Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes
Identifieur interne : 000008 ( Pmc/Corpus ); précédent : 000007; suivant : 000009Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes
Auteurs : Xueming Liu ; Dongdong Han ; Zhipei Sun ; Chao Zeng ; Hua Lu ; Dong Mao ; Yudong Cui ; Fengqiu WangSource :
- Scientific Reports [ 2045-2322 ] ; 2013.
Abstract
Multi-wavelength lasers have widespread applications (e.g. fiber telecommunications, pump-probe measurements, terahertz generation). Here, we report a nanotube-mode-locked all-fiber ultrafast oscillator emitting three wavelengths at the central wavelengths of about 1540, 1550, and 1560 nm, which are tunable by stretching fiber Bragg gratings. The output pulse duration is around 6 ps with a spectral width of ~0.5 nm, agreeing well with the numerical simulations. The triple-laser system is controlled precisely and insensitive to environmental perturbations with <0.04% amplitude fluctuation. Our method provides a simple, stable, low-cost, multi-wavelength ultrafast-pulsed source for spectroscopy, biomedical research and telecommunications.
Url:
DOI: 10.1038/srep02718
PubMed: 24056500
PubMed Central: 3779847
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes</title><author><name sortKey="Liu, Xueming" sort="Liu, Xueming" uniqKey="Liu X" first="Xueming" last="Liu">Xueming Liu</name><affiliation><nlm:aff id="a1"><institution>State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics</institution>, Chinese Academy of Sciences, Xi'an 710119,<country>China</country></nlm:aff></affiliation></author><author><name sortKey="Han, Dongdong" sort="Han, Dongdong" uniqKey="Han D" first="Dongdong" last="Han">Dongdong Han</name><affiliation><nlm:aff id="a1"><institution>State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics</institution>, Chinese Academy of Sciences, Xi'an 710119,<country>China</country></nlm:aff></affiliation></author><author><name sortKey="Sun, Zhipei" sort="Sun, Zhipei" uniqKey="Sun Z" first="Zhipei" last="Sun">Zhipei Sun</name><affiliation><nlm:aff id="a2"><institution>Department of Engineering, University of Cambridge</institution>, 9 JJ Thomson Avenue, Cambridge, CB3 0FA,<country>UK</country></nlm:aff></affiliation><affiliation><nlm:aff id="a3"><institution>Department of Micro- and Nanosciences, Aalto University</institution>, PO Box 13500, FI-00076 Aalto,<country>Finland</country></nlm:aff></affiliation></author><author><name sortKey="Zeng, Chao" sort="Zeng, Chao" uniqKey="Zeng C" first="Chao" last="Zeng">Chao Zeng</name><affiliation><nlm:aff id="a1"><institution>State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics</institution>, Chinese Academy of Sciences, Xi'an 710119,<country>China</country></nlm:aff></affiliation></author><author><name sortKey="Lu, Hua" sort="Lu, Hua" uniqKey="Lu H" first="Hua" last="Lu">Hua Lu</name><affiliation><nlm:aff id="a1"><institution>State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics</institution>, Chinese Academy of Sciences, Xi'an 710119,<country>China</country></nlm:aff></affiliation></author><author><name sortKey="Mao, Dong" sort="Mao, Dong" uniqKey="Mao D" first="Dong" last="Mao">Dong Mao</name><affiliation><nlm:aff id="a1"><institution>State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics</institution>, Chinese Academy of Sciences, Xi'an 710119,<country>China</country></nlm:aff></affiliation></author><author><name sortKey="Cui, Yudong" sort="Cui, Yudong" uniqKey="Cui Y" first="Yudong" last="Cui">Yudong Cui</name><affiliation><nlm:aff id="a1"><institution>State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics</institution>, Chinese Academy of Sciences, Xi'an 710119,<country>China</country></nlm:aff></affiliation></author><author><name sortKey="Wang, Fengqiu" sort="Wang, Fengqiu" uniqKey="Wang F" first="Fengqiu" last="Wang">Fengqiu Wang</name><affiliation><nlm:aff id="a2"><institution>Department of Engineering, University of Cambridge</institution>, 9 JJ Thomson Avenue, Cambridge, CB3 0FA,<country>UK</country></nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">24056500</idno><idno type="pmc">3779847</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3779847</idno><idno type="RBID">PMC:3779847</idno><idno type="doi">10.1038/srep02718</idno><date when="2013">2013</date><idno