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Abstract
We demonstrate Brillouin amplification of sub-phonon lifetime Stokes pulses based on an active frequency matching method. The main purpose is to extend Brillouin amplification to further applications requiring shorter pulse widths and break the phonon lifetime limit. A combination of theoretical simulations and experiments is used to achieve this goal. As a result, the Brillouin transient gain is identified as the key parameter to achieve sub-phonon lifetime Brillouin amplification. The experimental results agree well with the theoretical simulation.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Stimulated Brillouin scattering (SBS) is a process in which the pump and the Stokes pulses interact with one another through an acoustic wave excited by lasers. While the Stokes signal propagates backwards, the leading edge is amplified by the incident pulse and extracts much energy. Pulse compression comes from the rapid depletion of SBS gain. As a result, energy is transferred from the pump pulse to the phase-conjugated Stokes pulse and the Stokes pulse is compressed [1–3]. For a number of years, SBS has been known to provide high-efficiency laser pulse compression with high energy (joule level) [4–7], which has many applications in solid-state laser systems while providing phase conjugation, pulse compression, and power amplification.
In SBS pulse compression research, for the purpose of power enhancement, most studies strive to achieve the shortest pulse width. Generally, the compressed pulse width limit was regarded as the phonon lifetime [8], however, recent studies have demonstrated sub-phonon lifetime pulse compression experimentally [9–12] by special pulse compression configurations such as those with folded optical paths for compressing the pulse twice or comprising long amplification cells. Currently the SBS pulse compression limit is regarded as being determined by the acoustic field oscillation period, which can be explained by the construction and the development of the initial Stokes signal [13]. The boundary condition in the coupled equation determines the final compressed results [14]. However, further applications of SBS pulse compression are limited for several reasons. On the one hand, optical breakdown occurs in the SBS compressor limiting the compressed Stokes pulse to higher intensities. On the other hand, the Stokes signal is increased by noise [15], and the fluctuation in the medium reduces the temporal and spatial fidelity of the Stokes beam [16–18].
For further SBS applications, SBS pulse amplification with Stokes seed injection was proposed [19]. During injection of the Stokes seed, the phase of the acoustic field in the Brillouin medium is locked. Fluctuations of the Stokes beam can be reduced, and the stability improved. For seed injection, the boundary conditions are different from that of self-excited pulse compression, and pulse fidelity in this SBS configuration should be explained in another way. However, Stokes pulse broadening after amplification was observed experimentally. To solve this problem and to extend Brillouin amplification to new applications, the pulse fidelity in Brillouin amplification needs to be better understood.
In this paper, we theoretically and experimentally investigate the temporal pulse fidelity in seed injection SBS. Laser pulses achieved by SBS pulse compression can provide short pulses with narrow spectrum. Previous work has proposed that hundreds picoseconds can be amplified through SBS [19]. The purpose of this paper is to explore the pulse width limit in Brillouin amplification for further applications of tens of picosecond pulses. To achieve tens picosecond pulses amplification, sub-phonon lifetime pulse amplification through SBS must be texted. For most Brillouin medium has a phonon lifetime higher than 100 ps. To this end, we have theoretically and experimentally studied how the amplified Stokes pulse broadening is caused by the limited phonon lifetime. By providing higher transient gain in Brillouin amplification, sub-phonon lifetime Stokes pulse amplification with minimal pulse broadening is achieved experimentally.
2. Theoretical analysis
Stimulated Brillouin Scattering originates from light interaction with propagating acoustic waves. The light wave can be described by Maxwell equations, acoustic waves raise from electrostrictive effect and can be described through Navior-Stokes equation. These equations presents a describing the propagation and interaction of laser and acoustic waves, and energy will be transferred from the pump to the Stokes field. To analyze the effect of phonon lifetime on stimulated Brillouin scattering theoretical simulations are carried based on the SBS equations as follows:
where ES, Ep represent the Stokes and the pump optical fields in the SBS process, ρ represents the acoustic field, n is the refractive index of the medium, c is the speed of light in vacuum, γ is the electrostrictive coefficient, and ΓB is the Brillouin gain linewidth. qB = ks + kp represents the vector of the acoustic wave field, g = γ2ω2/(2nc3Vρ0) is the gain coefficient, and τB = 1/ΓB is the phonon lifetime, α reprents the absorption loss.
