This paper describes the tri-phase all-optical switching and broadband nonlinear optical response in Bi2Se3 nanosheets. Using Bi2Se3 nanosheets dispersion solution as the sample, the spatial phase of controlled light can be modulated as three phases (unchanging, focusing, diffraction) by changing the incident intensity of controlling light. The mechanism is conjectured that the controlling light changes the phase distribution of overlapping region and then modulates the phase distribution of the controlled light. Based on Gerchberg-Saxton algorithm, the phase distribution of the controlling light and controlled light is retrieved from the transmitted patterns. In dynamic spatial self-phase modulation (SSPM) experiment, the three processes including self-focusing, self-diffraction ring formation, and self-diffraction ring deformation can also be observed. In addition, the SSPM of controlling light is measured at the typical wavelengths from 350 nm to 1160 nm, which demonstrates that this all-optical switching is available in broadband. These results provide the great potential of Bi2Se3 as an all-optical switching for various optoelectronic applications.
© 2017 Optical Society of America
Self-diffraction, a kind of spatial self-phase modulation (SSPM), has been regarded as an important method to measure the nonlinear optical properties of layered materials. For example, Li et al. observed the gravitation-dependent thermally-induced self-diffraction in carbon nanotubes . The effective third-order nonlinear susceptibility χ(3) for graphene nanosheets has been reported [2, 3]. The nonlinear optical characters of transition metal dichalcogenides (TMDs) [4–7] and black phosphorous [8–10] were also measured. Wu et al. discovered the two-color all-optical switching in MoS2 dispersion solution based on self-diffraction. They utilized the intensity of controlling light beam to modulate the diffraction pattern of the controlled light, and conjectured that the mechanism was the electron coherence .
Topological insulators are a new class of quantum matter and also possess self-focusing and self-diffraction effects resulted from the spatial self-phase modulation. Recently, the self-diffraction phenomenon of Bi2Te3 nanosheets was observed from ultraviolet (UV) to near-infrared (NIR) regions and the corresponding χ(3) was obtained . Among various layered materials, Bi2Se3 nanosheet has aroused special research interest because it has a large energy gap of 0.3 eV (equivalent to 3600 K). Such topology behavior can even be observed at room temperature. Therefore, it enables the applications of corresponding spintronic devices at room temperature with low energy consumption condition. Very recently, the self-focusing character of Bi2Se3 was studied by using a closed aperture Z-scan measurement .
In this paper, we investigate the tri-phase all-optical switching and broadband nonlinear optical response of Bi2Se3 dispersed in solution. It is uncovered that the spatial phase of controlled light can be modulated as three phases (unchanging, focusing, diffraction) by changing the incident intensity of controlling light, and the corresponding mechanism is discussed. The dynamic spatial self-phase modulation (SSPM) experiment was performed by using the intense controlling laser beam, which irradiates on the left edge, middle area, and right edge of the cuvette. The SSPM induces three processes including self-focusing, self-diffraction ring formation, and self-diffraction ring deformation. In addition, the SSPM of the controlling light can be measured from 350 nm to 1160 nm, exemplifying that this all-optical switching is available in broadband. The third-order optical susceptibility χ(3) in the corresponding wavelengths of the Bi2Se3 dispersion solution can also be obtained.
2. Experiment and discussion
2.1 Characterization of the sample
The Bi2Se3 nanosheets were prepared by a simple solution-based method reported previously . Their size and morphology were characterized by atomic force microscope (AFM) and scanning electron microscope (SEM), as shown in Fig. 1. It can be observed that the Bi2Se3 nanosheets have a uniform disc-like morphology with height of about 8 nm and diameter of about 250 nm. Figure 1(c) shows the absorption spectrum of the Bi2Se3 nanosheets dispersed in ethanediol solution, which exhibits a broad absorption band ranging from 250 nm to 1000 nm, similar with that reported previously [15, 16]. Figure 1(d) shows the X-ray diffraction (XRD) pattern of the Bi2Se3 nanosheets. All the peaks in the pattern are in accordance with the peaks of bulk Bi2Se3 (JCPDS Card No. 33-0214) with lattice constants a = b = 0.414 nm, and c = 2.864 nm.
2.2 Tri-phase all-optical switching in Bi2Se3 dispersion solution
All-optical switching of the Bi2Se3 nanosheets dispersion solution was performed by using a femto-second pulse laser, which was produced by an optical parametric amplifier (TOPAS, USF-UV2). The laser beam was pumped by a Ti with the pulse repetition rate of 2 kHz. Sapphire regenerative amplifier system contained Spectra-Physics, Spitfire ACE-35F-2KXP, Maitai SP and Empower 30. The horizontal laser beam was used to investigate the all-optical switching of the sample. The Bi2Se3 nanosheets dispersion solution was contained in a 10 mm thick quartz cuvette. The excitation wavelength was 700 nm. The controlling light and controlled light were kept at the same level. The laser beams irradiated the dispersion through a focusing lens (f = 250 mm). The intensities of controlling light and controlled light were changed by attenuation slices. Two beams were focused on the center of cuvette. The angle of both beams was 2.6°, as shown in Fig. 2(a). The distance between the lens and the center of the cuvette was 165 mm. The transmitted laser was collected by a fixed CCD camera. The attenuation slices were used in front of CCD to avoid saturation and damage.