type="wicri:Area/Pmc/Corpus">000008</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000008</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes</title><author><name sortKey="Liu, Xueming" sort="Liu, Xueming" uniqKey="Liu X" first="Xueming" last="Liu">Xueming Liu</name><affiliation><nlm:aff id="a1"><institution>State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics</institution>, Chinese Academy of Sciences, Xi'an 710119,<country>China</country></nlm:aff></affiliation></author><author><name sortKey="Han, Dongdong" sort="Han, Dongdong" uniqKey="Han D" first="Dongdong" last="Han">Dongdong Han</name><affiliation><nlm:aff id="a1"><institution>State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics</institution>, Chinese Academy of Sciences, Xi'an 710119,<country>China</country></nlm:aff></affiliation></author><author><name sortKey="Sun, Zhipei" sort="Sun, Zhipei" uniqKey="Sun Z" first="Zhipei" last="Sun">Zhipei Sun</name><affiliation><nlm:aff id="a2"><institution>Department of Engineering, University of Cambridge</institution>, 9 JJ Thomson Avenue, Cambridge, CB3 0FA,<country>UK</country></nlm:aff></affiliation><affiliation><nlm:aff id="a3"><institution>Department of Micro- and Nanosciences, Aalto University</institution>, PO Box 13500, FI-00076 Aalto,<country>Finland</country></nlm:aff></affiliation></author><author><name sortKey="Zeng, Chao" sort="Zeng, Chao" uniqKey="Zeng C" first="Chao" last="Zeng">Chao Zeng</name><affiliation><nlm:aff id="a1"><institution>State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics</institution>, Chinese Academy of Sciences, Xi'an 710119,<country>China</country></nlm:aff></affiliation></author><author><name sortKey="Lu, Hua" sort="Lu, Hua" uniqKey="Lu H" first="Hua" last="Lu">Hua Lu</name><affiliation><nlm:aff id="a1"><institution>State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics</institution>, Chinese Academy of Sciences, Xi'an 710119,<country>China</country></nlm:aff></affiliation></author><author><name sortKey="Mao, Dong" sort="Mao, Dong" uniqKey="Mao D" first="Dong" last="Mao">Dong Mao</name><affiliation><nlm:aff id="a1"><institution>State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics</institution>, Chinese Academy of Sciences, Xi'an 710119,<country>China</country></nlm:aff></affiliation></author><author><name sortKey="Cui, Yudong" sort="Cui, Yudong" uniqKey="Cui Y" first="Yudong" last="Cui">Yudong Cui</name><affiliation><nlm:aff id="a1"><institution>State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics</institution>, Chinese Academy of Sciences, Xi'an 710119,<country>China</country></nlm:aff></affiliation></author><author><name sortKey="Wang, Fengqiu" sort="Wang, Fengqiu" uniqKey="Wang F" first="Fengqiu" last="Wang">Fengqiu Wang</name><affiliation><nlm:aff id="a2"><institution>Department of Engineering, University of Cambridge</institution>, 9 JJ Thomson Avenue, Cambridge, CB3 0FA,<country>UK</country></nlm:aff></affiliation></author></analytic><series><title level="j">Scientific Reports</title><idno type="eISSN">2045-2322</idno><imprint><date when="2013">2013</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>Multi-wavelength lasers have widespread applications (e.g. fiber telecommunications, pump-probe measurements, terahertz generation). Here, we report a nanotube-mode-locked all-fiber ultrafast oscillator emitting three wavelengths at the central wavelengths of about 1540, 1550, and 1560 nm, which are tunable by stretching fiber Bragg gratings. The output pulse duration is around 6 ps with a spectral width of ~0.5 nm, agreeing well with the numerical simulations. The triple-laser system is controlled precisely and insensitive to environmental perturbations with <0.04% amplitude fluctuation. Our method provides a simple, stable, low-cost, multi-wavelength ultrafast-pulsed source for spectroscopy, biomedical research and telecommunications.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Liu, X M" uniqKey="Liu X">X. M. Liu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Grelu, P" uniqKey="Grelu P">P. Grelu</name></author><author><name sortKey="Akhmediev, N" uniqKey="Akhmediev N">N. 