In seed injection SBS amplification, the Stokes seed is a modulated 200 ps Gaussian pulse. Under these conditions, a transient model should be used because the pulse width of the Stokes pulse is much shorter than that of the pump pulse. In contrast to self-excited SBS, the phase of the acoustic field is locked by the injected Stokes seed and is thus more stable than self-excited process.
To solve the SBS equations, the differential method is used to determine a numerical solution. It is assumed that the acoustic field will be excited as soon as the pump meets the injected Stokes seed. For seed injection SBS, the initial power determined by the injection When the pump pulse is exhausted, the amplification process is saturated. Theoretical simulation of how the output of the Stokes pulse width varies with the phonon lifetime has been performed at a pump intensity of 100 MW/cm2 with 200 ps Stokes seed injection. The Brillouin gain coefficient is set to 1.3cm/GW, which is the true gain coefficient of FC-43. The results are shown in Fig. 1. At a 100 MW/cm2 pump intensity, the amplified Stokes pulse is broadened with increasing of phonon lifetime. When the phonon lifetime is 1.5 times the Stokes pulse width, the broadened amplified Stokes pulse width grows linear with the phonon lifetime and ends at phonon lifetime 0.9 ns.
The performance of the Stokes pulse amplification are shown in the waveforms of Fig. 2. SBS amplification simulation of several typical phonon lifetimes are investigated. Since the phonon lifetime affects the relaxation time of the Stokes and the pump pulses in SBS. The relaxation time increases as the phonon lifetime increases, but the single-pass gain decreases with decreasing acoustic intensity. If the phonon lifetime is does not exceed the Stokes pulse width, the amplified Stokes pulse width remains the same as the injected pulse. As shown in Fig. 2(a), the amplified Stokes pulse width remains at 200 ps. If the Stokes pulse width is smaller than the phonon lifetime, after the Stokes main pulse passes, the pulse tail can still interact with the pump light to extract energy resulting in a trailing edge of the amplified pulse. As shown in Fig. 2(b), with a phonon lifetime of 0.6 ns, the amplified Stokes pulse width has broadened to 1.06 ns for FWHM (Full width at half maximum). The phonon lifetime also reflects the energy extraction efficiency. As the lifetime of the phonon increases, the gain of the pump pulse to the Stokes pulse decreases per unit time, and the overall energy extraction efficiency of the Stokes pulse decreases. With phonon lifetime increase, the tail of the Stokes pulse also increases. As shown in Fig. 2(c), the phonon lifetime increases to 1.3 ns, the FWHM of the amplified Stokes pulse under these conditions is 0.32 ns, but it has a large tail. The pulse falling edge has a duration of 2.7 ns from the peak to the bottom (10% of the peak). This is because as the phonon lifetime increases, the transient gain decreases. Under these conditions, the Stokes pulse can only extract a small amount of energy from the pump pulse, but the relaxation time of the acoustic field is long, thus the tail of the Stokes pulse continues interacting with the pump pulse resulting in waveform distortion.
Fig. 2 Theoretical analysis of SBS amplification at different phonon lifetimes (a) 0.2 ns, (b) 0.6 ns, and (c) 1.3 ns.
The transient represents the strength of coupling between the acoustic waves and the optical waves caused by electrostrictive effect. The unit of transient gain is(cm·ns)−1. As the figure shown in Fig. 3, the Y-axis represents the relative intensity of transient gain. Theoretical simulation is carried at gain coefficient 1.3cm/GW and pump intensity 100MW/cm2. It can be observed that the Brillouin transient gain decreases exponentially with the increasing of the phonon lifetime.
