We experimentally demonstrate the use of a bulk-structured Bi2Te3 topological insulator (TI) as an ultrafast mode-locker to generate femtosecond pulses from an all-fiberized cavity. Using a saturable absorber based on a mechanically exfoliated layer about 15 μm thick deposited onto a side-polished fiber, we show that stable soliton pulses with a temporal width of ~600 fs can readily be produced at 1547 nm from an erbium fiber ring cavity. Unlike previous TI-based mode-locked laser demonstrations, in which high-quality nanosheet-based TIs were used for saturable absorption, we chose to use a bulk-structured Bi2Te3 layer because it is easy to fabricate. We found that the bulk-structured Bi2Te3 layer can readily provide sufficient nonlinear saturable absorption for femtosecond mode-locking even if its modulation depth of ~15.7% is much lower than previously demonstrated nanosheet-structured TI-based saturable absorbers. This experimental demonstration indicates that high-crystalline-quality atomic-layered films of TI, which demand complicated and expensive material processing facilities, are not essential for ultrafast laser mode-locking applications.
© 2014 Optical Society of America
In the past decade, one of the main subjects in condensed-matter physics has been topological insulators (TIs), which possess extraordinary charge and spin properties on their edges and surfaces . TIs feature gapless metallic states on the surface due to the combination of strong spin-orbit coupling and time-reversal symmetry, even if they exhibit insulating energy gaps in the bulk of the material. Following the theoretical prediction by Bernevig et al.  a 2-dimensional (2D) topological insulator exhibiting the quantum spin Hall effect without an external magnetic field was experimentally realized in HgTe quantum well structures by König et al. in 2007 . A bulk crystal of Bi1-xSbx was then identified as the first 3-D topological insulator in an angle-resolved photoemission spectroscopy experiment by Hsieh et al. . Subsequently, the second generation TI materials such as Bi2Se3, Bi2Te3, and Sb3Te3 were confirmed to have the topological band structures [5–7].
Since TIs possess unique electronic properties, they are considered as a promising material platform for spintronic and quantum computing devices. Therefore, a number of investigations have been conducted for a better understanding of their electromagnetic properties [8–11]. However, the potential of their unique optical properties has attracted less technical attention until recently. In 2012, Bernard et al. opened the way to use a new Dirac material for photonic applications as a nonlinear saturable absorber . Soon after the work by Bernard et al., quite a few experimental investigations on the use of TI-based saturable absorbers for mode-locking or Q-switching were carried out [13–19]. The combination of the small bandgap bulk (0.2 to 0.3 eV) and the gapless surface enables TIs to possess an ultra-broad bandwidth of saturable absorption operation . For example, a recent report by Yu et al. mentioned that the Bi2Se3 TI could provide saturable absorption for input light wavelengths up to 4.1 μm .
Until now, commonly used saturable absorbers have been fabricated with semiconductor materials [20, 21]. In the past decade, carbon-based nanomaterials such as carbon nanotubes, graphene, and graphene oxide have been intensively investigated as alternative saturable absorption materials since they possess several noticeable advantages over semiconductor-based counterparts (for example, wide operating bandwidth, ease of fabrication, and low cost) [22–27]. Even if TIs have been proven to have capabilities comparable to the aforementioned counterparts as a new saturable absorption material, they still need to be further investigated for a better understanding of the pros and cons with regard to practical applications.
