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Abstract
For minimizing the spatial cross-sectional pulse width difference in the reflected SBS compressed beam, two new methods, blocking beam edge and parameter optimization, are proposed and compared experimentally. Results show that the sub-nanosecond compressed pulse width at the beam edge can be obtained by using both two methods in this paper. The pulse width difference between the beam center and the edge is minimized through selecting a proper medium and the optimized structural parameters in a single-cell SBS compressor. Its energy efficiency reaches up to 81.5% by using the medium HT110 and is two times higher than that of the blocking beam edge method. The compressed pulse width’s stability improved greatly by using these two methods.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The single-longitudinal mode sub-nanosecond pulse laser has important and extensive applications in the fields of high-resolution spectroscopy [1], laser microfabrication manufacturing technology [2], medical laser cosmetology [3], Doppler wind radar [4], and high spatial resolution in LIDAR Thomson scattering diagnostics [5]. Currently, the technology to obtain a sub-nanosecond pulse laser mainly includes the short pulse amplification with a low efficiency, the mode locking accompanied by a multi-longitudinal-mode pulse, and the stimulated Brillouin scattering (SBS) pulse compression. Many investigations [6–16] have demonstrated that the SBS pulse amplification technology is a highly-efficient and simple means to compress a nanosecond pulse to a sub-nanosecond laser pulse under a high peak power. Furthermore, SBS also has many advantages in terms of simple and easy operation of structural devices, low cost, a high pulse compression ratio, and effective improvement of beam quality [6–10]. Many previous theoretical and experimental studies have been conducted to obtain a high-energy and narrow pulse width beam, mainly focusing on the pulse time-domain compression characteristic [6–13]. The spatial cross-sectional duration distribution of the SBS compressed pulse has also received considerable attention [14–16].
Many experimental studies have indicated that the spatial cross-sectional duration distribution of the SBS pulse compression strongly depends on the spatial intensity distribution of the pump beam [9,14,16–18]. The spatial cross-sectional duration distribution for a Gaussian pumping beam is illustrated in Fig. 1. Similar experimental results were also reported in some previous studies [14,16]. From Fig. 1, the temporal pulse width is compressed to several hundred picoseconds in the vicinity of the beam center and less compressed to several nanoseconds in the wing side of the beam profile. For such a pulse width distribution, the nanosecond pulse duration in the beam edge region will broaden the pulse width of the entire beam profile and reduce the pulse peak power density, thus limiting the application. This problem observed in experiments is not expected. To date, few studies have reported such remarkable results to obtain a uniform spatial pulse-width distribution of a SBS compressed pulse.
Fig. 1 Pulse width distribution of a conventional SBS compressed pulse for Gaussian pumping beam. (R is the beam radius.)
To achieve a uniform spatial pulse-width distribution, it is necessary to minimise the pulse width difference between the center and the edge of the SBS compressed beam. The cause of the nanosecond pulse width of the beam spot edge is the Stokes incomplete compression due to the weak pump power density and the short interaction length. The Stokes incomplete compression will generate pulse tail modulation, which will result in a non-uniform cross-sectional pulse-width distribution. According to the literatures, there are three potential ways to obtain a uniform cross-sectional duration distribution pulse. The first is to suppress the pulse tail. Yoshida et al. [9] stated that the broad pulse width of the beam spot edge can lead to a slow falling tail of the compressed pulse, and suppressing the pulse tail can make the spatial pulse width distribution more uniform. To accomplish this, Liu et al. [19,20] used the methods of absorption attenuation and laser-induced breakdown for a two-cell pulse compressor. Also, some studies reported that the SBS pulse compression with a long SBS cell can suppress the pulse tail [17,21,22]. However, these works only focused on the compression in the time domain and did not consider the cross-sectional pulse width distribution in the spatial domain. The second approach is to adopt a pump beam with a uniform intensity distribution. Neshev et al. [14] and Feng et al. [16] argued that the pump with super-Gaussian or flattop beam pattern could obtain uniform cross-sectional pulse width distributions. However, this suggestion has not been verified by relevant experiments. The third approach is to use a long interaction length between the pump and the Stokes beams. Feng et al. [17] obtained a compressed pulse with a uniform spatial pulse width distribution through a double SBS pulse compressor. This method reduces the pump pulse width by the first SBS compressor, thereby shortening the interaction length required for the well pulse compression of the second SBS compressor. Experiment results showed that increasing of the interaction length can decrease the influence of the pump intensity distribution on the spatial pulse width distribution. The experiment obtained a SBS pulse compression with a uniform spatial pulse width distribution, but the energy efficiency of 20% is too low with use of this method. To sum up, these methods are not sufficient to obtain a pulse with a uniform cross-sectional pulse width distribution and high energy efficiency in the SBS pulse compressor.
