Stimulated Raman scattering (SRS) is an important parametric instability in laser propagation in underdense plasma. It is a three-wave process with a pump electromagnetic (EM) wave (
In addition to long laser pulses, SRS also plays key roles in ultrashort relativistic-intensity laser–plasma interactions (
In past studies, the chirp of ultrashort laser pulses has been proposed to control the SRS process. It can be adjusted by introducing second-order dispersion (SOD) (
Sign up for High Power Laser Science and Engineering TOC. Get the latest issue of High Power Laser Science and Engineering delivered right to you！Sign up now
In this paper, the influence of SOD on SRS is experimentally studied. Optical spectroscopy and shadowgraphy were used to measure backward stimulated Raman scattering (B-SRS), side stimulated Raman scattering (S-SRS) and forward stimulated Raman scattering (F-SRS), respectively. For both positive and negative
2 Experimental setup
The experiment was performed with the 200 TW Ti:sapphire laser system at Shanghai Jiao Tong University. The schematic setup is shown in Figure 1(a). The main laser beam was focused by an F/4 off-axis parabola (OAP) mirror to a spot of 6 μm in diameter, containing approximately 25% of the laser energy. The laser has a central wavelength of
Figure 1.(a) Schematic layout of the experimental setup. (b) Image of the typical electron density distribution and the on-axis density lineout (red solid line) with = 0. (c) The corresponding shadowgraph, where the color bar denotes the signal count in the charge-coupled device (CCD). The laser is incident from the left-hand side. Here, ps is denoted when the main laser is at μm. The interferogram and shadowgraphs were taken at ps.
Table 1. Laser parameters for different with fixed energy (2.2 J).
A probe pulse was split from the main pulse and frequency doubled. The timing between the probe and the main pulse was adjusted by a variable delay line as shown in Figure 1(a). After passing through the interaction region, the probe beam was further split by a biprism for interferometric and shadowgraphic measurements. Figure 1(b) shows the typical density distribution of a plasma channel from the Abel-inverted interferogram, where
3 Experimental results and analysis
3.1 Influence of
Figure 2 shows spectra of the back-scattered light under different
Figure 2.The back-scattered light spectra with various (a) positive and (b) negative second-order dispersions. The absence of light within 730–870 nm is due to the total reflection of the M1 mirror in front of the collection fiber (Fiber 1 in Figure 1(a)).
To quantitatively compare the results, the red-shifted back-scattering (840–1100 nm) was integrated and plotted as a function of pulse duration
Figure 3.Integrated B-SRS spectral signal (840–1100 nm) versus pulse duration. The red solid squares are experimental results of positive and the blue solid squares correspond to negative . The error bars are due to shot-to-shot fluctuations. The red dashed line presents the theoretical calculation of with nm, whereas the blue dashed line is that with nm. The inset shows the calculated with duration for nm (red solid line) and nm (blue solid line), respectively.
In order to understand the influence of
The analysis of the Stokes sidebands has shown that B-SRS arises in the region of non-relativistic laser intensity (
As SRS develops in the rising edge of the laser pulse, where different wavelength components are contained, the chirp effect is straightforward. To simplify the estimation and investigate the effect of the laser wavelength on SRS growth, two cases with different single wavelengths, simulating the positive and negative chirps, were used to calculate the growth rates. We take
The inset in Figure 3 shows the growth rate as a function of pulse duration. Here,
3.2 Influence of
Figure 4 shows shadowgraphs of laser-produced plasma with different
Figure 4.Shadowgraphs showing side filaments at different second-order dispersions . (a) = +500 , (b) = +1000 , (c) = +2000 , (d) = –500 , (e) = –1000 and (f) = –2000 . The red arrows denote the filament direction at different spatial position. The white lines show the edges of the plasma channel.
Figure 5.The transverse plasma density profile in the cases of and . The solid lines and the dash-dot lines represent the profiles obtained at μm and μm, respectively.
The effect of
In addition, with the increase of
3.3 Influence of
Figures 6(a) and 6(b) show the transmitted spectra under positive
Figure 6.The spectra of transmitted light with (a) positive second-order dispersion and (b) negative second-order dispersion.