In this paper, to verify the ultimate potential of TIs for ultrafast photonics, we experimentally demonstrate an all-fiberized mode-locked laser based on a bulk-structured Bi2Te3 TI that can readily produce femtosecond pulses. It should be noted that recent works on the use of TIs for laser mode-locking demonstrated limited output pulse-width performance of 1.2 ps, 1.57 ps, 666 ns, and 1.8 ps, even if high modulation depths of no less than 30% were readily achieved [13, 14, 16, 19]. The limited temporal performance could be attributed to unoptimized cavity dispersion. As a matter of fact, such a large modulation depth is not essential to achieving a stable ultrafast mode-locking condition in a laser cavity, because a large modulation depth could result in passive Q-switching, rather than mode-locking, due to reduced stability of gain saturation [28, 29]. Our fiberized saturable absorber in this experimental demonstration was prepared by depositing mechanically exfoliated TI particles onto a side-polished optical fiber. Incorporating a Bi2Te3 TI-deposited side-polished optical fiber into an all-fiberized, erbium-doped fiber-based cavity showed that high-quality ultrashort pulses with a temporal width of ~600 fs can readily be generated through evanescent field interaction between an oscillating beam and the Bi2Te3 TI layer. Unlike the aforementioned TI-based mode-locked laser demonstrations, we used a bulk-structured, thick TI layer rather than an ultrathin nanosheet-based layer due to ease of fabrication, and we demonstrated that a bulk-structured, micrometer-thick Bi2Te3 TI film can readily act as an efficient mode-locker when it is placed on side-polished optical fiber.
2. Preparation of Bi2Te3 TI-based saturable absorber
In order to prepare the Bi2Te3 TI film, we used the mechanical exfoliation method, which is a well-known technique for obtaining layered graphene from graphite flakes . In fact, this method was already applied to prepare Bi2Te3 atomic layers from crystalline bulk Bi2Te3 . The starting material was commercially available Bi2Te3 bulk single crystal (Alfa Aesar). Bi2Te3 particles were repeatedly peeled from the surface of the bulk crystal by using scotch tape to form a film. Note that no special care was taken to obtain nanometer-thick atomic layers during the exfoliation process, because we aimed to obtain bulk-structured film with a thickness in micrometers. The prepared Bi2Te3 film, which was attached to a small segment of scotch tape, was then transferred together with the scotch tape and placed onto the flat side of the side-polished fiber, as shown in Fig. 1(a). When the Bi2Te3 film was applied to the side-polished fiber, a small amount of index match oil was spread on the flat surface to ensure proper light coupling with the Bi2Te3 film from the fiber core. The use of index match oil with a proper index is essential to preparing an efficient saturable absorber based on a side-polished fiber platform, since the degree of evanescent field interaction is influenced by it. In our side-polished fiber-based saturable absorber, the index match oil acted as a buffer layer between the fiber core and the deposited Bi2Te3 layer to induce large evanescent filed interaction. It was observed that the evanescent field interaction with the deposited Bi2Te3 layer became larger when the refractive index of the index match oil was closer to that of the fiber core. Without index match oil used, we could not obtain the mode-locked output pulses due to large scattering loss on the polished fiber surface as well as substantially reduced evanescent field interaction.
For the preparation of the side-polished fiber, one side of SMF28 was polished while the fiber was fixed onto a V-grooved quartz block. The distance between the flat side and the fiber core was measured at ~11 μm, as shown in the inset of Fig. 1(a). The minimum insertion loss and polarization-dependent loss of the Bi2Te3 TI-based saturable absorber were ~1.7 dB and 1.36 dB, respectively, at 1.55 μm.
Before transferring the Bi2Te3 film onto side-polished fiber, we characterized the film using a scanning electron microscope (SEM), Raman spectroscopy, and X-ray diffraction (XRD) while some portion of the film was placed onto a quartz substrate. The inset of Fig. 1(a) shows the SEM image of the prepared Bi2Te3 film. Distinctive layered structures were not identified from the figure, which indicates that the prepared film was bulk-structured. The thickness of the prepared film was measured at ~15 μm by using an alpha-step profiler (Surface Profiler P-10, KLA-Tencor) as shown in Fig. 1(b). It is well known that the evanescent field interaction with a deposited film is not influenced by the film thickness in the case of , where and are the refractive index and the thickness of the deposited film, respectively, and is the wavelength of light . In our case, is much larger than the light wavelength of 1.55 μm because is ~15 μm. Therefore, it is obvious that the saturable absorption performance of our prepared bulk-structured Bi2Te3 TI-deposited side-polished fiber is not influenced by the film thickness.