To obtain SBS compressed pulses with a uniform spatial pulse width distribution and a high energy efficiency, two new methods, blocking beam edge method and parameter optimization method, are proposed to minimize the cross sectional pulse width difference between the center and the edge parts of the SBS compressed beam. To study the effect of the medium parameters on pulse compression, the dependence of the output energy, the pulse width, and the temporal waveform of the reflected beam on the pump energy will be studied in two different kinds of SBS media using a single-cell compressor. Furthermore, the optimized parameters will be calculated theoretically by simulating different media and structural parameters. On the basis of the simulation results, the high energy efficiency SBS pulse compression with a more uniform cross sectional pulse width distribution will be obtained in single-cell and two-cell compressors. Finally, a SBS experiment using the blocking beam edge method is carrried out, and the results will be compared with those yielded by the parameter optimization method.
2. Experimental setup
The experimental setup employed in this research is shown in Fig. 2. The laser pumping source is p-polarized light originating from an injection seeded single-longitudinal-mode laser with a line width of 90 MHz at a fundamental wavelength of 1064 nm. The pulse waveform of the input beam has a Gaussian distribution with a beam quality factor M2 ~2, and the beam has a pulse width of 10 ns operating at a repetition rate of 10 Hz. It is convenient to use the combination of a half-wave plate (HWP1) and a polarization beam splitter (PBS1) to control the input beam energy. The pump beam size is reduced from 8 mm to 5.2 mm using a beam reducer comprising two lenses L1 and L2 with focal lengths of 30 cm and −20 cm, respectively. The input beam is introduced into the SBS cell through a QWP and lens L3 with a focal length of 50 cm. The parameter d is the distance between lens L3 and the front surface of the SBS cell. The amplified Stokes pulse is separated by a system consisting of PBS1 and the QWP. To measure the temporal pulse width distribution of the whole beam pattern, the compressed beam is attenuated by a combination of HWP2 and PBS2. The sub-nanosecond pulse sample is then picked up by a 69 μm pinhole and detected by a photodetector Thorlabs DET02 (1.2 GHz bandwidth; rise time: 50 ps; fall time: 250 ps). The signal waveform from each individual horizontal position is recorded by a digital oscilloscope with a 3 GHz bandwidth. Both the phototube and the pinhole are translated along the horizontal axis to measure the spatial pulse width distribution within the whole beam cross section.
Fig. 2 Schematic of experimental setup for single-cell SBS compressor. QWP, quarter wave plate; HWP1~2, half wave plate; L1~3, lens.
3. Theoretical modeling
According to the principle of the SBS pulse compression, three coupled differential equations can be used to describe the relationship among the optical field of input beam EL, reflected beam ES, and the acoustic field ρ, which has been detailed in our previous work [19]:
where represents the electrostrictive coupling constant, c is the speed of light,is the unperturbed density, and is the absorption coefficient. The Eqs. (1) mentioned above are partial differential equations, which are solved numerically by the split-step method:In the process of SBS pulse compression, the Brillouin linewidth (inversely proportional to the phonon lifetime of the medium) and the gain coefficient are two significant parameters affecting the compressed pulse width. As is well known, it is easy to obtain a short pulse in the case of a medium with a broad Brillouin linewidth and a large gain coefficient. Notably, the Brillouin linewidthand the gain coefficient g are associated with the kinetic viscosity η of the medium. It has been demonstrated that these two parameters are mutually restricted, namely∝η, g∝1/η [23]. Thus, the weight between the two parameters, the Brillouin linewidth and the gain coefficient, is necessary to obtain good SBS compression. Based on this, we choose two commonly used media of perfluoropolyether liquid HT110 and heavy fluorocarbon liquid FC40 as the objectives, considering the large difference between their Brillouin linewidths. The parameters of HT110 and FC40 are listed in Table 1.
