1. Introduction

Recently, nanoscale lasers have attracted a great deal of interest due to their great potential to generate highly localized integrable coherent light sources used in a great variety of scientific and technological applications including communications, metrology and biology [1–4]. Semiconductor nanowires (NWs) are promising for realization of the nanoscale lasers owing to their unique properties as gain media, resonant cavities and passive waveguides [5–10]. On the other hand, with the virtue of high-aspect-ratio, easily bent semiconductor NWs have contributed a lot to the development of the flexible electronics [11, 12]. A great number of theoretical and experimental studies have been devoted for a better understanding of the optical and electronic properties of bent semiconductor NWs [13–20]. Central to progress in this area have been the investigations about passive waveguides [16, 17, 19, 21] and luminescence properties [14, 20, 22]. However, to the best of our knowledge, the bending effects on the lasing action of semiconductor NWs have not yet been reported,which could be very helpful to further investigations about nanoscale lasers that include curved structures such as ring [23], loop [24], knot [25] and so on, in order to improve the cavity quality factor and decrease the threshold. Furthermore, the study of bending effects on NW lasers may provide important information for their practical applications since strain and deformation are common in the package of micro/nanoscale devices [26].

In this letter, we report the bending effects on the properties of optical-excited lasing action in CdSe NWs by gradually changing curvatures. With the curvature radius of the bent NWs becoming smaller, the threshold increases and the differential efficiency decreases. And the strain-induced change in band structure, which is indicative of the coupling of mechanical and electronic properties, is responsible for obvious red shift of the lasing peaks. Due to the oscillation of light in resonant cavity, the bending loss of NW laser is N times as large as that of PL. The N-fold amplification of bending loss of laser predicts a more sensitive approach to measure the perturbation of light induced by fairly small deformation or strain [27]. We also conduct some numerical simulations to investigate the diameter and mode dependence on the bending loss. Moreover, through bending the NWs into different angles continuously, we could modulate the polarization of laser emission linearly.

2. Experimental

The CdSe NWs used in this work are synthesized by chemical vapor transport process [28]. We transfer CdSe NWs to a substrate and bend them into different radius through a nanotaper which is fabricated by directly drawing a commercial optical fiber. The bent NWs, which are elastic, are able to remain the curved shape due to Van der Walls force between the substrate and the CdSe NWs. One end of the NW is excited by 532 nm laser pulses (2 kHz repetition rate, 6 ns pulse width) from a frequency doubled laser under an 100 × optical microscope with a spot size ~20 μm. The light emission from the other end of CdSe NW is collected for imaging and spectral measurement respectively through a dichroic beam splitter. The process of optical excitation is schematically illustrated in Fig. 1(a) . All above measurements are performed at room temperature.

 

Fig. 1 (a) Schematic diagram of the experimental setup for optical excitation and bending process. (b) Bright-field optical images of a 50 μm length 650 nm diameter CdSe NW with gradually decreased bending radius without optical excitation. (c) Dark-field optical images for the corresponding bending process under the same intensity of optical excitation. Two of the most weakened optical emissions from the bending end of the NW are indicated by the white arrows. Scale bar in (b) applies to (c).

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Figures 1(b) and 1(c) illustrate the bright-field and dark-field CCD images of a CdSe NW with gradually decreased bending radius, respectively. In Fig. 1(c), the left end of the NW is excited at the same pumping power and the optical emission from the right end of the NW weakened continuously with the curvatures increase step by step, which could be explained by the increased bending loss induced by decreased bending radius.

3. Results and discussion

Generally, laser oscillation occurs when the round-trip gain equals to the round-trip loss [29]. For straight semiconductor NWs, the losses consist of propagation loss and mirror loss that dominates [30]. When the NWs are bent, the phase front at where is more distant from the center of curvature, needs to travel faster than the nearer ones. At some critical distance, the phase front travels as fast as the local light speed, which can be seen in Fig. 2 . And the field beyond the critical distance has to travel faster than the light speed, which is impossible to happen. So it breaks away and the light leaks away through radiation, thus leads to bending loss [31]. Therefore, the losses in bent NWs consist of propagation loss, mirror loss and bending loss.

 

Fig. 2 Diagram of phase front in a bent NW. R is bending radius, and R_c represents for the critical radius, where the phase front travels as fast as local light speed.

