Broadband Pulsed Fiber Laser Generation with Topological Insulator： Towards the Mid-Infrared Regime

Guobao Jiang, Lili Miao, Yu Chen, Shunbin Lu, Shuqing Chen,Chujun Zhao, Han Zhang, and Shuangchun Wen

1. Introduction

Topological insulators (TIs) are a new state of quantum matters with spin-orbit coupling and time-reversal symmetry[1]. The electronic band structure in the bulk of these matters behaves like the electrons in ordinary band insulators, with the Fermi level falling between the conduction and valence bands. However, the surface state electrons of TIs can flow as easily as in metal. Moreover,the spin and momentum of the carriers will be locked at a right angle. At a given energy, the only other available electronic states have different spin, so the scattering is strongly suppressed and conduction on the surface is highly metallic[1]. The “protected” conducting states in the surface are required by the time-reversal symmetry and the band structure of the material, which cannot be removed by surface passivation unless the time-reversal symmetry is broken. As representative TIs, Bi2Se3, Bi2Te3, and Sb2Te3have robust and simple surface states consisting of a single Dirac cone, they are stoichiometric rhombohedral crystals with the layered structure consisting of stacked quintuple layers (QLs) with relatively weak van der Waals coupling between the QLs. The surface states of such a thin film have been predicted and observed to open a gap when they are thinner than 6 QLs as shown in Fig. 1. On the other hand, the single Dirac cone on the Bi2Se3surface can be imagined as 1/4 of graphene[3]. It is straightforward to study the optical properties and relevant applications of TIs in analogy to the optoelectronics applications of graphene due to these unique properties, and TIs can be widely applied in many areas, such as spintronics[3], high speed transistor with low power, topological quantum[5], surface catalytic,clean energy, and optical applications.

Fig. 1. Surface state and bulk state band structures of TIs.

Three-dimensional TIs, such as Bi2Se3, Bi2Te3, and Sb2Te3, stoichiometric rhombohedral crystals with stacked QLs, were theoretically predicted to have an energy gap in the bulk state and gapless surface state consisting of a single Dirac cone[6],[7]. Like graphene, linear Dirac spectrum dispersion from the Dirac point of TIs has been identified through angle-resolved photoemission spectroscopy (ARPES)[7],[8], indicating its broadband spectral response ranging from terahertz to infrared for optoelectronics applications.

2. Preparation and Integration Methods for TI devices

The unique properties of TIs are derived from the metal surface state and insulator bulk state. Compared with the three dimensional TI, two dimensional (2D) counterparts have very large surface-to-volume ratios that can significantly enhance the contribution of exotic surface states, and their unique quasi-2D geometry also facilitates their integration into functional devices for manipulation and manufacturing. The high quality TI nanomaterials can be prepared by top-down and bottom-up methods, such as molecular beam epitaxy (MBE) growth, vapor-liquid-solid growth, mechanical exfoliation of thin sheets from bulk crystals[9], and chemistry fabrications[10],[11]. With the nanoscale films, how to integrate these films with fiber devices is another challenge. Up to now, there are many methods to validate the effectiveness of integration listed in Fig. 2, such as optical deposition[9], drop-casted self-assembled fabrication[12], TI polymer composite films[13], evanescent wave deposition which includes D-shaped fiber deposition[14]-[16]and tapered fiber deposition[17], injecting solutions into photonic crystal fiber[18].

Fig. 2. Various TI saturable absorber (TI-SA) integration methods for fiber devices.

3. Linear and Nonlinear Optical Properties of TIs

The Dirac-like electronic band structure of TIs endows them the broadband optical response like graphene. By Zhang’s theoretical results[3], the low-energy optical absorbance of thin-film Bi2Se3thicker than 6 QLs is a universal quantity πα/2 (α is the fine-structure constant),which does not depend on the photon energy or chemical composition of the material. This result originates from Dirac nature of the 2D topological surface states. Moreover,the optical transitions from the valence to conduction surface bands depend solely on the spin states in contrast to the conventional semiconductors. When the thickness of such a thin film is less than 6 QLs, a gap is opened up for the surface states, and the resulting 2D insulator can either be topologically trivial or nontrivial, depending on the thickness of the film. Therefore, the optical absorbance near the band edge is either smaller or larger than πα, depending on it being a conventional insulator or a 2D quantum spin Hall (QSH) insulator. We have measured the linear absorption of Bi2Te3and Bi2Se3nanomaterials prepared by liquid phase exfoliation, and the experimental result shows that TIs have a weak wavelength dependence[19],[20].