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<front><journal-meta><journal-id journal-id-type="nlm-ta">Sci Rep</journal-id><journal-id journal-id-type="iso-abbrev">Sci Rep</journal-id><journal-title-group><journal-title>Scientific Reports</journal-title></journal-title-group><issn pub-type="epub">2045-2322</issn><publisher><publisher-name>Nature Publishing Group</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">24056500</article-id><article-id pub-id-type="pmc">3779847</article-id><article-id pub-id-type="pii">srep02718</article-id><article-id pub-id-type="doi">10.1038/srep02718</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Liu</surname><given-names>Xueming</given-names></name><xref ref-type="corresp" rid="c1">a</xref><xref ref-type="aff" rid="a1">1</xref></contrib><contrib contrib-type="author"><name><surname>Han</surname><given-names>Dongdong</given-names></name><xref ref-type="aff" rid="a1">1</xref></contrib><contrib contrib-type="author"><name><surname>Sun</surname><given-names>Zhipei</given-names></name><xref ref-type="aff" rid="a2">2</xref><xref ref-type="aff" rid="a3">3</xref></contrib><contrib contrib-type="author"><name><surname>Zeng</surname><given-names>Chao</given-names></name><xref ref-type="aff" rid="a1">1</xref></contrib><contrib contrib-type="author"><name><surname>Lu</surname><given-names>Hua</given-names></name><xref ref-type="aff" rid="a1">1</xref></contrib><contrib contrib-type="author"><name><surname>Mao</surname><given-names>Dong</given-names></name><xref ref-type="aff" rid="a1">1</xref></contrib><contrib contrib-type="author"><name><surname>Cui</surname><given-names>Yudong</given-names></name><xref ref-type="aff" rid="a1">1</xref></contrib><contrib contrib-type="author"><name><surname>Wang</surname><given-names>Fengqiu</given-names></name><xref ref-type="aff" rid="a2">2</xref></contrib><aff id="a1"><label>1</label><institution>State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics</institution>, Chinese Academy of Sciences, Xi'an 710119,<country>China</country></aff><aff id="a2"><label>2</label><institution>Department of Engineering, University of Cambridge</institution>, 9 JJ Thomson Avenue, Cambridge, CB3 0FA,<country>UK</country></aff><aff id="a3"><label>3</label><institution>Department of Micro- and Nanosciences, Aalto University</institution>, PO Box 13500, FI-00076 Aalto,<country>Finland</country></aff></contrib-group><author-notes><corresp id="c1"><label>a</label><email>liuxueming72@yahoo.com</email></corresp></author-notes><pub-date pub-type="epub"><day>23</day><month>09</month><year>2013</year></pub-date><pub-date pub-type="collection"><year>2013</year></pub-date><volume>3</volume><elocation-id>2718</elocation-id><history><date date-type="received"><day>02</day><month>08</month><year>2013</year></date><date date-type="accepted"><day>03</day><month>09</month><year>2013</year></date></history><permissions><copyright-statement>Copyright © 2013, Macmillan Publishers Limited. All rights reserved</copyright-statement><copyright-year>2013</copyright-year><copyright-holder>Macmillan Publishers Limited. All rights reserved</copyright-holder><license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by-nc-nd/3.0/"><pmc-comment>author-paid</pmc-comment>
<license-p>This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. To view a copy of this license, visit <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by-nc-nd/3.0/">http://creativecommons.org/licenses/by-nc-nd/3.0/</ext-link></license-p></license></permissions><abstract><p>Multi-wavelength lasers have widespread applications (e.g. fiber telecommunications, pump-probe measurements, terahertz generation). Here, we report a nanotube-mode-locked all-fiber ultrafast oscillator emitting three wavelengths at the central wavelengths of about 1540, 1550, and 1560 nm, which are tunable by stretching fiber Bragg gratings. The output pulse duration is around 6 ps with a spectral width of ~0.5 nm, agreeing well with the numerical simulations. The triple-laser system is controlled precisely and insensitive to environmental perturbations with <0.04% amplitude fluctuation. Our method provides a simple, stable, low-cost, multi-wavelength ultrafast-pulsed source for spectroscopy, biomedical research and telecommunications.