In addition, the laser chirp was found to have a significant impact on F-SRS. Sections 3.1and3.2 show similar features of B-SRS and S-SRS for both negative and positive chirps. For F-SRS, however, the transmitted optical spectrum depends significantly on the sign of the laser chirp. As shown in Figure 6(b), in all cases with a negative laser chirp, the spectra are similar to that with
3.4 Side-scattering angle dependence on
As shown in Figure 4 , there is a trend that the inclined angle of filaments relative to the laser axis gets smaller with the laser propagation (denoted by red arrows). In Figure 7, we plot the angles of both upward and downward filaments as a function of spatial position for different
Figure 7.The side-scattering angle at different spatial positions with (a) , (b) and (c) . Orange circles and green squares correspond to the measurements of the upward scattering angle with positive and negative , respectively. Blue triangles are the measurements of the downward scattering angle with negative . The orange (blue) dashed line is the calculation based on the maximum spatial growth rate with ().
To explain the spatially-dependent scattering angles, a model incorporating the growth of Raman scattering and the energy damping processes was used. The energy damping rate of plasma waves is expressed as follows:
Since side filaments were found to originate from the plasma channel edge, the local plasma density
Figure 8(a) shows the calculated plasma temperature distribution in the spatial position for different
Figure 8.(a) The plasma temperature for different . (b) The typical angular distributions of the spatial growth rate that correspond to the black crosses in (a). LD is for , and HD for .
Since filaments should be most evident near
In summary, we have reported a detailed study on the influence of the SOD,
 C. S. Liu, M. N. Rosenbluth, R. B. White. Phys. Fluids, 17, 1211(1974).
 S. C. Wilks, W. L. Kruer, K. Estabrook, A. B. Langdon. Phys. Fluids B, 4, 2794(1992).
 S. C. Wilks, W. L. Kruer, E. A. Williams, P. Amendt, D. C. Eder. Phys. Plasmas, 2, 274(1995).
 T. M. Antonsen, P. Mora. Phys. Rev. Lett., 69, 2204(1992).
 K. Krushelnick, A. Ting, H. R. Burris, A. Fisher, C. Manka, E. Esarey. Phys. Rev. Lett., 75, 3681(1995).
 K.-C. Tzeng, W. B. Mori, C. D. Decker. Phys. Rev. Lett., 76, 3332(1996).
 A. G. R. Thomas, S. P. D. Mangles, Z. Najmudin, M. C. Kaluza, C. D. Murphy, K. Krushelnick. Phys. Rev. Lett., 98, 054802(2007).
 T. Matsuoka, C. Mcguffey, P. G. Cummings, Y. Horovitz, F. Dollar, V. Chvykov, G. Kalintchenko, P. Rousseau, V. Yanovsky, S. S. Bulanov, A. G. R. Thomas, A. Maksimchuk, K. Krushelnick. Phys. Rev. Lett., 105, 034801(2010).
 E. Esarey, C. B. Schroeder, W. P. Leemans. Rev. Mod. Phys., 81, 1229(2009).
 T. Nakamura, S. V. Bulanov, T. Z. Esirkepov, M. Kando. Phys. Rev. Lett., 105, 135002(2010).
 M. H. Helle, D. F. Gordon, D. Kaganovich, Y. Chen, J. P. Palastro, A. Ting. Phys. Rev. Lett., 117, 165001(2016).
 O. Silva, M. Marti, J. R. Davies, R. A. Fonseca, C. Ren, F. S. Tsung, W. B. Mori. Phys. Rev. Lett., 92, 015002(2004).
 S. Corde, K. T. Phuoc, G. Lambert, R. Fitour, V. Malka, A. Rousse, A. Beck, E. Lefebvre. Rev. Mod. Phys., 85(2013).
 G. B. Zhang, M. Chen, X. H. Yang, F. Liu, S. M. Weng, Y. Y. Ma, D. B. Zou, T. P. Yu, F. Q. Shao, Z. M. Sheng. Opt. Express, 28, 29927(2013).
 A. Modena, Z. Najmudin, A. E. Dangor, C. E. Clayton, K. A. Marsh, C. Joshi, V. Malka, C. B. Darrow, C. Danson, D. Neely, F. N. Walsh. Nature, 377, 606(1995).
 N. Hafz, M. S. Hur, G. H. Kim, C. Kim, I. S. Ko, H. Suk. Phys. Rev. E, 73, 016405(2006).
 A. E. Hussein, J. Ludwig, K. Behm, Y. Horovitz, P.-E. Masson-Laborde, V. Chvykov, A. Maksimchuk, T. Matsuoka, C. McGuffey, V. Yanovsky, W. Rozmus, K. Krushelnick. New J. Phys., 20, 073039(2018).