Table 1. Parameters of SBS medium used in simulations and experiments [9,11]
In a single-cell compressor, the SBS compressed pulse may show the phenomena of tail modulation and pulse width broadening due to the restriction of the interaction length and the pump intensity. To study the effect of medium parameters on the compressed pulse tail, the temporal Stokes waveforms at different input energies are compared for the two media HT110 and FC40 in Fig. 3. The experimental setup is the same as that shown in Fig. 2 without lenses L1 and L2. The beam spot size is 8 mm and the focal length of lens L3 is 0.5 m. The length of the SBS cell is 1.0 m and the distance between L3 and the SBS cell is 15 cm. With an increase of the pump energy, the effective pump pulse width broadens significantly, and the interaction length between the pump light and Stokes light is not sufficiently long, resulting in apparent tail modulation, as shown in Fig. 3. It can be seen from Figs. 3(a)-3(c) and Figs. 3(d)-3(f) that the tail modulation becomes increasingly evident with greater pump energy. A comparison of pulse waveforms between the simulated and measured results is also shown in Fig. 3. The results show that the simulated results have a good agreement with the experimental data.
Fig. 3 Temporal Stokes waveform of the medium (a)-(c) HT110 and (d)-(f) FC40 at different pump energies.
There are several factors that affect the SBS compressed pulse waveform, including fluctuation initiation of the Stokes signal, interaction length, injection energy, gain coefficient, and Brillouin linewidth. Comparing Figs. 3(c) and 3(f), the results show that the intensity fluctuation of the Stokes pulse tail modulation in HT110 with the Brillouin linewidth of 553 MHz is much lower than that of FC40 with Brillouin linewidth of 1292 MHz. The Stokes pulse width will broaden if the tail modulation intensity is higher than the half maximum intensity of its first peak. Thus, the SBS medium with a narrow Brillouin linewidth and a large gain coefficient can appropriately suppress the intensity fluctuation of pulse tail modulation in a single-cell compressor.
4. Basic experiment and blocking beam edge method
SBS pulse compression is studied in the conventional approach of a single-cell configuration without a beam reducer, as shown in Fig. 2. The experimental conditions are the same as those given in Fig. 1 and Fig. 3. The dependence of the energy reflectivity and compressed pulse width on the pump energy is measured in HT110 and FC40, respectively, as shown in Fig. 4. The experimental results show that the energy extraction efficiency improves and the compressed pulse width becomes narrow with an increase of the input energy. The measured maximum energy extraction efficiency and the narrowest pulse width of the two media are 86.3% and 0.6 ns for HT110, and 85% and 0.62 ns for FC40, respectively. In Fig. 4 (a), the output energy and the extraction efficiency of HT110 are slightly higher than those of FC40. In the input energy range from 5 mJ to 70 mJ, the energy extraction efficiencies of HT110 and FC40 change by 47.2% and 64.5%, respectively. In comparison with FC40, the extraction efficiency and pulse width of HT110 are not sensitive to the pump power change in this situation. This is because HT110 has a larger gain coefficient than FC40, as shown in Table 1. The leading edge of the Stokes wave amplifies gradually through coupling of the acoustic field and the pump beam. In this event, the Stokes pulse is compressed effectively. It can be seen from Fig. 4(b) that the narrowest pulse width of HT110 is 0.6 ns. This pulse width reaches the phonon lifetime of HT110, which indicates good compression. The measured SBS thresholds of HT110 and FC40 are 2.3 mJ and 4.0 mJ, respectively. The low SBS threshold value of HT110 is beneficial for the single-cell SBS pulse compression.