</p></abstract></article-meta></front><body><p>Ultrafast mode-locked fiber lasers have widespread applications (e.g. fiber telecommunications, pump-probe measurements, terahertz generation), due to their various advantages (e.g. small footprint, high stability, efficient heat dissipation, low-cost<xref ref-type="bibr" rid="b1">1</xref><xref ref-type="bibr" rid="b2">2</xref><xref ref-type="bibr" rid="b3">3</xref><xref ref-type="bibr" rid="b4">4</xref><xref ref-type="bibr" rid="b5">5</xref><xref ref-type="bibr" rid="b6">6</xref>). Thus far, single-wavelength ultrafast fiber lasers have been investigated theoretically and demonstrated experimentally<xref ref-type="bibr" rid="b7">7</xref><xref ref-type="bibr" rid="b8">8</xref><xref ref-type="bibr" rid="b9">9</xref><xref ref-type="bibr" rid="b10">10</xref><xref ref-type="bibr" rid="b11">11</xref>. However, there are few papers reporting multi-wavelength ultrafast fiber lasers<xref ref-type="bibr" rid="b12">12</xref><xref ref-type="bibr" rid="b13">13</xref><xref ref-type="bibr" rid="b14">14</xref><xref ref-type="bibr" rid="b15">15</xref><xref ref-type="bibr" rid="b16">16</xref>, which mainly use the naturally formed birefringence of single-mode fiber (SMF) for lasing wavelength selection. In such fiber lasers, the output wavelengths cannot be controlled precisely due to the difficulty of accurately adjusting the birefringence in SMF. Therefore, these multi-wavelength pulsed fiber lasers are not very stable, and output central wavelengths are not selectable to meet the requirements of various applications. To address this issue, a simple way is to use fiber Bragg gratings for the wavelength selection, which can offer all-fiber based alignment-free structure<xref ref-type="bibr" rid="b17">17</xref><xref ref-type="bibr" rid="b18">18</xref><xref ref-type="bibr" rid="b19">19</xref>. Furthermore, fast development in the chirped fiber Bragg grating (CFBG) fabrication technology has been achieved to provide changeable dispersion, broad bandwidth, and tunable transmittance wavelength covering all major laser wavelengths (e.g. 1, 1.55, and 2 μm). These make CFBG an ideal wavelength selection component for ultrafast broadband fiber lasers.</p><p>To achieve multi-wavelength pulsed lasers, another key element is the saturable absorber, which can operate at multi-wavelengths (i.e. broad operation bandwidth<xref ref-type="bibr" rid="b20">20</xref>). Currently, various saturable absorbers, such as nonlinear loop mirrors<xref ref-type="bibr" rid="b21">21</xref><xref ref-type="bibr" rid="b22">22</xref>, nonlinear polarization rotation<xref ref-type="bibr" rid="b23">23</xref><xref ref-type="bibr" rid="b24">24</xref>, semiconductor saturable absorber mirrors (SESAMs)<xref ref-type="bibr" rid="b20">20</xref><xref ref-type="bibr" rid="b25">25</xref><xref ref-type="bibr" rid="b26">26</xref>, carbon nanotubes<xref ref-type="bibr" rid="b7">7</xref><xref ref-type="bibr" rid="b10">10</xref><xref ref-type="bibr" rid="b11">11</xref><xref ref-type="bibr" rid="b27">27</xref><xref ref-type="bibr" rid="b28">28</xref><xref ref-type="bibr" rid="b29">29</xref><xref ref-type="bibr" rid="b30">30</xref>, and graphene<xref ref-type="bibr" rid="b8">8</xref><xref ref-type="bibr" rid="b31">31</xref><xref ref-type="bibr" rid="b32">32</xref><xref ref-type="bibr" rid="b33">33</xref><xref ref-type="bibr" rid="b34">34</xref>, have been employed for ultrafast pulse generation. Among these saturable absorbers, nanotube and graphene are particularly interesting for multi-wavelength pulsed lasers as they both exhibit extraordinarily broad operation bandwidth for multi-wavelength pulse generation. Indeed, such unique broadband property has been experimentally confirmed for nanotube<xref ref-type="bibr" rid="b29">29</xref><xref ref-type="bibr" rid="b35">35</xref> and graphene<xref ref-type="bibr" rid="b33">33</xref> by wavelength tunable<xref ref-type="bibr" rid="b32">32</xref><xref ref-type="bibr" rid="b35">35</xref> and dual-wavelength<xref ref-type="bibr" rid="b30">30</xref><xref ref-type="bibr" rid="b34">34</xref> pulsed lasers. However, triple-wavelength mode-locking laser has not been demonstrated with carbon nanotubes.</p><p>In this article, we report a compact nanotube-mode-locked all-fiber laser system based on CFBGs, delivering three lasing wavelengths simultaneously. The output central wavelengths are 1539.5, 1549.5, and 1559.5 nm, respectively, which can be accurately selected by CFBGs. The output wavelengths are tunable by stretching CFBGs. The pulse durations of three wavelengths are 6.3, 6.7, and 5.9 ps, respectively. Our laser is insensitive to environmental perturbation with near-transform-limited pulses, and thus is viable for various practical applications, such as fiber telecommunications, pump-probe measurements, and terahertz generation. The proposed method of precisely selecting output wavelengths by fiber gratings and using nanotubes with broad operation bandwidth can be readily adopted for other fiber lasers from 1 to 2 μm.