Abstract
1 Introduction
With the development of laser technology, especially the invention of the chirped-pulse amplification (CPA) technique[1], laser peak power and focused intensity have been increasing dramatically[2,3]. Simultaneously, intense laser–matter interactions have attracted great interest since they not only promise wide potential applications but also give birth to rich physical phenomena[4,5]. With the increase of laser power, however, the generation and manipulation of intense laser pulses have become more and more challenging due to the limited damage threshold of traditional optical devices[6]. In contrast, plasma-based optical elements can sustain ultra-high light intensity and hence provide an alternative approach to the generation and manipulation of intense lasers.
In the last decades, plasma optics has developed into an attractive methodology for the manipulation and further amplification of intense lasers. For example, plasma mirrors have been widely used to enhance the contrast of intense laser pulses[7] or tightly focus laser pulses toward extreme intensities[8]. More significantly, both stimulated Raman and Brillouin scatterings in plasmas could be employed to amplify intense laser pulses[9–12]. Moreover, magnetized plasmas may have some specific advantages in the control and amplification of intense laser pulses[13–16]. Further, holographic plasma lenses have recently been proposed as a novel plasma optical device for broad applications[17–19]. In particular, laser-induced plasma density gratings (PDGs) have been extensively studied and proposed for wide potential applications, including the temporal compression, polarization control and manipulation of intense laser pulses[20–25]. Analogously, laser-induced plasma density modulations can tune laser power distribution to achieve a symmetric inertial confinement fusion (ICF) implosion in the so-called crossed-beam energy transfer[26–28].
In this paper, we investigate the spatial and temporal distributions of the polarization state of a probe laser pulse after it passes through a PDG. As shown in Figure 1, the PDG is driven by two intersecting laser pulses that have Gaussian intensity profiles in both the longitudinal and transverse directions. Due to the birefringence caused by the PDG, it could be employed as a waveplate for an ultrashort laser pulse. In this study, however, the formed PDG is not only nonuniform in space but also varies over time. Therefore, the refractive index modulation induced by such a PDG will be nonuniform and time-dependent. As a result, the probe laser pulse may be depolarized by such a dynamic PDG, that is, its polarization state becomes variable in both space and time. The laser beams with varying polarization states may play an important role in mitigating parametric instabilities in laser–plasma interactions relevant to ICF[29,30]. The paper is organized as follows. The formation and evolution of the PDG are simulated and analyzed in Section 2. The laser depolarization by the dynamic PDG is illustrated in Section 3. Finally, the conclusion and some discussions are presented in Section 4.
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
Figure 1.Schematic of laser depolarization by a PDG. The PDG driven by intersecting laser pulses #1 and #2 will be nonuniform in the direction and also time-dependent. After the probe laser pulse passes through such a PDG, its polarization state will become nonuniform and time-dependent.
2 Dynamics of the plasma density grating
To understand the depolarization of laser beams, we first investigate the dynamics of the PDG, which can be well described by the fluid model in the linear stage in 1D cases[31,32]. For simplicity, two driver laser beams in the theoretical analysis are assumed to have constant intensities, and they propagate oppositely along the positive or negative
Here, the two driver laser beams have the same frequency
Driven by such a pondermotive force, the electron density will be modified firstly. Then, the ions will follow the electrons due to the charge-separation field. Finally, a periodic plasma density structure that is termed as the PDG will be induced. In the linear growth stage, the density perturbation of the PDG can be estimated as follows:
where
To illuminate the complicated dynamics of the PDG, a 2D particle-in-cell (PIC) simulation is conducted using the Osiris code[34]. The simulation box is
The PDG structure at
Figure 2.The electron density distribution of (a) the overall plasma region and (b) the center region at , respectively. (c) The corresponding electron density profiles along the
More importantly, the plasma density modulation will be time-dependent. The time evolution of the plasma density profile along the
Figure 3.The time evolution of the electron density profile along the -axis. Note that the PDG experiences a time periodic process of formation, saturation and collapse. The simulation parameters are the same as those in
3 Depolarization of the laser pulse
The propagation of an electromagnetic wave through the PDG is similar to the electron movement in crystalline solids. Therefore, the theory of energy bands in solid physics can be employed for the theoretical analysis of the laser propagation through the PDG. For simplification, the PDG is assumed to be composed of alternating high- and low-density layers. Each high-density layer has a uniform density
while for the p-polarized (transverse magnetic (TM) mode) wave it is given by the following:
where
Due to their different dispersion relations, the s- and p-polarized electromagnetic waves will have different phase velocities. More importantly, the phase velocity difference will vary in both time and space as long as the PDG is spatially nonuniform and temporally variable. Using the electron density profile presented in Figure 2(d), the phase velocity of the s- and p-polarized light waves along the
Figure 4.The phase velocities of the s-polarized () and p-polarized () light waves obtained from Equations (
Since the phase velocity difference varies in time and space, the resultant phase difference between the s- and p-polarized light components of a probe laser pulse will also change with time and space. Therefore, the final polarization state of the probe laser pulse that initially has both non-zero s- and p-polarized light components will vary in both space and time. That is to say, the probe laser pulse will be depolarized by the dynamic PDG.