The measured Raman spectrum of the Bi2Te3 film is shown in Fig. 1(c). We observed four Raman optical phonon peaks, which are typical in bulk crystalline Bi2Te3, and they were identified as Eg1 at 40 cm−1, A1g1 at 62 cm−1, Eg2 at 101 cm−1, and A1g2 at 137 cm−1. The A1u2 peak, which is known to be generated by the broken symmetry in atomically thin films, was not observed . This confirms that our prepared micrometer-thick Bi2Te3 layer is in a bulk crystalline state.
The measured XRD pattern is shown in Fig. 2(a). The positions of the four diffraction peaks were observed to be consistent with those of single crystal Bi2Te3 . The multiple peaks, which are generally seen in the nanostructures, were not observed . This XRD measurement result also confirms that our prepared sample is in a bulk crystalline state.
Next, we characterized the prepared saturable absorption device of the Bi2Te3-deposited side-polished fiber in terms of nonlinear saturable absorption. We measured its absorption as a function of the input optical pulse peak power using a 1 ps mode-locked fiber pulse laser operating at 1.55 μm with a repetition rate of 14.15 MHz, as shown in Fig. 2(b). We used the following formula  to obtain the fitting curve shown in Fig. 2(b).
The saturation power was found to be ~44 W. The estimated modulation depth was ~15.7%, which is much lower than the values reported for other TI-based saturable absorbers [13–16]. It is well-known that the following condition needs to be satisfied to obtain stable, continuous-wave mode-locking without Q-switching instabilities .
where is the intracavity pulse energy and is the modulation depth of the saturable absorber. and represent the effective saturation energy of the gain medium and saturable absorber, respectively. It is obvious from Eq. (2) that the simple increase of without controlling and could result in an undesired passive Q-switching phenomenon from the cavity. Therefore, we believed that a modulation depth of ~15.7% would be high enough for stable femtosecond pulse mode-locking, and we then conducted a laser experiment with the prepared saturable absorber to verify our belief. It should be noted that a saturable absorber with a modulation depth of only ~2.6% can readily produce femtosecond pulses from a dispersion-optimized cavity, according to a recent report by Xu et al. .
It should be noticed that the ~15.7% modulation depth is about twice higher than the value of our recently reported, graphene oxide-based saturable absorber that had a similar side-polished fiber platform . We obtained ~780 fs mode-locked pulses at ~1558 nm using the graphene oxide-based saturable absorber in Ref . It is technically interesting to see that the bulk-structured Bi2Te3 TI-deposited side-polished fiber exhibited a saturation power (~44 W) about ten times larger than the graphene oxide-deposited one (~4.56 W). One reason for such a high saturation power in the bulk-structured Bi2Te3 TI-deposited side-polished fiber can be attributed to substantially reduced evanescent field interaction caused by larger distance between the polished flat side and the core. The other reason is believed to be associated with the bulk crystalline structure; however, a further study needs to be conducted to clarify this. The bulk-structured Bi2Te3 TI-deposited side-polished fiber had twice larger thickness (~11 μm) of residual cladding than the graphene oxide-deposited one (~5 μm). Note that we could not increase the thickness of residual cladding in the case of the graphene oxide-deposited side-polished fiber since nonlinear satuable absorption was observed to significantly weaken at the thickness larger than ~5 μm. In general, larger thickness of residual cladding means less evanescent field interaction, but induces less beam propagation loss. Due to larger thickness of residual cladding the minimum insertion loss (~1.7 dB) of the Bi2Te3 TI-deposited side-polished fiber was found to be much less than that (~4.2 dB) of the graphene oxide-deposited one. Larger thickness of residual cladding is also beneficial in terms of ease of side-polishing of an optical fiber.