</p><sec disp-level="1" sec-type="results"><title>Results</title><sec disp-level="2"><title>Nanotube-based compact all-fiber triple-wavelength laser system</title><p>The schematic diagram of our nanotube-based compact all-fiber triple-laser system is shown in <xref ref-type="fig" rid="f1">Fig. 1(a)</xref>. The laser system consists of a wavelength-division multiplexer (WDM), a fused coupler with 10% output ratio, two polarization controllers (PCs), three CFBGs, a 5-m-long erbium-doped fiber (EDF) with 6 dB/m absorption at 980 nm, a single-wall carbon nanotube (SWNT) saturable absorber, and a circulator. The EDF and SMF have dispersion parameters of about 11.6 and −22 ps<sup>2</sup>/km at 1550 nm, respectively. CFBGs, written on a standard SMF, have a super-Gaussian reflection profile with a bandwidth of ~1 nm (<xref ref-type="fig" rid="f1">Fig. 1(b)</xref>). The dispersion parameter of these three CFBGs is ~2.2 ps<sup>2</sup>/cm with the length of ~10 mm, and the corresponding central transmittance wavelengths <italic>λ</italic><sub>1–3</sub> are 1539.5, 1549.5, and 1559.5 nm, respectively. The wavelengths of our laser output are separated by another three CFBGs for characterization of individual wavelengths.</p><p>The integrated SWNT-based fiber device is realized by sandwiching a ~2 mm<sup>2</sup> sample between two fiber connectors (see Methods), as shown in inset of <xref ref-type="fig" rid="f1">Fig. 1(a)</xref>. The normalized nonlinear absorption of our integrated SWNT absorber is experimentally measured with a homemade ultrafast laser at 1550 nm, as shown in <xref ref-type="fig" rid="f1">Fig. 1(c)</xref>. According to a simplified two-level saturable absorber model<xref ref-type="bibr" rid="b35">35</xref><xref ref-type="bibr" rid="b36">36</xref>, the experimental data are fitted as the solid curve of <xref ref-type="fig" rid="f1">Fig. 1(c)</xref>. <xref ref-type="fig" rid="f1">Figure 1(d)</xref> shows the absorption spectrum of the SWNT–polycarbonate composite in comparison with pure polycarbonate, which is measured by a spectrometer (JASCO V-570 UV-vis-NIR).</p></sec><sec disp-level="2"><title>Experimental observations</title><p>Continuous wave (CW) operation starts at the pump power of <italic>P</italic> ≈ 9 mW, and self-starting mode-locking is observed at <italic>P</italic> ≈ 15 mW. With the appropriate setting of two PCs, output at three wavelengths is generated from the oscillator. The typical output spectra of three lasers <italic>λ</italic><sub>1–3</sub> at <italic>P</italic> ≈ 45 mW are shown in <xref ref-type="fig" rid="f2">Figs. 2(a), 2(c), and 2(e)</xref> with the central wavelengths at 1539.5, 1549.5, and 1559.5 nm, respectively. The corresponding autocorrelation traces of the experimental data and the sech<xref ref-type="bibr" rid="b2">2</xref>–shaped fit for <italic>λ</italic><sub>1–3</sub> are shown in <xref ref-type="fig" rid="f2">Figs. 2(b), 2(d), and 2(f)</xref>. It is found that the optical spectra have sidebands, which are the typically spectral characteristics of standard solitons<xref ref-type="bibr" rid="b1">1</xref><xref ref-type="bibr" rid="b37">37</xref><xref ref-type="bibr" rid="b38">38</xref>. The full width at half maximum (FWHM) spectral widths at different wavelengths are about 0.47, 0.41, and 0.49 nm, respectively. The output pulse durations (Δ<italic>τ</italic>) are about 6.3, 6.7, and 5.9 ps. The calculated time-bandwidth products at three different wavelengths are about 0.37, 0.35, and 0.36, respectively, which are slightly larger than the value of 0.315 for the transform-limited sech<xref ref-type="bibr" rid="b2">2</xref>-shaped pulses. It is worth noting that here the output spectral width and pulse duration are limited by the bandwidth (i.e. 1 nm) of CFBGs used in the cavity. Broader bandwidth CFBGs in principle can offer broader spectral width, and thus shorter pulse duration.