To illuminate the laser depolarization by the dynamic PDG, some additional PIC simulations are conducted. In the first simulation, the parameters of two driver laser pulses and the initial plasma are the same as those used in Figure 3. In addition to two driver laser pulses, a probe laser pulse whose polarization plane is oriented at 45° with respect to the
To describe the laser polarization state, the Stokes parameters
During the probe laser propagation in the PDG, its s- and p-polarized light components gradually become out of phase due to their different phase velocities. More importantly, the phase difference between them varies in time and space. As a result, the Stokes parameter distributions of the probe laser pulse become very complicated after it passes through the PDG, as shown in Figure 5. Above all, the parameters
Figure 5.The spatial distributions of the Stoke parameters (a) , (b) , (c) and (d) of the probe laser pulse at after it passes through the PDG. Here, all Stokes parameters are normalized to the instantaneous maximum laser intensity . The simulation parameters are given in the text.
Figure 6.(a) Longitudinal profiles of the Stokes parameters at and (b) transverse profiles of the Stokes parameters at . (c) Longitudinally averaged polarization degree and (d) transversely averaged polarization degree . The simulation parameters are the same as those in
For the Stokes parameters, they always satisfy
will be obviously smaller than one, where
In the above analysis, the PDG is induced by two counter-propagating driver laser pulses, and the probe laser is incident along the direction orthogonal to the driver lasers. Actually, the PDG can also be induced by two intersecting driver laser pulses with an intersection angle
Figure 7.Laser depolarization by the PDG that is induced by two intersecting laser pulses with an intersection angle .
where the second term on the right-hand side induces the formation of the PDG. According to Equation (7), the periodic length of the PDG is related to the angle as
To investigate the laser depolarization in the beam-crossing region, an additional PIC simulation is performed. In the simulation, a plasma with a uniform density
Analogous to Figure 5, Figure 8 shows that the Stokes parameter distributions of the probe laser pulse become very complicated after it passes through the PDG in this case. The periodic variations in parameters U and V are clearly illustrated in Figures 8(c) and 8(d), respectively. Such periodic variations in the Stokes parameters are also shown by the longitudinal (at
Figure 8.The spatial distributions of the Stoke parameters (a)
Figure 9.(a) Longitudinal profiles of the Stokes parameters at
4 Discussion and conclusions
Since the normalized parameters are used in the simulations, such a dynamic PDG can in principle be used to depolarize the intense laser pulses at any wavelength. However, the density of the employed background plasma should increase for a shorter laser wavelength, which is often used in ICF. Correspondingly, collisional absorption may become the dominant process in a denser plasma. Fortunately, laser energy deposition via the collisional absorption usually is of benefit to ICF[36]. In addition, we find that the plasma temperature will increase gradually. Correspondingly, the peak density of the PDG will decrease due to the enhanced thermal pressure[32,33]. This may finally set a limitation on the use of dynamic PDGs in hot plasmas. On the other hand, it is worth noting that the theoretical growth rates of parametric instabilities will be reduced due to the enhanced Landau damping in plasmas with high temperatures[37].