3. Laser configuration and characterization
Figure 3(a) shows our constructed laser schematic. The optical fiber-based ring cavity consisted of a 2.3 m long erbium-doped fiber (LIEKKITM Er20-4/125, nLIGHT Corporation) with a peak absorption of 20 dB/m at a pump wavelength of 1530 nm, an isolator, a 90:10 coupler, a polarization controller, a 980/1550 nm pump wavelength division multiplexing (WDM) coupler, and a Bi2Te3-deposited side-polished fiber. A 980 nm semiconductor laser diode with ~150 mW of power was used as a pump source. A 10% output port from the 90:10 fiber coupler was used to extract the laser output beam. All of the components within the cavity were fusion-spliced; the total length of the ring cavity was ~13.69 m. The net cavity dispersion was measured at −0.187 ps2 at 1550 nm. The insertion losses of the coupler, isolator, and WDM were measured at ~0.4, ~0.7, and ~0.7 dB, respectively, at 1.55 μm. With the laser setup ready, we tried to obtain mode-locked output pulses from the cavity by increasing pump power while the polarization controller within the cavity was properly adjusted. Stable mode-locked pulses could be achieved at pump power of 55 mW, and average power of the laser output measured about 0.8 mW. The measured oscilloscope trace of the output pulses is shown in Fig. 3(b). The output pulse period was measured at ~66.18 ns, which is equal to the round-trip time of the 13.69 m cavity. The pulse repetition rate was 15.11 MHz, which was coincident with the fundamental cavity resonance frequency.
The measured optical spectrum of the output pulses is shown in Fig. 4(a) together with its sech2() fitting curve. The center wavelength and 3 dB bandwidth were measured at ~1547 nm and ~4.63 nm, respectively. Assuming that the pulses were in a transform-limited soliton form, the output pulse width was expected to be ~543 fs. Kelly sidebands were clearly observed on the spectrum . We then tried to figure out whether or not the output mode-locked pulses are transform-limited through the use of Kelly sideband spectral positions relative to the center wavelength of the pulses by using the following well-known relation between the mth order of the Kelly sideband position and the center wavelength (Δλ) for chirped free soliton pulses .Fig. 4(b). It can be inferred from the curve that our laser output pulses were slightly chirped since the measured Δλ of ~9.71 nm is a little different from the theoretical value ~9.57 nm .
We then conducted an autocorrelation measurement using a two-photon absorption-based autocorrelator (FR103-PD, Femtochrome), and Fig. 5(a) shows the measured curve together with secant hyperbolic-fitting curves. The pulse width was measured at ~600 fs. The estimated time-bandwidth product was 0.348, which is slightly higher than the 0.315 of transform-limited sech2() pulses, indicating that the output pulses were slightly chirped, as predicted from the Kelly sideband position calculation. Finally, electrical spectrum measurement of the output pulses was conducted, as shown in Fig. 5(b). A strong signal peak with a fundamental repetition rate of 15.11 MHz was clearly observed, and the peak-to-background ratio was measured at ~65 dB.
We have demonstrated that a bulk-structured Bi2Te3 TI-based saturable absorber can readily be used to produce stable femtosecond pulses from a dispersion-controlled, all-fiberized cavity. Using a side-polished fiber deposited with a bulk-structured, Bi2Te3 TI layer ~15 μm-thick, stable optical pulses with a temporal width of ~600 fs were shown to be obtainable from an erbium-doped fiber-based ring cavity.
Through this experimental demonstration, we also showed that high-crystalline-quality atomic-layered films of TI, which demand complicated and expensive material processing facilities, are not essential for ultrafast laser mode-locking applications. We believe that the nonlinear saturable absorption effect occurs mainly due to the narrow bandgap of the bulk, rather than the surface, in our bulk-structured Bi2Te3 TI layer (unlike nanosheet-based TIs, in which both the bulk and surface states contribute to nonlinear saturable absorption). However, further detailed investigations would be needed to figure out whether or not any performance difference exists between bulk- and nanosheet-structured TIs when they are used as a saturable absorption material for mode-locked laser applications.
This work was supported by the National Research Foundation (NRF) of Korea grant funded by the Ministry of Education, Republic of Korea (No. 2012R1A1B3000587). This work was also supported by the Industrial Strategic Technology Development Program (10039226, Development of actinic EUV mask inspection tool and multiple electron beam wafer inspection technology) funded by the Ministry of Trade, Industry & Energy, Republic of Korea.