Fig. 4 Experimentally detected (a) output energy (b) and Stokes pulse duration with different media.
The experimental results show that the energy extraction efficiency improves and the compressed pulse width becomes narrow with an increase of the input energy. The measured maximum energy extraction efficiency and the narrowest pulse width of the two media are 86.3% and 0.6 ns for HT110, and 85% and 0.62 ns for FC40, respectively. In Fig. 4(a), the output energy and the extraction efficiency of HT110 are slightly higher than those of FC40. In the input energy range from 5 mJ to 70 mJ, the energy extraction efficiencies of HT110 and FC40 change by 47.2% and 64.5%, respectively. In comparison with FC40, the extraction efficiency and pulse width of HT110 are not sensitive to the pump power change in this situation. This is because HT110 has a larger gain coefficient than FC40, as shown in Table 1. The leading edge of the Stokes wave amplifies gradually through coupling of the acoustic field and the pump beam. In this event, the Stokes pulse is compressed effectively. It can be seen from Fig. 4(b) that the narrowest pulse width of HT110 is 0.6 ns. This pulse width reaches the phonon lifetime of HT110, which indicates good compression. The measured SBS thresholds of HT110 and FC40 are 2.3 mJ and 4.0 mJ, respectively. The low SBS threshold value of HT110 is beneficial for the single-cell SBS pulse compression.
A comparison of the cross-sectional pulse width distributions between HT110 and FC40 at the pump energy of 50 mJ is shown in Fig. 5. The horizontal axis in Fig. 5 is normalised, and this can be used for directly comparing the pulse width of the two media. In Fig. 5, there is an asymmetric pulse width distribution, which is attributed to the pump asymmetry. The pulse width of FC40 shows significant fluctuation at the horizontal position nearby 0.5 of the beam cross-section. This can be ascribed to instability of the tail modulation during the SBS compression process. Comparing the cases of HT110 and FC40, it is clear that the pulse width and fluctuation of HT110 are smaller than those of FC40. Therefore, the medium HT110 with a narrow Brillouin linewidth is good for the single-cell SBS compressor and FC40 is beneficial for the two-cell SBS compressor.
In this paper, we proposed a novel method, referred to here as the blocking beam edge method, to obtain a uniform spatial pulse width distribution. In this method, the edge of the beam spot is intercepted using an iris diaphragm to remove part of the nanosecond order pulse width. The iris diaphragm is placed in front of a phototube, and its position and size are determined by measuring the pulse width at different horizontal axis locations. Figures 6(a) and 6(b) show the output energy concerning the input energy and pulse width distribution at 50 mJ injection energy, respectively. It can be seen from Fig. 6(a) that the SBS energy efficiency is below 40.7% under the condition of a 60 mJ injection energy. This indicates that the energy efficiency of 40.7% is low and should be improved further. As shown in Fig. 6(b), the large pulse width fluctuation at the beam edge is due to the incomplete amplification of the Stokes wave.
Fig. 6 The (a) output energy and (b) pulse width distribution at 50 mJ input energy using the blocking beam edge method. (R is the beam radius.)
5. Theoretical simulation and experimental results
To improve the energy efficiency (Criterion 1) and compress the pulse width of the beam spot edge to the sub-nanosecond level (Criterion 2), a parameter optimization method is proposed in this study. In this method, the optimised parameters mainly focus on two aspects, the medium type and structural parameters. As mentioned above, the media of HT110 and FC40 are applied, and the structural parameters of the experiment setup include the pump beam radius and the lens focal length. For the sake of clarity, we will firstly investigate the dependence of the pulse width and energy efficiency on the medium and structural parameters using a simulation method. The optimised structural parameters are obtained through a numerical simulation to fulfill Criterion 1 and Criterion 2. Corresponding experiments are then carried out for validation.