3. Experimental setup
A schematic diagram of the experiment is shown in Fig. 4. The Before SBS interaction, the frequency shift between the Stokes and the pump pulses is modulated at the front-end [19], then the stacked pulse is amplified in main amplifier. As SBS produces a frequency shift in the scattered wave spectra, it is necessary for the seed laser to be downshifted so that coupling between the laser beams is realized. Thus, the acoustic wave is driven by the coherence of the Stokes and pump light. Frequency-mismatch conditions will result in a decrease in the gain. In our case, the pump and the Stokes pulses are coupled with pulse stacking, so the frequency shift between the Stokes and pump light should be modulated carefully. The Stokes pulse is a 200-ps Gaussian pulse and the pump pulse is a 5-ns eighth-order super-Gaussian pulse. The amplified Stokes and pump pulses are amplified to the same intensity to reduce the risk of optical damage. Finally, the energy is transferred from the pump pulse to the Stokes pulse through a non-collinear SBS structure.
The experimental optical path is shown in Fig. 5. In the experiments, the laser wavelength is 527 nm, a noncollinear SBS cell is used for energy transmission. Compared with collinear structure, this non-collinear structure does not require complex optical systems, i.e., the use of polarizers and wave plates for beam separation and coupling is not required. Therefore, it can simplify the optical path and reduce the damage risk of the amplification system. The stacked pulse is injected into the SBS cell after frequency doubling and spatial filtering in the laser system [20] (not shown). In order to increase the pump intensity, the laser beam diameter is reduced 2:1 by a 1000 mm convex lens and a 500 mm concave lens, and the spot size is 21 × 21 mm. After passing through the cell, the laser will re-enter the cell after reflections from two mirrors, so that the Stokes pulse can extract energy from the pump pulse. The delay time between the Stokes pulse and the pump pulse is determined to 11.3 ns by the optical path length. This time delay is designed to ensure that the Stokes pulse will be able to interact with the pump pulse as soon as it re-enters into the Brillouin cell. The crossing angle is set to 1.9° to ensure an adequate interaction volume in the Brillouin medium.
All beam measurements are sampled by wedge plates, and before experimental data collection, the alignment of the wedge plates is inspected for accuracy of measurement. There are two wedge plates in the optical path, one before and one after the SBS cell. Each wedge plate is a piece of quartz. The measured light is sampled from its Fresnel reflection on both the front and the back surface. the reflected light from the front and the back surface propagate in different direction and get separated, for there is a 3° angle. The energy, the waveform and the beam profile can be measured separately. Waveform are measured by photodiodes (UPD-50-UP, ALPHALAS GmbH), and displayed on an oscilloscope (DPO71604B, Tektronix, Inc.). The energy is measured by energy meter (PE100BF-DIF ROHS, Ophir Optronics Solutions Ltd). The measured energy is the sum of the Stokes and the stacked pump pulse. The Stokes and the pump energies can be calculated according to the integrated area which can be obtained from the oscilloscope.
To experimentally investigate the effect of the phonon lifetime on SBS amplification, three SBS media are characterized, the parameters of these media are listed in Table 1.
Table 1. Brillouin media parameters
In Table 1, FC-43 and FC-3283 are two kinds of fluorocarbon proposed as liquid at room temperature and Xe is a gas medium, for comparison with liquid and gas SBS media. According to Dolgopolov and Damzen's work [21,22], the Brillouin parameters of gases are associated with pressure (at room temperature, 20 °C), the Brillouin gain coefficient g of a gas is proportional to the square of the pressure, and the Brillouin phonon lifetime in the gas increases linearly with pressure. The Brillouin gain coefficient, the phonon lifetime and the acoustic frequency are theoretically calculated before the experiments.
In the experiments, the pump pulse is configured as an 8th order super-Gaussian pulse with a 5 ns pulse width, and the SBS cell length is adjusted for sufficient interaction between the pump and Stokes pulses. For liquid media, the cell length is set to 60 cm, because the refractive index of the two kinds of fluorocarbon are similar. For the gas medium, the cell length is set to 75 cm.