The corresponding results were shown in Figs. 2(b) and 2(c). When the intensities of the controlling light and controlled light were fixed at only 0.9 mW, the collected pattern of the sample was just Gauss laser spot, demonstrating no nonlinear optical effect at this incident intensity. When the controlling light was increased to 4 mW and the controlled light was kept at 0.9 mW, the sizes of transmitted spots of the controlled light gradually decreased. This phenomenon is similar to the transmitted spot of the controlling light. It can be attributed to the self-focusing property of the Bi2Se3 nanosheets . Gauss beam induced that the refractive index change of the sheet central part was larger than the edge part. Propagation velocity of the center is slower than that of the edge, hence the laser beam is focusing [17, 18]. Such distortion of wave-front is similar with the phenomenon of a laser beam passing through a plus lens. When the controlling light increased to 10 mW and the controlled light was still kept at 0.9 mW, the diffraction rings can be observed in the transmitted spots of both the controlling light and controlled light. We also done a similar experiment with ethanediol only in quartz cuvetter under the same measurement conditions. However, SSPM was not be observed. These results demonstrate that the controlled light can be modulated to realize the three phases (unchanging, focusing, and diffraction) by changing only the controlling light incident intensity.
In addition, according to the pattern of the transmitted light, the phase distribution of irradiated region can be obtained based on the Gerchberg-Saxton algorithm . Figures 2(d) - 2(f) show the rough phase distribution of the irradiated region of the controlling light with intensity of 0.9 mW, 4 mW, and 10 mW. The unchanged phase distribution shown in Fig. 2(d) exhibits the gradually enhanced signals from the top to bottom, which probably originates from the Boltzmann distribution of the Bi2Se3 nanosheets in the vertical direction. The phase distribution of self-focusing is shown in Fig. 2(e), in which the phase distribution of the center region is relatively weaker. The phase distribution of self-diffraction is shown in Fig. 2(f), in which the phase distribution of the center region is relatively greater. Such phase changes of Figs. 2(e) and 2(f) maybe originate from the laser Gaussian distribution. The powerful intensity causes the change of nonlinear refractive index of the Bi2Se3 nanosheets, resulting in self-focusing and self-diffraction.
Figures 2(g)-2(i) show the rough phase distribution of the irradiated region of controlled light with the intensity kept at 0.9 mW. Since the controlled light is oblique incidence and the overlapping region is in front of focus, the optical path of left is longer than right, thus the left phase distribution in all the images is greater than the right one. Similar phase changes can be observed in Figs. 2(h) and 2(i). The phase distribution of the center region becomes weaker in Fig. 2(h), while becomes stronger in Fig. 2(i). It is supported that the controlling light changed the spatial nonlinear refractive index of the center overlapping region, resulting in the phase change of the controlled light. These results confirm the realization of the tri-phase optical switching including unchanging, focusing, and diffraction.
The dynamic SSPM of intense controlling laser beam was further measured to prove that self-focusing is an essential step to realize the self-diffraction. The schematic diagram of the SSPM setup is shown in Fig. 3(a). In this experiment, the horizontal laser beam was same as aforementioned. The laser beam irradiated the dispersion by a focusing lens (f = 200 mm) in normal incidence with the distance between the focusing lens and center of the cuvette was 100 mm. The SSPM pattern of the controlling light was received by a CCD which was fixed at 130 mm. The excitation wavelength was 700 nm with average power of 110 mW. The irradiated positions included the left edge, middle area, and right edge of the cuvette, as shown in Fig. 3(b). The blue arrowhead is the direction of laser propagation.
The corresponding SSPM processes are shown in Figs. 3(c)-3(e). According to the patterns, the SSPM contains three processes: self-focusing process, self-diffraction ring formation process, and self-diffraction ring deformation process. The self-focusing process is extremely fast with time of less than 0.07 s. Then, the self-diffraction process turns up. The number of the rings increases with the diameter becomes bigger and bigger within 3.64 s. After that, the SSPM pattern distorts due to thermal convection, and the stable time is less than 10 s.