 D. Kaganovich, B. Hafizi, J. P. Palastro, A. Ting, M. H. Helle, Y.-H. Chen, T. G. Jones, D. F. Gordon. Phys. Plasmas, 23, 123104(2016).
 H. Jang, M. S. Hur, J. M. Lee, M. H. Cho, W. Namkung, H. Suk. Appl. Phys. Lett., 93, 071506(2008).
 W. P. Leemans, P. Catravas, E. Esarey, C. G. R. Geddes, C. Toth, R. Trines, C. B. Schroeder, B. A. Shadwick, J. van Tilborg, J. Faure. Phys. Rev. Lett., 89, 174802(2002).
 J. Faure, J.-R. Marquès, V. Malka, F. Amiranoff, Z. Najmudin, B. Walton, J.-P. Rousseau, S. Ranc, A. Solodov, P. Mora. Phys. Rev. E, 63, 065401(2001).
 T.-W. Yau, C.-J. Hsu, H.-H. Chu, Y.-H. Chen, C.-H. Lee, J. Wang, S.-Y. Chen. Phys. Plasmas, 9, 391(2002).
 B. S. Rao, A. Moorti, P. A. Naik, P. D. Gupta. Phys. Rev. ST Accel. Beams, 16, 091301(2013).
 A. Permogorov, G. Cantono, D. Guenot, A. Persson, C.-G. Wahlström. Sci. Rep., 12, 3031(2022).
 H. T. Kim, V. B. Pathak, K. H. Pae, A. Lifschitz, F. Sylla, J. H. Shin, C. Hojbota, S. K. Lee, J. H. Sung, H. W. Lee, E. Guillaume, C. Thaury, K. Nakajima, J. Vieira, L. O. Silva, V. Malka, C. H. Nam. Sci. Rep., 7, 10203(2017).
 E. S. Dodd, D. Umstadter. Phys. Plasmas, 8, 3531(2001).
 V. B. Pathak, J. Vieira, R. A. Fonseca, L. O. Silva. New J. Phys., 14, 023057(2012).
 C. B. Schroeder, E. Esarey, B. A. Shadwick, W. P. Leemans. Phys. Plasmas, 10, 285(2003).
 N. Pathak, A. Zhidkov, T. Hosokai, R. Kodama. Phys. Plasmas, 25, 013119(2018).
 Y. Fang, T. P. Yu, X. L. Ge, S. Yang, W. Q. Wei, T. Yuan, F. Liu, M. Chen, J. Q. Liu, Y. T. Li, X. H. Yuan, Z. M. Sheng, J. Zhang. Plasma. Phys. Control. F, 58, 45025(2016).
 P. Tournois. Opt. Commun., 140, 245(1997).
 C. A. Coverdale, C. B. Darrow, C. D. Decker, W. B. Mori, K.-C. Tzeng, K. A. Marsh, C. E. Clayton, C. Joshi. Phys. Rev. Lett., 74, 4659(1995).
 P. B. Corkum, N. H. Burnett, F. Brunel. Phys. Rev. Lett., 62, 1259(1989).
 N. H. Burnett, P. B. Corkum. J. Opt. Soc. Am. B, 6, 1195(1989).
 M. V. Ammosov, N. B. Delone, V. P. Krainov. Sov. Phys. JETP, 64, 1191(1986).
 F. Sylla, A. Flacco, S. Kahaly, M. Veltcheva, A. Lifschitz, G. Sanchez-Arriaga, E. Lefebvre, V. Malka. Phys. Rev. Lett., 108, 115003(2012).
 A. K. Arunachalam, M. B. Schwab, A. Sävert, M. C. Kaluza. New J. Phys., 20, 003027(2018).
 W. M. Wood, C. W. Siders, M. C. Downer. Phys. Rev. Lett., 67, 3523(1991).
 J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa, H. Kotaki, T. Tajima. Phys. Plasmas, 7, 5223(2000).
 A. Higginson, S. Zhang, M. Bailly-Grandvaux, C. McGuffey, K. Bhutwala, B. J. Winjum, J. Strehlow, B. Edghill, M. Dozières, F. S. Tsung, R. Lee, S. Andrews, S. J. Spencer, N. Lemos, F. Albert, P. King, M. S. Wei, W. B. Mori, M. J.-E Manuel, F. N. Beg. Phys. Rev. E, 103, 033203(2021).
Set citation alerts for the article
Please enter your email address