4. Results and discussion
Since the chosen Brillouin media in the experiment have different gain coefficients, we modulated the pump intensity to ensure the steady state single-pass gains (G = gIL, I represents the pump intensity, L represents the interaction length of the Stokes and the pump) of each medium are equal under the respective experimental conditions in order to reduce the effect of this difference. Further, to reduce the risk of optical damage, the Stokes and pump pulses are amplified to the same intensities.
Typical experimental results are shown in Fig. 6. In Fig. 6(a), while the phonon lifetime of the medium is close to the Stokes pulse width, under these conditions, the oscillation period of the acoustic field is smaller than the Stokes pulse width. During the phonon relaxation time, the energy can be completely transferred by the acoustic field. As a result, the amplified Stokes pulse has a high fidelity and no significant broadening effect was observed, and the output Stokes pulse width remains at 200 ps with an energy extraction efficiency of 51%. As the phonon lifetime increases, as shown in Fig. 6(b), Stokes pulse gain decreases. Thus, power increase and energy extraction efficiency are decreased. As the relaxation time further increases, the Stokes pulse tail continues to interact with the pump pulse, resulting in an amplified Stokes pulse that has been noticeably broadened. The amplified Stokes pulse width is 0.53 ns and the energy extraction efficiency has dropped to 29%. In Fig. 6(c), the Brillouin medium has been replaced by Xe, increasing the phonon lifetime to 5.5 times the injected Stokes pulse width. It can be observed that the broadening of the amplified Stokes pulse is more noticeable than that of Fig. 6(b). The pulse tail has a duration of 2.7 ns from the peak to the bottom (10% of the peak) and the energy extraction efficiency is now only 14%. The tail of the amplified Stokes pulse contains most of the energy extracted from the pump pulse, resulting in an amplified laser pulse that is deformed.
Fig. 6 SBS amplification with different Brillouin media (a) FC-43 at pump 210 MW/cm2, (b) FC-3283 at pump 90 MW/cm2, and (c) 6 atm Xe at pump 650 MW/cm2.
While at a certain Brillouin gain, the phonon lifetime in the Brillouin medium has a significant effect on the amplified pulse waveform. Increasing the phonon lifetime reduces the Brillouin transient.
In order to analyze the influence of the transient gain caused by the phonon lifetime and its effect on Brillouin amplification, a theoretical simulation of how the amplified Stokes pulse width varies with the pump intensity for FC-3283 for an injected pulse width of 200 ps was conducted, and is shown in Fig. 7. The injected Stokes intensity is with the pump intensity as is the case in the experiment. The output pulse width decreases with the square of the injected pump intensity. It can be observed that as the pump intensity increases further, pulse broadening in FC-3283 decreases. As the injection pump intensity increases, the Brillouin transient gain increases, the Stokes pulse leading edge extracts more energy and undergoes steepening, reducing pulse broadening.
Experimental results of Brillouin amplification in FC-3283 with a pump intensity of 150 MW/cm2 for comparison with the theoretical simulation are shown in Fig. 8. Compared with the experimental results for a pump intensity of 90 MW/cm2, the power increase and energy extraction efficiency are significantly increased. Further, pulse broadening is suppressed and the amplified Stokes pulse width is 360 ps. In addition to phonon lifetime affecting the Stokes pulse width, the Brillouin gain also has an effect on the output Stokes pulse width. With increasing transient gain, the pump pulse is gradually depleted after interaction with the Stokes pulse. Once the Stokes pulse is established, less of the pump pulse residual energy will be transferred to the tail of the Stokes pulse and pulse broadening can be suppressed. Thus, by increasing the transient gain in Brillouin amplification, even in long phonon lifetime media Stokes pulse broadening can be suppressed.
A further parameter that affects Brillouin amplification, is the pump pulse shape, in this case the pump pulse is an 8th order super Gaussian wave. Since the pump pulse approximates to a square wave, the power distribution is relatively stable. In comparison with traditional generator-amplifier SBS structures in which the pump is a Gaussian pulse, the super Gaussian pulse has a steeper rising front edge, when it meets the Stokes pulse, the pump power is at a high level. For a Gaussian pump pulse, when the pulse front interacts with the Stokes pulse at low power, it is difficult for the Stokes pulse to deplete the pump energy, resulting in remaining energy to continue to interact with the Stokes tail, and pulse broadening occurs in long phonon lifetime media.