5.1 Numerical parameter analysis
As is well known, it is easy to acquire a short pulse for the SBS medium with a broad Brillouin linewidth and a large gain coefficient. However, tail modulation of the compressed pulse also regularly appears in the SBS medium with a broad Brillouin linewidth, as shown in Fig. 3, resulting from an inhomogeneous pump intensity and an insufficient interaction length. This will reduce the pulse peak power density and the actual SBS extraction efficiency. In order to estimate the effect of pulse trailing on the energy efficiency, the effective energy efficiency is defined by the ratio of the output energy of the first peak within the SBS pulse waveform to the total input energy. Therefore, for the medium selection it is necessary to consider a tradeoff between the pulse width and the effective energy efficiency.
Figure 7 shows the dependence of the SBS output parameters on the Brillouin linewidth and the gain coefficient at input power of 1 MW. The black circles represent the SBS medium of HT110 and FC40. The current simulation conditions are as follows: the sound velocity is 550 m/s, the refractive index is 1.28, the input beam size is 8 mm, the focal length of lens is 50 cm, and d = 15 cm. It can be seen from Fig. 7(a) that the pulse width is short for the medium with a broad Brillouin linewidth and a large gain coefficient. The right upper corner of Fig. 7(a) appears as a blue (short pulse width) region. Figure 7(b) shows the relationship between the effective energy efficiency and the two main medium parameters. It indicates that the maximum effective energy efficiency appears in the medium that has a large gain coefficient and a small Brillouin linewidth. The effective energy efficiency in a broad Brillouin linewidth medium is very low due to the presence of the pulse tail modulation. Therefore, taking into account Criterion 1 and Criterion 2, we choose HT110 for the single-cell compressor owing to its weak intensity fluctuation of the pulse tail modulation and highly effective energy efficiency. For a two-cell SBS compressor, FC40 is better because the long interaction length can weaken the intensity fluctuation of the pulse tail modulation, and its broad Brillouin linewidth can acquire a short SBS compressed pulse.
Fig. 7 Dependence of (a) pulse width and (b) effective energy efficiency on Brillouin linewidth and gain coefficient with the input power 1 MW.
Figure 8 shows the variations of the pulse width and energy efficiency with the pump beam radius and the lens focal length for HT110 at a pump power of 5 MW. This information can be used for optimising of the structural parameters. With an increase of the pump size, the energy efficiency, and the effective energy efficiency increase gradually, and the pulse width decreases initially and then increases. It can be seen from Fig. 8(a) that the pulse width can decrease with an appropriate pump beam size for its intensity distribution. Thus, the pump beam radius is selected to be 2.5 mm. The relationship between the pulse width and the energy efficiency as a function of the focal length of lens L3 is shown in Fig. 8(b). As the focal length increases, the energy efficiency decreases gradually, the effective energy efficiency increases rapidly, and the pulse width decreases initially and then increases. The cause of this phenomenon is that the interaction length becomes longer with an increase of the focal length, and the leading edge of the Stokes light is amplified effectively. However, the reduction of the pump power density at the focus position will bring about a deduction of the energy efficiency with a long focal length lens. When the focal length of lens L3 is increased above 55 cm, the decrease of the pump power density will broaden the pulse width. Also, the difference value between the effective energy efficiency and energy efficiency becomes smaller and smaller, and finally they become identical. Thus, a 50 cm focal length of lens L3 and a 2 cm distance between L3 and the SBS cell are selected as the optimized parameters, and they are used to obtain a short compressed pulse with a high energy efficiency.
Fig. 8 Simulated dependence of output parameters on (a) pump beam radius and (b) focal length with HT110. Simulation parameters: (a) the focal length of lens L3 is 50 cm, d = 15 cm; (b) the pump beam size is 5 mm, d = 2 cm.
To obtain SBS pulse compression with a uniform cross-sectional pulse width distribution, we optimise experiment parameters of the single-cell compressor. The simulation results indicate that high energy efficiency SBS compression with a short duration pulse can be obtained under the following conditions: 1) selection of an appropriate SBS medium, 2) optimization of the power density of the pump beam, and 3) increasing the interaction length appropriately. The experiment thus can be optimized in the following three aspects. First, HT110 is selected for the single-cell compressor because it has a large gain coefficient and a narrow Brillouin linewidth. Second, the pump beam size in this experiment is reduced from 8 mm to 5 mm. It has been reported that the pulse width difference between the beam center and edge can be minimized when the SBS pulse compression process reaches the saturation condition [9]. Finally, lens L3 with a focal length of 50 cm is selected.
