulations unravel the influence of nonlinear properties of a saturable absorber on bound states. It is found that mode-lockers with different modulation depth and/or saturation intensity play a role in interpulse separation and individual pulsewidth of generated soliton molecules while keeping the relative phases between bound solitons unchanged. This paper is instructive to explain current research works on bound states in fiber lasers with sorts of saturable absorbers and is of importance to understand the dissipative dynamics of soliton molecules.https://ieeexplore.ieee.org/document/8360765/Soliton moleculesbound statesphase differencefiber lasersgraphene. |
| spellingShingle | Lili Gui Changxi Yang Soliton Molecules With <inline-formula><tex-math notation="LaTeX">$\pm \pi {{/ 2, 0}}$</tex-math> </inline-formula>, and <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math></inline-formula> Phase Differences in a Graphene-Based Mode-Locked Erbium-Doped Fiber Laser IEEE Photonics Journal Soliton molecules bound states phase difference fiber lasers graphene. |
| title | Soliton Molecules With <inline-formula><tex-math notation="LaTeX">$\pm \pi {{/ 2, 0}}$</tex-math> </inline-formula>, and <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math></inline-formula> Phase Differences in a Graphene-Based Mode-Locked Erbium-Doped Fiber Laser |
| title_full | Soliton Molecules With <inline-formula><tex-math notation="LaTeX">$\pm \pi {{/ 2, 0}}$</tex-math> </inline-formula>, and <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math></inline-formula> Phase Differences in a Graphene-Based Mode-Locked Erbium-Doped Fiber Laser |
| title_fullStr | Soliton Molecules With <inline-formula><tex-math notation="LaTeX">$\pm \pi {{/ 2, 0}}$</tex-math> </inline-formula>, and <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math></inline-formula> Phase Differences in a Graphene-Based Mode-Locked Erbium-Doped Fiber Laser |
| title_full_unstemmed | Soliton Molecules With <inline-formula><tex-math notation="LaTeX">$\pm \pi {{/ 2, 0}}$</tex-math> </inline-formula>, and <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math></inline-formula> Phase Differences in a Graphene-Based Mode-Locked Erbium-Doped Fiber Laser |
| title_short | Soliton Molecules With <inline-formula><tex-math notation="LaTeX">$\pm \pi {{/ 2, 0}}$</tex-math> </inline-formula>, and <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math></inline-formula> Phase Differences in a Graphene-Based Mode-Locked Erbium-Doped Fiber Laser |
| title_sort | soliton molecules with inline formula tex math notation latex pm pi 2 0 tex math inline formula x00a0 and inline formula tex math notation latex pi tex math inline formula phase differences in a graphene based mode locked erbium doped fiber laser |
| topic | Soliton molecules bound states phase difference fiber lasers graphene. |
| url | https://ieeexplore.ieee.org/document/8360765/ |
| work_keys_str_mv | AT liligui solitonmoleculeswithinlineformulatexmathnotationlatexpmpi20texmathinlineformulax00a0andinlineformulatexmathnotationlatexpitexmathinlineformulaphasedifferencesinagraphenebasedmodelockederbiumdopedfiberlaser AT changxiyang solitonmoleculeswithinlineformulatexmathnotationlatexpmpi20texmathinlineformulax00a0andinlineformulatexmathnotationlatexpitexmathinlineformulaphasedifferencesinagraphenebasedmodelockederbiumdopedfiberlaser |