As a result of the above analysis, sub-phonon lifetime pulses can be achieved if high Brillouin transient gain is applied. While the energy of the pump pulse is depleted, there is no more energy for the Stokes trailing edge to interact with, and the Stokes pulse fidelity after amplification is guaranteed. In the future experimental setup, the laser pulse with pulse width ~50 ps will be built in the fiber front end by using an arbitrary waveform generator with a bandwidth of 25G or higher. And then, by selecting Brillouin medium with short phonon lifetime (for example, FC-43), Brillouin amplification with a pulse width less than 100 ps can be achieved by providing high pump intensity.
5. Conclusion
In summary, we demonstrate how to achieve sub-nanosecond pulses Brillouin amplification. This is achieved by an active frequency matching seed injection SBS structure. We show that sub-nanosecond pulses Brillouin amplification can be achieved by providing high transient gain and super-Gaussian pump pulse, as a result, the amplified pulse broadening is suppressed due to pump exhausted. Therefore, sub-phonon lifetimes of tens picosecond pulses amplification can be expected and demonstrated by further experimental work.
Funding
China Postdoctoral Science Foundation (No. BX20180085) and the National Natural Science Foundation of China (NSFC) (No. 61622501).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. R. W. Boyd, Nonlinear optics (Springer, 2003).
2. M. J. Damzen, V. I. Vlad, V. Babin, and A. Mocofanescu, Stimulated Brillouin scattering: fundamentals and applications (Taylor and Francis, 2003).
3. D. T. Hon, “Pulse compression by stimulated Brillouin scattering,” Opt. Lett. 5(12), 516–518 (1980). [CrossRef] [PubMed]
4. C. Feng, X. Xu, and J.-C. Diels, “Generation of 300 ps laser pulse with 1.2 J energy by stimulated Brillouin scattering in water at 532 nm,” Opt. Lett. 39(12), 3367–3370 (2014). [CrossRef] [PubMed]
5. A. Mitra, H. Yoshida, H. Fujita, and M. Nakatsuka, “Sub nanosecond pulse generation by stimulated Brillouin scattering using FC-75 in an integrated setup with laser energy up to 1.5J,” Jpn. J. Appl. Phys. 45(3A), 1607–1611 (2006). [CrossRef]
6. X. Zhu, Y. Wang, Z. Lu, and H. Zhang, “Generation of 360 ps laser pulse with 3 J energy by stimulated Brillouin scattering with a nonfocusing scheme,” Opt. Express 23(18), 23318–23328 (2015). [CrossRef] [PubMed]
7. H. Yoshida, T. Hatae, H. Fujita, M. Nakatsuka, and S. Kitamura, “A high-energy 160-ps pulse generation by stimulated Brillouin scattering from heavy fluorocarbon liquid at 1064 nm wavelength,” Opt. Express 17(16), 13654–13662 (2009). [CrossRef] [PubMed]
8. M. Damzen and H. Hutchinson, “Laser pulse compression by stimulated Brillouin scattering in tapered waveguides,” IEEE J. Quantum Electron. 19(1), 7–14 (1983). [CrossRef]
9. C. Feng, X. Xu, and J. C. Diels, “High-energy sub-phonon lifetime pulse compression by stimulated Brillouin scattering in liquids,” Opt. Express 25(11), 12421–12434 (2017). [CrossRef] [PubMed]
10. Z. Liu, Y. Wang, Y. Wang, S. Li, Z. Bai, D. Lin, W. He, and Z. Lu, “Pulse-shape dependence of stimulated Brillouin scattering pulse compression to sub-phonon lifetime,” Opt. Express 26(5), 5701–5710 (2018). [CrossRef] [PubMed]