References and links
1. M. Z. Hasan and C. L. Kane, “Colloquium: topological insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010). [CrossRef]
3. M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, “Quantum spin Hall insulator state in HgTe quantum wells,” Science 318(5851), 766–770 (2007). [CrossRef] [PubMed]
5. Y. S. Hor, A. Richardella, P. Roushan, Y. Xia, J. G. Checkelsky, A. Yazdani, M. Z. Hasan, N. P. Qng, and R. J. Cava, “p-type Bi2Se3 for topological insulator and low-temperature thermoelectric applications,” Phys. Rev. B 79(19), 195208 (2009). [CrossRef]
6. Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009). [CrossRef] [PubMed]
7. H.-J. Noh, H. Koh, S.-J. Oh, J.-H. Park, H.-D. Kim, J. D. Rameau, T. Valla, T. E. Kidd, P. D. Johnson, Y. Hu, and Q. Li, “Spin-orbit interaction effect in the electronic structure of Bi2Te3 observed by angle-resolve photoemission spectroscopy,” Europhys. Lett. 81(5), 57006 (2008). [CrossRef]
8. Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5(6), 398–402 (2009). [CrossRef]
9. X.-L. Qi and S.-C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83(4), 1057–1110 (2011). [CrossRef]
10. X.-L. Qi, T. L. Hughes, and S.-C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78(19), 195424 (2008). [CrossRef]
11. Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009). [CrossRef] [PubMed]
12. F. Bernard, H. Zhang, S. P. Gorza, and P. Emplit, “Towards mode-locked fiber laser using topological insulators,” in Nonlinear Photonics, OSA Technical Digest (online) (Optical Society of America, 2012), paper NTh1A.5.
13. C. Zhao, H. Zhang, X. Qi, Y. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett. 101(21), 211106 (2012). [CrossRef]
14. C. Zhao, Y. Zou, Y. Chen, Z. Wang, S. Lu, H. Zhang, S. Wen, and D. Tang, “Wavelength-tunable picosecond soliton fiber laser with topological insulator: Bi2Se3 as a mode locker,” Opt. Express 20(25), 27888–27895 (2012). [CrossRef] [PubMed]
15. Y. Chen, C. Zhao, H. Huang, S. Chen, P. Tang, Z. Wang, S. Lu, H. Zhang, S. Wen, and D. Tang, “Self-assembled topological insulator: Bi2Se3 membrane as a passive Q-switcher in an erbium-doped fiber laser,” J. Lightwave Technol. 31(17), 2857–2863 (2013). [CrossRef]
16. H. Yu, H. Zhang, Y. Wang, C. Zhao, B. Wang, S. Wen, H. Zhang, and J. Wang, “Topological insulator as an optical modulator for pulsed solid-state lasers,” Laser Photon. Rev. 7(6), L77–L83 (2013). [CrossRef]
17. P. Tang, X. Zhang, C. Zhao, Y. Wang, H. Zhang, D. Shen, S. Wen, D. Tang, and D. Fan, “Topological insulator: Bi2Te3 saturable absorber for the passive Q-switching operation of an in-band pumped 1645-nm Er:YAG Ceramic laser,” IEEE Photon. J. 5(2), 1500707 (2013). [CrossRef]
18. Z. Luo, Y. Huang, J. Weng, H. Cheng, Z. Lin, B. Xu, Z. Cai, and H. Xu, “1.06μm Q-switched ytterbium-doped fiber laser using few-layer topological insulator Bi2Se3 as a saturable absorber,” Opt. Express 21(24), 29516–29522 (2013). [CrossRef] [PubMed]
19. J. Sotor, G. Sobon, W. Macherzynski, P. Paletko, K. Grodecki, and K. M. Abramski, “Mode-locking in Er-doped fiber laser based on mechanically exfoliated Sb2Te3 saturable absorber,” Opt. Mater. Express 4(1), 1–6 (2014). [CrossRef]