</p><p><xref ref-type="fig" rid="f3">Figures 3(a–d)</xref> show the RF spectra and oscilloscope traces of lasers, respectively. <xref ref-type="fig" rid="f3">Figures 3(a–b)</xref> are the fundamental RF spectra with the 1 Hz resolution and the 100 Hz span for three lasers <italic>λ</italic><sub>1–3</sub>. <xref ref-type="fig" rid="f3">Figures 3(c) and 3(d)</xref> are the wideband RF spectrum up to 1 GHz and the oscilloscope traces up to 2 μs for the laser <italic>λ</italic><sub>2</sub>, respectively. <xref ref-type="fig" rid="f3">Figure 3(a)</xref> exhibits that the repetition rate of the fundamental harmonic frequency is 6.17917 MHz, corresponding to ~161.8 ns round-trip time, as shown in <xref ref-type="fig" rid="f3">Fig. 3(d)</xref>. No spectrum modulation is observed over 1 GHz (<xref ref-type="fig" rid="f3">Fig. 3(c)</xref>), indicating no Q-switching instabilities.</p><p>The RF spectrum in <xref ref-type="fig" rid="f3">Fig. 3(a)</xref> gives a signal-to-noise ratio ~ 70 dB (10<sup>7</sup> contrast), showing low-amplitude fluctuations and good mode-locking stability<xref ref-type="bibr" rid="b10">10</xref><xref ref-type="bibr" rid="b39">39</xref>. With the power ratio of Δ<italic>P</italic> ≈ 10<sup>−7</sup>, the frequency resolution Δ<italic>f<sub>res</sub></italic> = 1 Hz, and the frequency width (FWHM) of Δ<italic>f<sub>A</sub></italic> ≈ 1.3 Hz (<xref ref-type="fig" rid="f3">Fig. 3(a)</xref>), we estimate an amplitude fluctuation Δ<italic>E</italic>/<italic>E</italic> ≈ 3.6 × 10<sup>−4</sup> from the equation Δ<italic>E</italic>/<italic>E</italic> = (Δ<italic>P</italic>Δ<italic>f<sub>A</sub></italic>/Δ<italic>f<sub>res</sub></italic>)<sup>1/2</sup> <xref ref-type="bibr" rid="b39">39</xref>. Note that no pulse is observed in the experimental observations if SWNT is removed.</p></sec><sec disp-level="2"><title>Numerical results</title><p>The typical results of numerical simulations for three lasers <italic>λ</italic><sub>1–3</sub> in the mode-locking regime are demonstrated in <xref ref-type="fig" rid="f4">Fig. 4</xref>. Parameters are chosen to match the experimental values (see Methods). We can see from <xref ref-type="fig" rid="f4">Fig. 4</xref> that the spectral width and pulse duration of <italic>λ</italic><sub>1–3</sub> are 0.474, 0.401, 0.486 nm, and 6.39, 6.79, 6.01 ps, respectively. So the time-bandwidth products of <italic>λ</italic><sub>1–3</sub> are about 0.38, 0.34, and 0.36, respectively, showing that they are sech<xref ref-type="bibr" rid="b2">2</xref>-shaped pulses rather than Gaussian-shaped pulses. The numerical results (<xref ref-type="fig" rid="f4">Fig. 4</xref>) are in good agreement with the experimental observations, as shown in <xref ref-type="fig" rid="f2">Fig. 2</xref>. <xref ref-type="fig" rid="f5">Figure 5</xref> shows the evolution of pulse along the oscillator for the laser <italic>λ</italic><sub>2</sub>. Obviously, it is dynamic rather than static. The evolution of pulse profile in a round trip is demonstrated in the <xref ref-type="supplementary-material" rid="s1">supplemental material</xref>.</p></sec></sec><sec disp-level="1" sec-type="discussion"><title>Discussion</title><p>In the experiments, the proposed oscillator (<xref ref-type="fig" rid="f1">Fig. 1</xref>) fails to simultaneously delivering three wavelengths if SWNT is replaced by such saturable absorbers as nonlinear loop mirror, nonlinear polarization rotation, SESAM, and graphene. It attributes to the inherent characteristic of SWNT, which has highly environmental stability and is independent of the polarization of pulses evolving in the laser cavity<xref ref-type="bibr" rid="b10">10</xref><xref ref-type="bibr" rid="b35">35</xref><xref ref-type="bibr" rid="b40">40</xref><xref ref-type="bibr" rid="b41">41</xref>.</p><p>Based on the cascade of CFBGs, the laser system with more than three wavelengths (e.g. four and five wavelengths) can be achieved in principle. By stretching CFBGs in our experiments, its central wavelength is tunable. <xref ref-type="fig" rid="f6">Figure 6</xref> demonstrates the output spectra at ten wavelengths within the tuning range from ~1560 to 1565 nm. The experimental results show that the spectral width and pulse duration are almost unchanged, indicating the stability of our output pulses. Note that other two wavelengths also can be tuned but with limited wavelength range. For example, the <italic>λ</italic><sub>1</sub> can be tuned from 1540 to 1546 nm, and the <italic>λ<sub>2</sub></italic> can be tuned from 1550 to 1556 nm. The tuning range is determined by the CFBGs.