The simulated spatial pulse width distribution of the SBS pulse compression considering the transverse dimension is illustrated in Fig. 9. The time compression of each radial component is treated independently using the Gaussian intensity profile of the pump beam. The pulse radial profile is I(r) = exp(−4r4/R4) [17] under conditions of a pump beam radius R of 4 mm (before parameter optimization) and 2.5 mm (after parameter optimization) at an input pump power of 5 MW. The simulated spatial pulse width distribution in Fig. 9 has similar characteristics with the experimental observations in Fig. 5 before parameter optimization. Also, it can be observed from Fig. 9 that the pulse width of the Stokes beam edge can be compressed to the sub-nanosecond level by the parameter optimization method. The simulated results after parameter optimization are better than those before optimization.
5.2 Experimental results using HT110
Using the optimized parameters in section 5.1, the dependence of the pulse width and the reflected energy on the input energy is respectively measured, as shown in Fig. 10, using HT110. As the pump energy increases from 6 mJ to 70 mJ, the compressed pulse width is at the sub-nanosecond level, and the maximum relative standard deviation (RSD) is less than 5%. At the input energy of 50 mJ, the narrowest average compression pulse width is 0.63 ns. In this situation, the compression process reaches the saturation condition. The inset in Fig. 10(a) plots an SBS pulse compression waveform at the pump energy of 65 mJ, and the corresponding pulse compression factor is about 17. The second peak behind the first main peak of the compressed pulse is an experimental artifact that is due to the limited resolution of the measurement device. In this situation, the maximum energy extraction efficiency is up to 81.5% and is two times higher than the result using the blocking beam edge method.
Fig. 10 Experimentally detected (a) Stokes duration and (b) output energy by parameter optimization method with HT110.
The pulse width and its RSD values are measured within the whole beam pattern at a pump energy of 50 mJ, as shown in Fig. 11(a). It can be seen from Fig. 11(a) that the RSD values are large at the beam edge and small at the beam center, which is related to the pump intensity and interaction length. The measured cross-sectional pulse width distribution in Fig. 11(a) has similar characteristics with the simulation results in Fig. 9. The discrepancy between the simulated and measured results can be explained by ignoring the real pump intensity profile and the coupling effects among the Stokes components across the transverse direction. The pulse width across the whole beam cross-section is from 640 ps to 820 ps. The difference in the cross-sectional pulse width value decreases to 180 ps from the value of ~5360 ps before parameter optimization. The SBS compression process will filter away the outer wings [14]. In Fig. 11(a), the pulse width at the beam edge increases initially and then decreases. This may be caused by the complex combination of pump intensity, interaction length and other nonlinear effects during the SBS pulse compression process. Figure 11(b) shows the pulse temporal waveforms at different positions of the beam profile. There is no tail modulation within a normalized radius range of 0.6. With an increase of the radius, the tail modulation effect becomes increasingly apparent, which is due to the reduction of the pump power density. A reasonable explanation is that the pump beam does not completely amplify the Stokes signal but amplifies the pulse tail. Increasing the interaction length further can reduce the pulse tail at the beam edge, but with sacrifice of energy efficiency and the use of a rather long SBS cell. After optimizing the single-cell compressor experimental conditions, a SBS compressed beam with a more uniform cross-sectional pulse width distribution is obtained. The maximum RSD of the Stokes beam is only 8% in Fig. 11(a), which shows that the pulse stability also improves after the parameter optimization.
Fig. 11 Measured (a) pulse width distribution and (b) temporal waveforms after parameter optimization with HT110. (R is the beam radius.)