Under strong illumination, TIs show broadband and strong nonlinear optical properties. F. Bernard et al. have studied the nonlinear optical property of TI: Bi2Te3and found that its absorbance could become transparent under strong illumination[21]. Lu et al. have measured the third order nonlinear optical property of Bi2Se3in detail[19]. By employing the polyol method, the Bi2Se3nanoplatelets were synthesized, dispersed in isopropyl alcohol, dropped cast onto a common quartz plate, and dried in a drying oven.The prepared sample of Bi2Se3has been investigated under a femto-second laser excitation at 800 nm wavelength. The open and close aperture Z-scan measurements were used to unambiguously distinguish the real and imaginary parts of the third order optical nonlinearity of the Bi2Se3, Fig. 3 shows that the Bi2Se3exhibits saturable absorption with a saturation intensity of 10.12 GW/cm2, a modulation depth of 61.2%, and a giant nonlinear refractive index of 10-14m2/W almost six orders of magnitude larger than that of bulk dielectrics.

Fig. 3. Z-scan traces for Bi2Se3 sample at an average power of 40 μW,corresponding to a peak power at focus of 10.4 GW/cm2: (a) near field(open aperture), (b) far field (closed aperture). Upon dividing by the near field curve one obtains the data of panel, and (c) typical shape of a Z-scan curve with positive nonlinear phase shift, having an on-axis value of ΔΦ=1.1 rad[19].

Fascinated by the similar electronic band structure as graphene, Chen et al. have studied the saturable absorption of Bi2Te3at different wavelengths: 800 nm, 1570 nm, and 100 GHz microwave. Liquid exfoliated Bi2Te3nano-platelets were dispersed in isopropyl alcohol and coated onto a piece of squartz glass, then dried in an oven[20]. A modulation depth and a saturation intensity of 75% and 13.82 μW/cm2at 100 GHz microwave, 23.5% and 6.02 GW/cm2at 800 nm wavelength, 21% and 0.13 GW/cm2at wavelength of 1570 nm were obtained,respectively. Lee et al. reported the saturable absorption of bulk-structured Bi2Te3at 1.55 μm with a ～1.5 ps pulse width and a repetition rate of 14.5 MHz, and a YDF laser at the 1064 nm wavelength was achieved[14]. The measured modulation depth was ～2.5% and the saturation power was～101 mW. Jung et al. have also measured the saturable absorption of TIs at 1935 nm wavelength[22]. The fiberized saturable absorber was prepared by depositing a mechanically exfoliated ～30 μm thick Bi2Te3layer on a side-polished optical fiber platform. The modulation depth of the prepared saturable absorber was measured to be～20.6% and the saturation power was ～29 W. This measurement was conducted with a ～1 ps mode-locked fiber pulsed laser at 1.95 μm. These findings suggest that the TIs are indeed a promising nonlinear optical material and thus can be find potential applications in fiber lasers.

4. TI-Based Broadband Pulsed Fiber Laser Generation

With the broadband nonlinear saturable absorption of TIs, as can be seen in Fig. 4, they can act as broadband nonlinear modulators to obtain Q-switched or mode-locked fiber lasers with different wavelengths ranging from near infrared to mid-infrared regime, as shown in Table 1.

Table 1: Representative performance of pulsed fiber lasers using a TI as the saturable absorber. These results show that TIs have remarkable optical properties and in turn verify the broadband saturable absorption of TIs.

Fig. 4. Schematic of absorption: (a) optical absorption and (b) microwave saturable absorption in the TI: Bi2Te3[19].

4.1 1.06 μm

Luo et al. realized passive Q-switching of an ytterbium-doped fiber laser with few-layer TI: Bi2Se3[23].The Q-switched pulses had the shortest pulse duration of 1.95 μs, the maximum pulse energy of 17.9 nJ, and a tunable pulse-repetition-rate from 8.3 kHz to 29.1 kHz. Lee et al. have reported an all-fiberized passively Q-switched ytterbium-doped fiber laser with a bulk-structured Bi2Te3deposited on a side-polished fiber[14]. The temporal width and repetition rate of the output pulses were tunable from 1 μs to 1.3 μs and from 77 kHz to 35 kHz, respectively. Yan et al. reported a mode-locking ytterbium-doped fiber laser with Bi2Te3nanosheets solution filled in a photonic crystal fiber[18]. The evanescent wave mode-locking operation was achieved and the output pulses were centered at 1064.47 nm with a pulse width of 960 ps and a SNR of 60 dB. Chi et al. demonstrated a 1.06 μm dissipative-soliton fiber laser incorporating a saturable absorber based on a bulk-structured Bi2Te3[15]. The bulk-structured Bi2Te3film-deposited side-polished fiber can provide the dual functions of nonlinear saturable absorption and spectral comb filtering, and ～230 ps dissipative-soliton pulses with a composite temporal shape were readily produced at a repetition rate of 1.44 MHz using the laser cavity configuration.