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More gain would be needed to overcome the higher threshold loss induced by increased bending loss when the NWs are bent to smaller radius, assuming the propagation loss and mirror loss are constant during the bending process. As a consequence, the threshold lifts up, as illustrated in Fig. 3(a) and black square dots in Fig. 3(b). The value of the slope (differential efficiency) indicates the efficiency of converting the pumping photons into the emitting lasing photons. The blue triangle dots in Fig. 3(b) show that the differential efficiency decreases when the bending angle increases. It may be explained by the fact that the photons excited by the pumping laser would suffer greater bending loss and have a less chance to lase at smaller bending radius. In Fig. 3(c), the intensities of the laser peaks reduce gradually with decreased bending radius. And at the smallest bending radius (11 µm), only PL spectrum rather than laser peaks appears. The relationship between the mechanical strain and the change of threshold may lead to applications in optical switches [32], logic gates [33], and sensors [34].

 

Fig. 3 (a) Integrated emission intensity versus pump power of a 60 µm length 500 nm diameter CdSe NW with different bending radius: ∞, 36, 13, 11 μm, respectively. (b) The plot of threshold and differential efficiency versus bending angles. Bending angles are reversely proportional to the bending radius since the length of the bending portion of the NWs keeps almost the same during the bending process. (c) Red shift output spectra of a 60 μm length 500 nm diameter CdSe NW under the same pump power with different bending radius: ∞, 36, 13, 11 μm. (d) Mode-reduction spectra of a 40 μm length 500 nm diameter CdSe NW under the same pump power with different bending radius: ∞, 22, 13 μm.

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It is also observed that obvious red shift occurs during the bending process from Fig. 3(c). This phenomenon originates from bandgap reduction induced by strain, which is theoretically and experimentally demonstrated in recent works [14, 18]. In addition, the decrease of the number of modes deserves considerable notice, as shown in Fig. 3(d). The modes at larger wavelength, which have more portion out of the waveguides, suffer greater bending loss and leak away more likely. With further investigation, maybe it could be designed as a very simple single-NW single-mode nanolaser [24].

Figure 4(a) shows the curvature-dependent bending loss. The pure bending loss for PL (α_b) and laser (α’_b) are obtained by normalizing the output intensity of the curved NWs to that of the straight NWs [5]. And it can be expressed as:

 

Fig. 4 (a) The plot of bending loss versus bending radius of a 37 μm length 310 nm diameter CdSe NW. Black exponential line is for PL, and red one for laser. (b) Simulation results of diameter-dependent bending losses of PL. (c) The electric field intensity distributions in x-z plane, the corresponding output mode profiles are shown above. The NW diameter D is 400 nm, and the bending radius are 0.75 μm and 4μm, respectively. (d) Diameter-dependent bending losses of laser obtained from experiments. The blue square dots represent a 35 μm length 410 nm diameter NW, and the purple round dots represent a 38 μm length 260 nm diameter NW. (e) Simulation results of bending losses for the first three guided modes. Diameter of NW used here is 300 nm. (f) The input (left) and output (right) mode profiles in y-z plane of the first three guided modes. The NW diameter is 300 nm, and the bending radius is 2 μm.

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where I₁ and I’₁ are the output intensity of PL and laser in straight NWs, respectively. And I₂ and I’₂ are the output intensity in bent NWs, respectively. As shown in Fig. 4(a), bending loss of PL (black line) and laser (red line) both show exponential relationships with the bending radius, and the bending loss for laser is N times as large as that of PL. Similar with the N-times enhancement of absorption loss when placing an absorbing sample inside the laser cavity, the bending loss of laser will be increased by times compared with that of PL. Thus N could be considered as the average times the photons travel back and forth between the resonator mirrors. The N-fold amplification of bending loss of laser predicts that it may provide a more sensitive approach to measure the perturbation of light induced by small deformation or strain.