20. U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996). [CrossRef]
21. O. G. Okhotnikov, L. Gomes, N. Xiang, T. Jouhti, and A. B. Grudinin, “Mode-locked ytterbium fiber laser tunable in the 980-1070-nm spectral range,” Opt. Lett. 28(17), 1522–1524 (2003). [CrossRef] [PubMed]
22. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yang, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009). [CrossRef]
23. S. Yamashita, “A tutorial on nonlinear photonic applications of carbon nanotube and graphene,” J. Lightwave Technol. 30(4), 427–447 (2012). [CrossRef]
24. G. Sobon, J. Sotor, J. Jagiello, R. Kozinski, M. Zdrojek, M. Holdynski, P. Paletko, J. Boguslawski, L. Lipinska, and K. M. Abramski, “Graphene oxide vs. reduced graphene oxide as saturable absorbers for Er-doped passively mode-locked fiber laser,” Opt. Express 20(17), 19463–19473 (2012). [CrossRef] [PubMed]
25. Z. Sun, T. Hasan, and A. C. Ferrari, “Ultrafast lasers mode-locked by nanotubes and graphene,” Physica E 44(6), 1082–1091 (2012). [CrossRef]
27. M. Jung, J. Koo, J. Park, Y.-W. Song, Y. M. Jhon, K. Lee, S. Lee, and J. H. Lee, “Mode-locked pulse generation from an all-fiberized, Tm-Ho-codoped fiber laser incorporating a graphene oxide-deposited side-polished fiber,” Opt. Express 21(17), 20062–20072 (2013). [CrossRef] [PubMed]
28. P. Cerný, G. Valentine, D. Burns, and K. McEwan, “Passive stabilization of a passively mode-locked laser by nonlinear absorption in indium phosphide,” Opt. Lett. 29(12), 1387–1389 (2004). [CrossRef] [PubMed]
29. F. Dausinger, F. Lichtner, and H. Lubatschowski, Femtosecond technology for technical and medical applications, (Springer, Heidelbert, 2004, Series: Topics in Applied Physics, vol. 96).
30. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004). [CrossRef] [PubMed]
31. D. Teweldebrhan, V. Goyal, and A. A. Balandin, “Exfoliation and characterization of bismuth telluride atomic quintuples and quasi-two-dimensional crystals,” Nano Lett. 10(4), 1209–1218 (2010). [CrossRef] [PubMed]
32. E. A. Vinogradov, “Cavity electrodynamics in polariton spectra of thin films,” Laser Phys. 6(2), 326–333 (1996).
33. L. Ren, X. Qi, Y. Liu, G. Hao, Z. Huang, X. Zou, L. Yang, J. Li, and J. Zhong, “Large-scale production of ultrathin topological insulator bismuth telluride nanosheets by a hydrothermal intercalation and exfoliation route,” J. Mater. Chem. 22(11), 4921–4926 (2012). [CrossRef]
34. F. Qu, F. Yang, J. Shen, Y. Ding, J. Chen, Z. Ji, G. Liu, J. Fan, X. Jing, C. Yang, and L. Lu, “Strong superconducting proximity effect in pb-bi2te3 hybrid structures,” Sci. Rep. 2, 339 (2012). [CrossRef] [PubMed]
35. W. Lu, Y. Ding, Y. Chen, Z. L. Wang, and J. Fang, “Bismuth telluride hexagonal nanoplatelets and their two-step epitaxial growth,” J. Am. Chem. Soc. 127(28), 10112–10116 (2005). [CrossRef] [PubMed]
36. J. Lee, J. Koo, P. Debnath, Y.-W. Song, and J. H. Lee, “A Q-switched, mode-locked fiber laser using a graphene oxide-based polarization sensitive saturable absorber,” Laser Phys. Lett. 10(3), 035103 (2013). [CrossRef]
37. S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28(8), 806–808 (1992). [CrossRef]
38. N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10(10), 1329–1333 (1992). [CrossRef]