4.2 1.55 μm

In 2012, Zhao et al. reported an ultrashort pulse fiber laser with a TI: Bi2Te3as the SA[24]. A TI based saturable absorber device was fabricated and used as a passive mode locker for ultrafast pulse formation at the telecommunication band. In this work, a self-started mode locked fiber laser was realized as shown in Fig. 5 and ultrashort pulses centered at 1558 nm with a pulse width of 1.21 ps were achieved. By incorporating Bi2Se3nanosheets into an erbium-doped fiber laser, a wavelength tunable soliton operation was also demonstrated[25]. The excellent nonlinear characteristics of TIs attracted so much attention,and many groups began to investigate the nonlinear optic application of TIs.

Fig. 5. Typical TIs optical characterization and TI based mode-locking fiber laser setup: (a) near infrared linear absorption spectra of TIs (The insert shows the crystal structure of TIs), (b) typical Z-scan peak curve of TIs at 1550 nm (Insert: Z-scan experimental setup), (c) corresponding nonlinear saturable absorption curve, and (d) schematic of the fiber laser (PC: polarization controller. WDM: wavelength division multiplexer. EDF: erbium doped fiber. SMF:single mode fiber. LD: laser diodes. Insert: schematic of the surface-state linear band dispersion of the TI[24]).

To the best of my knowledge, the shortest pulse output from fiber lasers based on TIs was reported by Sotor et al.[26]. As a saturable absorber, a ～0.5 mm thick lump of Sb2Te3deposited on a side-polished fiber was used. The ring laser resonator based on an erbium-doped active fiber with managed intracavity dispersion was capable of generating ultrashort optical pulses with a full width at half maximum of 30 nm centered at 1565 nm. The pulses with the duration of 128 fs were repeated with a frequency of 22.32 MHz. With the TI as the SA, large energy and wavelength widely tunable Q-switched erbium-doped fiber laser was obtained by Chen et al.[9]. With optical deposited TI onto the fiber end, an all-fiber laser cavity was set up.Stable passively Q-switched pulses were achieved with single pulse energy up to 1.525 μJ and center wavelength tunable from 1510.9 nm to 1589.1 nm. These results verified that the TI-SA possesses advantages for high energy and broadband tunable laser applications.

4.3 2.0 μm

Mid-infrared lasers have been used in a range of application fields, such as plastic and glass processing, gas detection, long-range light detection and ranging, freespace optical communication, medical diagnostics, and laser surgery. For the unique electronic band, TIs become an ideal candidate for mid-infrared applications. Luo et al.exploited a Q-switched double-clad fiber laser based on Bi2Se3[27]. The optical deposition technique was used to efficiently assemble the Bi2Se3nanosheets in thermal solution onto a fiber ferrule to construct a fiber compatible SA. By inserting the SA into a diode pumped thulium-doped double-clad fiber laser, stable Q-switching operation at 1.98 μm was successfully achieved with the shortest pulse width of 4.18 μs and the tunable repetition rate from 8.4 kHz to 26.8 kHz. Another TI based passively Q-switched fiber laser at 1.89 μm was reported[29]. A bulk-structured Bi2Te3film with a thickness of ～31 μm was prepared using a mechanical exfoliation method, and the fabricated film was transferred onto a side-polished SM2000 fiber to form a fiberized SA based on evanescent field interaction. By incorporating the SA into a thuliumholmium co-doped fiber based ring cavity, it was shown that Q-switched pulses with a minimum temporal width of～1.71 μm could readily be produced at a wavelength of 1.89 μm. The output pulse repetition rate was tunable from 35 kHz to 60 kHz depending on the pump power. The maximum output pulse energy was ～11.54 nJ at a pump power of 250 mW. Up to now, the only mode locking fiber laser at 1935 nm was demonstrated by Jung et al.[27]. The fiberized SA was prepared by depositing a mechanically exfoliated ～30 μm-thick Bi2Te3TI layer on a side-polished optical fiber platform. Using the SA, it showed that stable ultrafast pulses with a temporal width of ～795 fs could readily be generated at a wavelength of 1935 nm from a thulium/holmium co-doped fiber ring cavity.