The diameter of a NW plays an important role in optical confinement, and thus also determines the bending loss. We conduct numerical simulations to investigate the dependence of bending losses on the NW diameter by using a Comsol Multiphysics finite elements method. The refractive index of the NW is assumed to be 2.85 and the incident wavelength is 725 nm. The computational domain is discretized into a triangular mesh with an element size of one fifteenth of the NW diameter, and terminated by perfectly matched layer (PML) boundaries. Figure 4(b) shows the diameter-dependent bending loss of the fundamental mode (HE₁₁ mode) propagating in the NW. The electric field distribution and output mode profiles of a 400 nm diameter NW are shown in Fig. 4(c). Reasonably, in a thick NW, the mode is mostly contained in the NW core; while in a thin NW, a large field distribution of the mode is outside the core of the NW and could be easily affected by bending of the NW. Therefore the thinner NW suffers larger bending loss.

While in experiments, we found a very interesting phenomenon, as shown in Fig. 4(d): the laser’s bending loss of the thin NW (260 nm diameter) is larger than that of the thick one (410 nm diameter) at small bending radius (region I), but becoming smaller at comparably large bending radius (region II), which may be suggested arising from mode dependence of bending loss. According to previous reports, HE₁₁ mode dominates in the thin NWs, while the high order modes may occupy a fairly amount in the thick NWs because of their higher reflectivity [35]. Figures 4(e) and 4(f) show the simulated bending loss of the first three guided modes (HE₁₁, TE₀₁, TM₀₁) and the corresponding input and output profiles. It can be seen that the bending loss of TE₀₁ and TM₀₁ are both larger than that of HE₁₁, and TM₀₁ is significantly larger than the other two modes. Therefore, at large bending radius, the bending loss of the thick NW may be determined by high order modes (e.g. TE₀₁ and TM₀₁ modes), while the bending loss of the thin NW is determined by HE₁₁ mode. According to Fig. 4(e), it is possible that the bending loss of the thick NW surpasses that of the thin NW in region II. However, at small bending radius, the high order modes may have almost leaked away and the bending loss of the thick NW would also be determined by HE₁₁ mode. As shown in Fig. 4(b), the bending loss of the thick NW is smaller than that of the thin NW in region I. We also investigate the polarization of the laser emission in the plane parallel to the substrate using a linear polarizer, as shown in Figs. 5(a) and 5(b). Usually, semiconductor NWs support the modes which are polarized perpendicular to the axis of NWs [36, 37]. On the other hand, the shape of endface could also influence the polarization [38]. Through bend-to-fracture process [39], we could get a quite flat endface. Figure 5(c) shows the scanning electron microscope (SEM) image of a 40 μm length 260 nm diameter Cdse NW, and from the inset we can see a flat endface clearly.

 

Fig. 5 (a), (b) Polar plots of the laser emission from the bending endface parallel to the substrate with the bending angles of 0 and 90 degrees, respectively. θ represents the polarization angle. Insets, the dark-field optical images of the straight and 90-degree-bent CdSe NW, respectively. Scale bar in (a) applies to (b). (c) SEM image of a 40 μm length 260 nm diameter CdSe NW. Inset, a close view of the bending end of the NW with a flat endface. Scale bar, 500nm. (d) The linear fitting of polarization angles versus bending angles.

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The polarization of the laser emission from the bending end can be tuned gradually as the emission end being bent to different bending angles. Figures 5(a) and 5(b) show typical plots of the polarization of the laser emission of the bent NWs. We plot the relationship between the bending angles and the predominant polarization of the NW laser emission in Fig. 5(d). And it fits well into the linear relationship β = α + 90°, where α is the angle between the axis along the bending end of NW and the horizontal direction, β is the angle between the predominant polarization direction and the horizontal direction. When the emission end is bent to 90 degrees, we can reduce the unwanted signals to minimum thus greatly enhance the signal-noise ratio.

5. Conclusion

In conclusion, we have investigated the bending effects on the lasing action of CdSe NWs. Threshold increases and differential efficiency decreases when the bending radius decreases. The bending loss of laser is about N times as large as the bending loss of PL and shows the same exponential dependence on the bending radius. We also found that the bending loss depends on diameters of the NWs and mode types. A novel phenomenon is observed: the laser’s bending loss of the thick NW is larger than that of the thin NW at comparably large bending radius. We explain the results with numerical simulation. Red shift of laser peaks and mode reduction are also observed. The linear relationship between the polarization direction and the bending angles may be utilized to modulate the polarization of the laser emission just in a simple way through bending NWs. These bending effects on the lasing action of CdSe NWs deserve further investigations and may contribute a lot to the constructions of nanoscale laser world.