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We experimentally studied the nonlinear response of topological insulator (TI): Bi2Te3 at both the optical and microwave band, and found that the absorbance of topological insulator decreases with the increase of the incident power and reaches at a constant value once the incident power exceeds a threshold. By the open-aperture Z-scan and balanced twin detector measurement techniques, the optical saturable absorption property of TI: Bi2Te3 from 800 nm to 1550 nm was experimentally demonstrated. Based on a power dependent microwave transmittance experimental setup, TI: Bi2Te3 was also identified to show a saturation intensity of ~12 μW/cm2 and a normalized modulation depth of ~70%. We argue that the optical (resp. microwave) saturable absorption in topological insulator is a natural consequence of the Pauli-blocking principle of the electrons filled in the bulk insulating state (resp. surface metallic state). Our experimental results illustrate the potential photonic applications of TI: Bi2Te3 at both the optical and microwave band.
© 2014 Optical Society of America
1. Introduction
Materials with Dirac electronic spectra (also well known as Dirac materials) had attracted much attention since the first demonstration of quantum electronic transport in graphene at 2004 [1]. Dirac quasi-particles possess novel physical properties, such as absence of back scattering and Klein tunneling [2]. TI is a new class of Dirac materials with a small band gap in its bulk state and a gapless metallic state in its edge/surface. The surface state in 3D TIs has a Dirac electronic spectrum like graphene, but the directions of spin and momentum are locked together [3–7].
Due to the unique electronic band structure in graphene, it possesses many unique optical properties. Under intensive illumination, optical absorbance of graphene decreases with the increase of light intensity and becomes saturated once the incident light exceeds a threshold power, the mechanism of which is contributed by the Pauli blocking principle [8, 9]. This property associated with its application in mode-locked lasers had been widely demonstrated at different optical frequencies [10–12] and even at the microwave band [13]. Very recently, TI was also found to show saturable absorption at telecommunication wavelength [14–17], 800 nm [18], 1064 nm [19], 1645 nm [20], respectively. Furthermore, TI: Bi2Te3 as a saturable absorber (SA) had been employed to generate pico-second pulses at the telecommunication band [21]. Given the similarities between graphene and TI, some interesting fundamental questions arise: whether TI shows similar nonlinear optical response as graphene? Whether TI has broadband saturable absorption? Whether there is a limit of the operation bandwidth for the saturable absorption property in TI, that is, whether its saturable absorption feature could be extended from the optical band to other band, like graphene? What is the difference in the saturable absorption mechanisms between TI and graphene? In this contribution, we tried to answer those fundamental questions, by performing nonlinear absorption experiments on TI: Bi2Te3 at both the microwave and optical band. And we observed that TI: Bi2Te3 also exhibits broadband saturable absorption at microwave band, for the first time. Our experimental results demonstrated that saturable absorption features can be observed at the microwave frequency from 96 GHz to 100 GHz. And the saturable absorption features were also revealed by a femto-second laser illumination at 800 nm and by a picosecond laser at telecommunication band. This may lead to some promising applications of TI based nonlinear microwave and photonics devices.
2. Experimental setup
2.1 Characterization of Bi2Te3 sample
Generally, nano-structured TI materials are more appropriate to probe the surfaces states because of their large surface-to-volume ratio [5].The MBE growth, vapor-liquid-solid growth and mechanical exfoliation were widely used for nanostructured TI materials preparation [22–24]. Here, we used lithium solution through a common hydrothermal process to intercalate and exfoliate bulk Bi2Te3 to synthesize the Bi2Te3 nano-platelets, which had been elaborated in the Ref [25]. As shown in Fig. 1, the as-prepared TI: Bi2Te3 nano-platelets were dispersed in isopropyl alcohol and ultrasonicated for 4 hours. Later, the dispersion solution was dropped cast onto a piece of square quartz glass with a thickness of 1 mm, which was afterwards spin-coated with 500 rps for 20 seconds. Then it was placed in drying oven for evaporation over 8 hours.
The Bi2Te3 nano-platelets were characterized by the Raman spectrum and Atomic force microscopy (AFM, SPM-9500J3). The Raman spectra of Bi2Te3 nano-platelets and bulk Bi2Te3 as reference is shown in Fig. 2(a).Three typical Raman active modes , , are observed in bulk Bi2Te3 and Bi2Te3 nano-platelets at 60.47 cm−1, 99.84 cm−1, and 137.03 cm−1, respectively. With the thinning of the exfoliated Bi2Te3 flakes, the peak intensity of these three modes becomes stronger in Bi2Te3 nano-platelets [25]. And an additional strongest peak is observed at 115.16 cm−1 which is likely related to the symmetry breaking in atomically thin films [25]. Moreover, the AFM topography images of Bi2Te3 nano-platelets are shown in Fig. 2(b). We observed that Bi2Te3 nano-platelets exhibit symmetric hexagonal morphology, indicating relatively higher stability. The XRD pattern shown in Fig. 2(c) also indicated that the Bi2Te3 nano-platelets have the rhombohedral phase with good crystalline. The as-prepared nano-platelets have an average thickness of 100 nm, as measured by the AFM topography images. Figure 2(d) shows the linear absorption spectra of Bi2Te3 nano-platelets. It clearly shows that the TI has a relatively flat transmission curve at the wavelength from 500 nm to 2600 nm, indicating that the TI may be a promising wideband optical material [21].