5.3 Experimental results using FC40
For FC40, the interaction length should be increased to suppress the large pulse tail modulation resulting from the broad Brillouin linewidth. Therefore, to obtain a more uniform cross-sectional pulse width distribution of the SBS compressed beam, it is necessary to employ a compact two-cell structure for FC40, as shown in Fig. 12(a). Similarly, the appropriate structural parameters of the two-cell compressor can be calculated according to the method given in Section 5.1. The pump beam size is reduced to 5 mm using a beam reducer comprising lenses L1 and L2 and is introduced into an amplifier cell with a length of 100 cm filled with FluorinertTM liquid FC-40. The beam is then focused into an 80 cm generator cell through lens L4 with 30 cm focal length.
Fig. 12 (a) Experimental setup for FC40. And measured values (b) output energy, (c) Stokes pulse width, (d) pulse width distribution, and (e) temporal waveforms after parameter optimization. (R is the beam radius.)
The experimental results obtained using the parameter optimized method are shown in Figs. 12(b)-12(e). The dependence of the SBS reflected energy and energy efficiency on the injection energy is shown in Fig. 12(b). It can be seen from Fig. 12(b) that the maximum energy efficiency is up to 81.2% at an input energy of 70 mJ. Figure 12(c) shows the relationship between the SBS compressed pulse width and the input energy. Figure 12(d) shows the pulse widths and RSD values within the whole beam pattern at a pump energy of 50 mJ. The pulse width distribution ranges from 630 ps to 860 ps, and the pulse width RSD value is less than 6%. Figure 12(e) shows the pulse temporal waveforms at different transverse positions of the beam profile. As can be seen from the illustration in Fig. 12(d), the cross-sectional pulse width difference value is 230 ps, this shows that the intensity distribution of the pump light still influences the spatial pulse width distribution of SBS pulse compression. However, the difference decreases to 4% compared with the value of ~5360 ps before parameter optimization. To further reduce this difference and obtain a more uniform spatial pulse width distribution, the interaction length should to be further increased, but this will obviously reduce the SBS energy efficiency.
The cross-sectional pulse width difference, the maximum duration RSD across the beam pattern, and the energy efficiency of the two methods are compared intuitively in Table 2. The maximum duration RSD values of the two new methods are both distinctly lower than those obtained with the conventional approach. The energy efficiency with the parameter optimization method is much better than that obtained with the blocking beam edge method. In addition, for the blocking beam edge method, high power laser will produce other nonlinear effects with the border of the iris diaphragm, which will limit its use. Therefore, the parameter optimization method is an excellent choice to obtain a SBS compressed pulse with Criterion 1 and Criterion 2.
Table 2. Comparison of experimental results between the two methods.
6. Conclusion
The spatial pulse width distributions in two different kinds of SBS media were compared, and both media show large differences in the pulse shapes at the beam center and the edge. The dependence of the energy efficiency, the pulse width, and the pulse temporal waveform of the reflected beam on the input energy were studied in a single-cell configuration. To make the pulse width distribution more uniform, we proposed two new methods: 1) blocking beam edge and 2) parameter optimization. A 40.7% energy efficiency was obtained using the first method. From the second method, the theoretical simulation and the experimental results for HT110 and FC40 showed that the medium HT110 with a narrow Brillouin linewidth can appropriately suppress the intensity fluctuation of pulse tail modulation in a single-cell configuration, and FC40 is better for a two-cell configuration during the SBS pulse compressed process. For HT110, the pulse width difference between the beam center and the edge can be minimized when the SBS pulse compression process reaches the saturation condition. The pulse width distribution range is from 640 ps to 820 ps, which represents a decrease of 96.6% relative to the value (~5360 ps) before the parameter optimization. In addition, the duration RSD value is reduced to less than 8%. The pulse stability is greatly improved after parameter optimization. An energy efficiency of 81.5% is obtained by the second method; this is two times higher than that of the first method. This work can provide meaningful guidance for both single-cell and two-cell SBS compressors to minimize the temporal pulse width difference between the central and the edge parts of the beam. It has a significant practical application value for the SBS pulse amplification technology.
Funding
Excellent Young Scientist Foundation (NSFC) (61622501); Air Force Office of Scientific Research (FA2386-16-1-4133).
Acknowledgments
Thank you very much for the support of the Ph.D. Short-Term Overseas Visiting Scholar Program of Harbin Institute of Technology.
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