4.4 Longer Wavelength

The fine-structured constant defined high optical absorption of a TI and its unique selection rules was discussed. Recently, Yin et al. have used Bi2Te3nano-sheets to realize a mid-infrared mode-locked fluoride fiber laser[30].Continuous wave lasing, Q-switched, and continuous-wave mode-locking (CW-ML) operations of the laser were observed sequentially by increasing the pump power. The observed CW-ML pulse train had a pulse repetition rate of 10.4 MHz, a pulse width of ～6 ps, and a center wavelength of 2830 nm. The maximum achievable pulse energy was 8.6 nJ with an average power up to 90 mW. This work demonstrates the promising applications of 2D TIs for ultra-short laser operation and nonlinear optics in the mid-infrared region. Another work that should be noted was done by Li et al.[31]. They obtained a stable Bi2Te3Q-switched fiber laser operating around 3 μm pumped by 1150 nm diodes. The Q-switched pulses at 2979.9 nm were obtained with the repetition rate of 81.96 kHz and pulse duration of 1.37 μs. The achieved maximum output power and pulse energy were 327.4 mW at a slope efficiency of 11.6% and 3.99 μJ, respectively only limited by the available pump power. With its unique nonlinear absorption,the pulsed laser towards longer wavelength can be expected.

5. Outlook

The broadband response of TIs was testified by various experimental results. Undeniably, due to the unique properties of TIs, different preparation and integration methods were proposed. Future investigations will be focused on improving the quality of the fabrication and integration of TIs and TI based devices. The controllable preparation of TIs will pave the way for their widespread applications, and the high efficient, low loss, and controllable transferring technique should be developed.Laser performance can also be improved by innovative cavity design and device optimization. With fiberized TI devices, all fiberized fiber lasers can be realized. It is worth noting that the laser output power can be improved by external cavity methods, such as increasing the power by external amplification or coherent combination of various lasers. Another important role for TIs to play is their broad optical response, which can be explored in the applications beyond conventional optical band, such as mid-infrared,far-infrared, and even microwave.

Due to the high absorbance, TIs can also be used as a high-performance THz to infrared (0 eV to 0.3 eV) photodetector whose SNR is comparable with the commercially used bulk Hg1-xCdxTe[3]. They also may find a wide range of photonic applications including thermal detection,high-speed optical communications, interconnects, terahertz detection, imaging, remote sensing, surveillance, and spectroscopy.

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Guobao Jiang is current pursuing his Ph.D. degree with the School of Physics and Electronics, Hunan University, Changsha,China. His research interest is mainly focused on ultrafast fiber lasers.

Lili Miao is current pursuing his Ph.D. degree with the School of Physics and Electronics, Hunan University, Changsha, China.His research interests are mainly focused on nonlinear optics and applications in two dimensional nano materials.

Yu Chen is currently pursuing his Ph.D. degree with the School of Physics and Microelectronic Science, Hunan University,Changsha, China. He has authored and co-authored more than 20 papers in SCI-cited international journals. His research interests are focused on ultrafast fiber lasers and nonlinear optics.

Shunbin Lu received the B.S. degree in communication engineering and the Ph.D. degree in circuit and system from Hunan University, Changsha in 2009 and 2014, respectively. He is currently a post-doctor with Shenzhen University, Shenzhen,China. His current research focuses on nonlinear optics and applications in two dimensional nano materials.

Shuqing Chen is now working with Shenzhen University,Shenzhen, China. His research interests are focused on optical communication and nonlinear optical device.

Chujun Zhao received the B.S. and the M.S. degrees in physics from Hunan University, Changsha, China in 2002 and 2005, respectively, and the Ph.D. degree in optics from the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China in 2008. He is currently an associate professor with Hunan University. His current research interests include ultrafast pulse generation and its applications.

Han Zhang received the B.S. degree from Wuhan University,Wuhan, China in 2006, and the Ph.D. degree from Nanyang Technological University, Singapore in 2011. Since 2014, he has been a professor with Shenzhen University, Shenzhen, China. His current research interests include nonlinear fi ber optics and its applications.

Shuangchun Wen received the B.S. degree in physics from Hunan Normal University, Changsha, China in 1987, the M.S.degree in physics from Central China Normal University, Wuhan,China in 1994, and the Ph.D. degree in optics from the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China in 2001. Since 2002, he has been a professor with Hunan University, Changsha, China, where he is currently the Head of the Photonics Technology Research Group.He has authored and co-authored over 100 scientif i c publications in international journals and conferences. He is the holder and co-holder of over ten patents. His current research interests include photonic materials and devices, optical communications,solidstate/f i ber lasers, and nonlinear optics. He is a member of the Optical Society of America and the International Society for Optical Engineering.

All authors’ photographs are not available at the time of publication.