Fig. 2 (a) Raman spectra of Bi2Te3 nano-platelets and Bi2Te3 bulk, respectively. (b) AFM image of the Bi2Te3 nano-sheets. (c) X-ray diffraction pattern of Bi2Te3 nano-platelets. (d) The linear absorption spectra of Bi2Te3 nano-platelets.
2.2 Microwave experimental setup and results
We employed the optical frequency multiplication technique to generate microwave signal [26], with the experimental setup shown in Fig. 3.The continuous-wave (CW) at 1565.3 nm emitted from the external cavity laser (ECL) functions as an optical source, with the corresponding optical spectrum shown in Fig. 4(a). A Mach-Zehnder modulator was used to produce the second-order sidebands. The odd-order optical sidebands were sufficiently suppressed, and the extinction ratio of the second-order sideband could reach up to 40 dB as shown in Fig. 4(b), at a driven voltage of 0.338 V. And an inter-leaver was used to separate optical mm-wave and original carrier. The second-order sidebands have an intensity of 30 dB higher than the others (Fig. 4(c)). After being amplified through a commercial EDFA, the optical signal could still retain its original property and the wavelength separation between the two second-order sidebands is about 0.8 nm, corresponding to 100 GHz (Fig. 4(d)). The 0.1 THz optical mm-wave was generated by a 12.5 GHz clock source and an electrical frequency doubler. An optical attenuator was used to control the incident optical mm-wave power that is further detected by the PDs.
Fig. 3 Schematic of the microwave generation and saturable absorption measurement, ECL: external cavity laser, LN-MZM: LiNbO3 Mach-Zehnder modulator, IL: 50/100 GHz optical inter-leaver, EDFA: erbium-doped fiber amplifier, ATT: optical attenuator, PD: photodiode, EA: electrical amplifier.
By changing the RF clock source, the frequency of mm-wave could be tuned. Limited by the bandwidth of the narrow-band electrical amplifier, we could only change the RF frequency with a frequency interval of 0.1 GHz. The microwave frequency was therefore tuned from 96 GHz to 100 GHz through a frequency tunable RF clock source (from 12 GHz to 12.5 GHz). The microwave signal was further amplified by electrical amplifier and radiated from an antenna, and a 30 MHz chopper (TTI, c-995) was employed to modulate the microwave signal. After passing through the sample, the output power was detected by an absolute THz power meter (Thomas Keating Instruments THz Power Meter). The optical chopper has an aperture diameter of 15 mm while the distance between the antenna and power meter was still kept around 4 cm. Based on this approach, the microwave power could reach up to about 1 mW. By adjusting the attenuator, microwave power could be controlled from 20 μW to 500 μW. Similar to the optical absorbance model in Ref [8], the absorption data can be fitted according to
where T is the transmission, is the linear limit of saturable absorption or the modulation depth, I is the intensity and is the saturation intensity and is the non-saturable loss. By changing the frequency of RF clock, we obtained the transmittance from 96 GHz to 100 GHz, as shown in Fig. 5.It indicates that the modulation depth and saturation intensity are 60% ~75% and 10.47 μW/cm2 ~13.82 μW/cm2, respectively, as shown in Fig. 6(a) and Fig. 6(b).Fig. 5 Nonlinear saturable absorption features of TI: Bi2Te3 nano-platelets at different microwave frequencies.
2.3 Optical experimental setup and results
We used an optical experimental setup similar to that in Ref [18, 27] to investigate the saturable absorption property of the TI: Bi2Te3 sample at the optical band, as shown in Fig. 7.The laser source is a Coherent femto-second laser with a repetition rate of 1 kHz and a pulse width of 100 fs at 800 nm. After passing through an optical attenuator, the average output power can be controlled from 0 mW to 5 mW. The incident laser beam is then focused by an objective lens (f = 500 mm), generating a beam waist of 70 μm, and propagates perpendicularly towards the sample. A 50% beam splitter was used to pick off a portion of the input laser beam and measured by Detector 1 as a reference of the optical power.