In the SSPM experiment, the SSPM contains three processes including self-focusing, self-diffraction ring formation, and self-diffraction ring deformation. The self-diffraction ring deformation process maybe originates from thermal convection [20, 21] rather than gravity . As shown in Figs. 3(c)-3(e), the left-edge irradiation induces the unbalanced SSPM pattern with right higher than the left, while right-edge irradiation induces the unbalanced SSPM pattern with left higher than the right. In contrast, the middle-area irradiation results in a left-right balanced SSPM pattern. This phenomenon can be ascribed to the following points: when the laser irradiates on the left-edge of the cuvette, the laser-induced thermal convection of the left and right sides is asymmetry because of viscous forces between the dispersion and cuvette wall. The left concentration of the upper part is higher than the right, resulting in the unbalanced SSPM pattern with right higher than the left. In contrast, the viscous force between the dispersion and the cuvette wall is perfectly symmetric with the middle-area irradiation, thus balanced SSPM pattern can be obtained. Therefore, thermal convection is perhaps the main reason for the distortion, which originates from the phase distribution.
The phenomenon of self-focusing is observed for the first time in SSPM processes of layered materials. The reasons are as follow: On the one hand, as the Fig. 3 (dynamic SSPM) shown, the emergence of self-focusing is instantaneous in high excited power. Then, this phenomenon is replaced by self-diffraction immediately. It is easy to be neglected. Self-focusing phenomenon is an ultrafast nonlinear optical property. The carrier dynamic relaxation process of Bi2Se3 nanosheets was observed in pump-probe system. The time range is about femtosecond level, as Fig. 4 shown. On the other hand, as Fig. 2 (steady SSPM) shown, self-focusing only exists steadily in low excited power (but high instantaneous intensity).The laser source in our experiments is a femtosecond pulsed laser, which has a low repetition rate (2 kHz). The higher instantaneous intensity of fs laser could arouse the self-focusing, while the smaller thermal effect restrains the self-diffraction. In previous works [1, 20], the thermal effect is very big in chosen CW laser, so the self-diffraction based on thermal effect  conceals the self-focusing immediately.
The ultrafast nonlinear process of Bi2Se3 can be observed in Fig. 4 by pump-probe system. The dynamic relaxation process exhibits an exponential decay, and it can be fitted by exponential decay function of, where is the fast relaxation time and is acquired as fs. It means, such as self-focusing, the timescale of these ultrafast nonlinear processes is femtosecond level.
For the more easily and earlier emergence, the self-focusing is an important state and process in SSPM of layered material. Furthermore, it is a meaningful attempt to use self-focusing and self-diffraction to realize tri-phase modulation.
2.3 Broadband SSPM of Bi2Se3 dispersion solution
Figure 5 shows the SSPM experiment by using the laser with four typical excitation wavelengths (350 nm, 600 nm, 700 nm, and 1160 nm) spanning from the UV to NIR region. The stable SSPM patterns (self-focusing and self-diffraction) can be observed in all these wavelengths, demonstrating that this all-optical switching is available in broadband. The relationships between the number of rings (N) and the incident intensity (I) are also obtained. The slopes (N/I) are 1.23 ± 0.23 cm2/W (λ = 350 nm), 0.98 ± 0.05 cm2/W (λ = 600 nm), 0.81 ± 0.03 cm2/W (λ = 700 nm), and 0.50 ± 0.02 cm2/W (λ = 1160 nm). It is obvious that the slope gradually decreases with the increase of the excitation wavelength. Furthermore, the slope value is larger than other layered materials such as graphene , TMDs (MoS2, WS2, MoSe2) , Bi2Te3 , and black phosphorous , demonstrating the excellently photosensitive properties of Bi2Se3.
The refractive index of the sample is proportional to the intensity, n(r) = n0 + n2I(r), where n0 and n2 are the linear and nonlinear refractive index, respectively. When the beam irradiates through the Bi2Se3, the phase shifts and refractive index can be expressed as [2, 20], where r is the radial position, and λ is excitation wavelength.2]22]20], N/I is the slope value.
The third-order nonlinear susceptibility χ(3) is an important parameter of optical nonlinear material. The effective nonlinear refractive index can be expressed as 5]
The third-order optical susceptibility χ(3) of the Bi2Se3 dispersion solution with the corresponding wavelengths is obtained, as shown in Table 1. The third-order optical susceptibility increases with the incident photon energy , however, we partly ignore the thermal effect of low repetition frequency fs laser pulses . The results accord with those in previous works [12, 13].
In summary, the tri-phase all-optical switching has successfully been realized in the Bi2Se3 dispersion solution. The controlled light can be modulated as three phases (unchanging, focusing, and diffraction) by changing the controlling light incident intensity. The dynamic SSPM experiment of intense controlling laser beam further proves that self-focusing is the essential step to realize the self-diffraction. In addition, the stable SSPM of controlling light can be achieved at different wavelengths from 350 nm to 1160 nm, demonstrating that this all-optical switching is available in broadband. These results provide the great potential of Bi2Se3 as an all-optical switching for various optoelectronic applications.
National Natural Science Foundation of China (NSFC) (11334014); Hunan Provincial Natural Science Foundation (2016JJ3140); Fundamental Research Funds for the Central Universities of Central South University (2016zzts225, 2017zzts327); Undergraduate Training Program for Innovation and Entrepreneurship of Central South University (ZY2016616, 201610533392).
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