</p></sec><sec disp-level="1" sec-type="methods"><title>Methods</title><sec disp-level="2"><title>SWNT film</title><p>SWNT with the tube diameter <2 nm is grown with the catalytic chemical vapor decomposition method using CH<sub>4</sub> as the carbon source and Co as the catalyst. 0.5 mg·mL<sup>−1</sup> SWNT solution is prepared by dispersing SWNT powder in de-ionized water with sodium dodecyl benzenesulfonate (SDBS) using a sonicator system operating at 20 kHz with 180 W power for 5 hours. To avoid unwanted scattering losses from aggregates and bubbles, the resulting dispersion is centrifuged at 12000 g for an hour, and the upper 90% of the supernatant is then collected. 10 wt% aqueous polyvinyl alcohol (PVA) solution and 0.5 mg·mL<sup>−1</sup> SWNT solution are mixed at the volume ratio of 1:2 overnight by a magnetic stirrer. Slow evaporation under ambient temperature and pressure results in a ~30-μm-thick freestanding SWNT-PVA composite film.</p></sec><sec disp-level="2"><title>Measurement method</title><p>An optical spectrum analyzer (Yokogawa AQ-6370), an autocorrelator, a 6-GHz oscilloscope, a radio-frequency (RF) analyzer, and a 10-GHz photodetector are used to measure the laser output performances.</p></sec><sec disp-level="2"><title>Numerical simulation</title><p>To confirm the experimental observations, we numerically simulate the pulse formation at three wavelengths in the oscillator. The modeling includes such the physics terms as the group velocity dispersion of fiber, the self-phase modulation, the dispersion of CFBGs, and the saturated gain with a finite bandwidth. Thus the extended nonlinear Schrödinger equation is used to describe the pulse propagation in the laser oscillator<xref ref-type="bibr" rid="b42">42</xref>, <disp-formula id="m1"><inline-graphic id="d33e474" xlink:href="srep02718-m1.jpg"></inline-graphic></disp-formula>Here <italic>A</italic>, <italic>β</italic><sub>2</sub>, and <italic>γ</italic> denote the electric filed envelop of the pulse, the fiber dispersion, and the cubic refractive nonlinearity of the fiber, respectively. The variables <italic>t</italic> and <italic>z</italic> represent the time and the propagation distance, respectively. <italic>Ω<sub>g</sub></italic> is the bandwidth of the gain spectrum. <italic>g</italic> describes the gain function for the EDF and is expressed by<xref ref-type="bibr" rid="b43">43</xref><disp-formula id="m2"><inline-graphic id="d33e505" xlink:href="srep02718-m2.jpg"></inline-graphic></disp-formula>where <italic>g</italic><sub>0</sub>, <italic>E<sub>p</sub></italic>, and <italic>E<sub>s</sub></italic> are the small-signal gain coefficient related to the doping concentration, the pulse energy, and gain saturation energy that relies on pump power, respectively. The normalized absorption is fitted according to a simple two-level saturable absorber model<xref ref-type="bibr" rid="b35">35</xref><xref ref-type="bibr" rid="b36">36</xref><disp-formula id="m3"><inline-graphic id="d33e526" xlink:href="srep02718-m3.jpg"></inline-graphic></disp-formula>Here <italic>α</italic>(<italic>I</italic>) is the intensity-dependent absorption coefficient, and <italic>α</italic><sub>0</sub>, <italic>α</italic><sub>ns</sub> and <italic>I</italic><sub>sat</sub> are the linear limit of saturable absorption, nonsaturable absorption, and saturation intensity, respectively.</p><p><xref ref-type="disp-formula" rid="m1">Eq. (1)</xref> is solved with a predictor–corrector split-step Fourier method<xref ref-type="bibr" rid="b44">44</xref>. To numerically simulate the feature and behavior of this laser system, the simulation has started from an arbitrary signal and converged into a stable solution after approximately 200 round trips. In the simulation, we use the following parameters to match the experimental conditions: <italic>g</italic><sub>0</sub> = 6 dB/m, Ω<sub>g</sub> = 25 nm, <italic>E<sub>s</sub></italic> = 55 pJ, <italic>γ</italic> = 4.5 W<sup>−1</sup>km<sup>−1</sup> for EDF, <italic>γ</italic> = 1.3 W<sup>−1</sup>km<sup>−1</sup> for SMF. The parameters for SWNT saturable absorber are set with the values measured (<xref ref-type="fig" rid="f1">Fig. 1 (c)</xref>), i.e. <italic>α</italic><sub>0</sub> = 12.05%, <italic>α</italic><sub>ns</sub> = 87.87%, and <italic>I</italic><sub>sat</sub> = 9.67 MW/cm<sup>2</sup>.