The sample was placed perpendicularly to the beam axis at the focal plane. By appropriately tuning the attenuator, the incident optical power could be controlled at a moderate intensity in order to avoid the optical damages of the sample. Then all light transmitted through the sample was collected by Detector 2. We firstly performed the balanced twin-detector measurement technique to characterize the nonlinear optical response. Briefly, by rotating the optical attenuator, the input laser could be controlled at various intensity values. Therefore, the corresponding output intensity under different input intensity could be systematically recorded. By increasing (resp. decreasing) the input intensity from high (resp. low) to low (resp. high) intensity, similar nonlinear absorption curves could be corresponding obtained, indicating that the sample is free of optical damage. The transmittance as a function of the incident laser intensity at 800 nm was shown in Fig. 8. Fitting the data with above formula yields a saturable absorption intensity of 6.02 GW/cm2 and a modulation depth of 23.5%, respectively. In the following, we carried out the open-aperture Z-scan measurement. By continuously moving the translation stage, the relative distance between the sample and focus point could be correspondingly changed, resulting in the variation of the laser beam size as well as the laser intensity incident upon the sample. Upon simultaneously recording the detected optical power from the Detector 2 and Detector 1 with respect to different z positions, we could obtain the open aperture Z-scan curve, as shown in Fig. 9, with the incident intensity increased from 3.4 GW/cm2 to 28 GW/cm2. From Fig. 9, a sharp and narrow peak located at the beam focus clearly shows the characteristic of saturable absorption. Furthermore, a clear dependence of the Z-scan saturable absorption curve on the input laser intensity can be seen in Fig. 9, which also persuasively confirms the existence of saturable absorption in TI.
Fig. 8 Relation between normalized transmittance and input peak intensity, Case 1: measured by continuously increasing the input power and Case 2: by decreasing the input power.
The nonlinear optical response experiment at 1570 nm can be performed by using a similar balanced twin detector measurement technique in Fig. 7 [27, 28], whereas a pico-second fiber laser with center wavelength 1570 nm (pulse duration: 1.2 ps, and repetition rate: 22 MHz) was used as the laser source. After out-coupling from the fiber, the average power could reach 20 mW. The beam was focused using a 20 × microscope objective, generating a beam waist about 3 μm. The transmittance as a function of the incident laser fluence at 1570 nm was shown in Fig. 10.Fitting the curve, the saturable intensity and modulation depth are 0.13 GW/cm2 and 21% at 1570 nm.
3. Discussions
The excitation process that can explain for the absorption of light in the TI: Bi2Te3 is shown in Fig. 11.Any photon with energy larger than the insulating band-gap value (about 0.15 eV for Bi2Te3) can excite electrons in the valence band (at the bulk state) towards the corresponding conduction band (at the bulk state) [29]. It also means that under weak light intensity, by absorbing any photon with energy larger than 0.15 eV, electrons in the valence band (at the bulk state) can be excited to conduction band (at the bulk state), which accounts for the broadband linear absorption mechanism of Bi2Te3. However, under more intensive illumination by light with single photon energy larger than 0.15 eV, due to the Pauli blocking principle, the generated carriers filling the valence bands prevents further excitation of electrons at valance band, leading to the occurrence of optical bleaching effect, also well-known as saturable absorption. This process can interpret the origin of saturable absorption at the optical band (with photon energy larger than 0.15 eV).
More interestingly, in view that the TI also has gapless metallic surface state, electrons at the surface state could play a central role in the absorption of microwave photon that lies within the absorption band of the surface metallic state. Thus, the Dirac cone surface states of TI endows the absorption of microwave photons at an arbitrary frequency around 100 GHz. Whereas, limited by the amount of electrons filled in the conduction band of the surface state, the total microwave absorbance can also exhibit the saturation effect if under strong microwave excitation, similar to the principle of the optical photon with larger energy than the bulk band-gap value. Consequently, we argue that determined by the unique electronic property in the TI, there are two different types of saturable absorption mechanisms that could account for the experimentally observed optical and microwave saturable absorption feature, respectively. That is, the optical saturable absorption originates from the bulk insulating state while the surface metallic state is responsible for the saturable absorption at microwave band. However, high quality TI samples with fewer defects are required to more persuasively distinguish the contributions from the bulk state and surface state, which will be our future work.
4. Conclusions
As a summary, the nonlinear optical and microwave absorption property in TI: Bi2Te3 were experimentally reported. The unique electronic band property in TI, that is insulating bulk state and metallic surface state, allows for the occurrence of the saturable absorption at both the optical and microwave band, respectively. Our experimental results verify that TI is not only a broadband nonlinear optical material but may also be a new microwave optical material. Enlightened by this contribution, we anticipate that researchers from the optical and microwave community may like to explore the potential applications of TI, paving the way towards the exploration of some special and novel topological insulator based microwave and optical devices.
Acknowledgments
This work is partially supported by the National 973 Program of China (Grant No. 2012CB315701), the National 863 Program of China (Grant No. 2011AA010203), the National Natural Science Fund Foundation of China (Grant Nos. 61205125 and 61025024), and Project supported by Hunan Provincial Natural Science Foundation of China (Grant No. 12JJ7005), the National Natural Science Foundation of China for the Youth (Grant No. 61205091). H. Z. Offers thanks to the MOE grant (Grant No. NCET 11-0135), National Natural Science Fund (Grant No. 61222505), and Project supported by Hunan Provincial Natural Science Foundation of China (Grant No.13JJ1012).
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