11. I. Velchev and W. Ubachs, “Statistical properties of the Stokes signal in stimulated Brillouin scattering pulse compressors,” Phys. Rev. A 71(4), 043810 (2005). [CrossRef]
12. I. Velchev, D. Neshev, W. Hogervorst, and W. Ubachs, “Pulse compression to the subphonon lifetime region by half-cycle gain in transient stimulated Brillouin scattering,” EEE J. Quantum Electron. 35(12), 1812–1816 (1999). [CrossRef]
13. S. Schiemann, W. Ubachs, and W. Hogervorst, “Efficient temporal compression of coherent nanosecond pulses in a compact SBS generator-amplifier setup,” EEE J. Quantum Electron. 33(3), 358–366 (1997). [CrossRef]
14. H. Yuan, Y. Wang, Z. Lu, Y. Wang, Z. Liu, Z. Bai, C. Cui, R. Liu, H. Zhang, and W. Hasi, “Fluctuation initiation of Stokes signal and its effect on stimulated Brillouin scattering pulse compression,” Opt. Express 25(13), 14378–14388 (2017). [CrossRef] [PubMed]
15. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990). [CrossRef] [PubMed]
16. S. Afshaarvahid, V. Devrelis, and J. Munch, “Nature of intensity and phase modulations in stimulated Brillouin scattering,” Phys. Rev. A 57(5), 3961–3971 (1998). [CrossRef]
17. M. S. Mangir, J. J. Ottusch, D. C. Jones, and D. A. Rockwell, “Time-resolved measurements of stimulated-Brillouin-scattering phase jumps,” Phys. Rev. Lett. 68(11), 1702–1705 (1992). [CrossRef] [PubMed]
18. J. Munch, R. F. Wuerker, and M. J. Lefebvre, “Interaction length for optical phase conjugation by stimulated Brillouin scattering: an experimental investigation,” Appl. Opt. 28(15), 3099–3105 (1989). [CrossRef] [PubMed]
19. H. Yuan, Y. Wang, Z. Lu, and Z. Zheng, “Active frequency matching in stimulated Brillouin amplification for production of a 2.4 J, 200 ps laser pulse,” Opt. Lett. 43(3), 511–514 (2018). [CrossRef] [PubMed]
20. S. Li, Y. Wang, Z. Lu, L. Ding, P. Du, Y. Chen, Z. Zheng, D. Ba, Y. Dong, H. Yuan, Z. Bai, Z. Liu, and C. Cui, “High-quality near-field beam achieved in a high-power laser based on SLM adaptive beam-shaping system,” Opt. Express 23(2), 681–689 (2015). [CrossRef] [PubMed]
21. M. J. Damzen, M. H. R. Hutchinson, and W. A. Schroeder, “Direct measurement of the acoustic decay times of hypersonic waves generated by SBS,” EEE J. Quantum Electron. 23(3), 328–334 (1987). [CrossRef]
22. A. M. Dudov, S. A. Buyko, Y. V. Dolgopolov, V. A. Eroshenko, G. G. Kochemasov, S. M. Kulikov, V. N. Novikov, A. F. Shkapa, S. A. Sukharev, L. I. Zykov, and A. M. Scott, “SBS properties of high-pressure xenon,” International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, (1997). [CrossRef]
23. Z. X. Zheng, W. L. J. Hasi, H. Zhao, S. X. Cheng, X. Y. Wang, D. Y. Lin, W. M. He, and Z. W. Lü, “Compression characteristics of two new SBS mediums to generate 100-ps pulse for shock ignition,” Appl. Phys. B 116(3), 659–663 (2014). [CrossRef]
24. W. L. J. Hasi, X. Y. Wang, S. X. Cheng, Z. M. Zhong, Z. Qiao, Z. X. Zheng, D. Y. Lin, W. M. He, and Z. W. Lu, “Research on the compression properties of FC-3283 and FC-770 for generating pulse of hundreds picoseconds,” Laser Part. Beams 31(2), 301–305 (2013). [CrossRef]