</p></sec></sec><sec disp-level="1"><title>Author Contributions</title><p>X.L. proposed the laser system, completed the numerical simulation, and wrote the main manuscript text. D.H. performed the main experimental results and discussed the numerical simulation. Z.S. discussed the design of the system and considerably improved the manuscript presentation. C.Z. performed the sample preparation of carbon nanotubes. H.L. carried out the data analysis and performed the video. D.M. and Y.C. provided technical support and prepared part figures. F.W. contributed to the scientific discussion and discussed the nanotube sample. All authors discussed the results and substantially contributed to the manuscript.</p></sec><sec sec-type="supplementary-material" id="s1"><title>Supplementary Material</title><supplementary-material id="d33e28" content-type="local-data"><caption><title>Supplementary Information</title><p>A supplemental material of Fig. 5</p></caption><media xlink:href="srep02718-s1.mov"></media></supplementary-material></sec></body><back><ack><p>This work was supported by the National Natural Science Foundation of China under Grants 10874239, 61223007, and 11204368.</p></ack><ref-list><ref id="b1"><mixed-citation publication-type="journal"><name><surname>Liu</surname><given-names>X. 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Lett.</source><volume>15</volume>, <fpage>1549</fpage>–<lpage>1551</lpage> (<year>2003</year>).</mixed-citation></ref></ref-list></back><floats-group><fig id="f1"><label>Figure 1</label><caption><p>(a) Laser setup. Inset: the assembly of SWNT saturable absorber. EDF, erbium-doped fiber; WDM, wavelength-division multiplexer; PC, polarization controller; LD, laser diode; CIR, circulator; CFBG, chirped fiber Bragg grating; SWNT, single wall carbon nanotube. (b) Reflection spectra of three CFBG<sub>1–3</sub>. (c) Nonlinear absorption characterization of the SWNT saturable absorber. The solid curve is fitted from the experimental data (circle symbols). (d) Absorption spectrum of the SWNT–polycarbonate composite and pure polycarbonate. The red stripe illustrates the spectral gain region of the Er<sup>3+</sup>-doped fiber.</p></caption><graphic xlink:href="srep02718-f1"></graphic></fig><fig id="f2"><label>Figure 2</label><caption><p>Optical spectra of the experimental observations for three lasers (a) <italic>λ</italic><sub>1</sub>, (c) <italic>λ</italic><sub>2</sub>, and (e) <italic>λ</italic><sub>3</sub>. Autocorrelation traces of the experimental data (circle symbols) and sech<xref ref-type="bibr" rid="b2">2</xref>–shaped fit (solid curves) for (b) <italic>λ</italic><sub>1</sub>, (d) <italic>λ</italic><sub>2</sub>, and (f) <italic>λ</italic><sub>3</sub>.</p></caption><graphic xlink:href="srep02718-f2"></graphic></fig><fig id="f3"><label>Figure 3</label><caption><p>Typically experimental results: the fundamental RF spectra with the resolution of 1 Hz and the span of 100 Hz for three lasers (a) <italic>λ</italic><sub>2</sub> and (b) <italic>λ</italic><sub>1</sub> and <italic>λ</italic><sub>3</sub>. The fundamental repetition rates of <italic>λ</italic><sub>1–3</sub> are 6.86678, 6.17917, and 5.60533 MHz, respectively. (c) Wideband RF spectrum up to 1 GHz and (d) oscilloscope traces up to 2 μs for the laser <italic>λ</italic><sub>2</sub>.</p></caption><graphic xlink:href="srep02718-f3"></graphic></fig><fig id="f4"><label>Figure 4</label><caption><title>Optical spectra and pulse profiles of the numerical simulations for three lasers (a) and (b) <italic>λ</italic><sub>1</sub>, (c) and (d) <italic>λ</italic><sub>2</sub>, (e) and (f) <italic>λ</italic><sub>3</sub>.</title></caption><graphic xlink:href="srep02718-f4"></graphic></fig><fig id="f5"><label>Figure 5</label><caption><title>Pulse evolution of laser <italic>λ</italic><sub>2</sub> along the intra- and extra-cavity position.</title><p>The <xref ref-type="supplementary-material" rid="s1">supplemental material</xref> demonstrates the evolution of pulse profile along the oscillator in detail.</p></caption><graphic xlink:href="srep02718-f5"></graphic></fig><fig id="f6"><label>Figure 6</label><caption><title>Output spectra at ten different wavelengths by stretching CFBG<sub>3</sub> in the cavity.</title></caption><graphic xlink:href="srep02718-f6"></graphic></fig></floats-group></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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