For the application of dynamic PDGs, the time-scale in which the polarization of the probe laser pulse becomes altered is a crucial factor. As shown in Figure 6(a), the dynamic PDG can make the polarization of the probe laser pulse vary obviously within a few tens of laser wave periods (
The time-scale in which the probe laser polarization is varied strongly depends on the typical variation time of the PDG. Further, it would decrease with the increase of the depth of the PDG (or the maximal achievable peak ion density). Moreover, it would also decrease with the increase of the width of the PDG, that is, the span of the PDG in the x-direction in the simulations. The latter is normally determined by the spot size of the driver laser pulses. However, it is difficult to give a formula for the time-scale in which the probe laser polarization is varied.
Concerning the variation time of the PDG, we have studied its dependence on the laser and plasma parameters by a series of 1D PIC simulations. As shown in Figure 10(a), we find that the saturation time
Figure 10.The saturation time (black solid lines) and the maximal achievable ion density (red solid lines) as functions of (a) the laser intensity for a given initial plasma density and (b) the initial plasma density for a given laser intensity . Except for the laser intensities and initial plasma densities, other laser–plasma parameters are the same as those used in
Based on the above analysis, one can see that the intensities and spot sizes of the driver laser pulses and the initial plasma density will combine to set a minimum time-scale in which the probe laser polarization can be varied. In general, the time-scale in which the probe laser polarization is varied is expected to decrease with the increase of the initial background plasma density as well as the increase of the intensity and spot size of the driver laser pulses.
In summary, we have shown that the PDG induced by two intersecting driver laser pulses is not only nonuniform in space but also varies over time. Such a dynamic PDG can induce a modulation upon the polarization state of the probe laser pulse passing through it. The time-scale in which the probe laser polarization is varied depends on the initial background plasma density, as well as the intensities and spot sizes of the driver laser pulses. The polarization degree of the probe laser that is averaged over either the longitudinal or transverse direction will be greatly reduced, that is, the probe laser pulse is depolarized by the dynamic PDG. The depolarized laser beams may play an important role in mitigating parametric instabilities relevant to laser-driven ICF. More importantly, the scenario of laser depolarization may spontaneously take place for crossed laser beams that are employed as the drivers in either indirect- or direct-drive ICF schemes.
References
[1] D. Strickland, G. Mourou. Opt. Commun., 55, 447(1985).
[2] C. N. Danson, C. Haefner, J. Bromage, T. Butcher, J.-C. F. Chanteloup, E. A. Chowdhury, A. Galvanauskas, L. A. Gizzi, J. Hein, D. I. Hillier, N. W. Hopps, Y. Kato, E. A. Khazanov, R. Kodama, G. Korn, R. Li, Y. Li, J. Limpert, J. Ma, C. H. Nam, D. Neely, D. Papadopoulos, R. R. Penman, L. Qian, J. J. Rocca, A. A. Shaykin, C. W. Siders, C. Spindloe, S. Szatmári, R. M. G. M. Trines, J. Zhu, P. Zhu, J. D. Zuegel. High Power Laser Sci. Eng, e54(2019).
[3] C. Radier, O. Chalus, M. Charbonneau, S. Thambirajah, G. Deschamps, S. David, J. Barbe, E. Etter, G. Matras, S. Ricaud, V. Leroux, C. Richard, F. Lureau, A. Baleanu, R. Banici, A. Gradinariu, C. Caldararu, C. Capiteanu, A. Naziru, B. Diaconescu, V. Iancu, R. Dabu, D. Ursescu, I. Dancus, C. A. Ur, K. A. Tanaka, N. V. Zamfir. High Power Laser Sci. Eng, 10, e21(2022).
[4] G. A. Mourou, T. Tajima, S. V. Bulanov. Rev. Mod. Phys., 78, 309(2006).
[5] K. A. Tanaka, K. M. Spohr, D. L. Balabanski, S. Balascuta, L. Capponi, M. O. Cernaianu, M. Cuciuc, A. Cucoanes, I. Dancus, A. Dhal, B. Diaconescu, D. Doria, P. Ghenuche, D. G. Ghita, S. Kisyov, V. Nastasa, J. F. Ong, F. Rotaru, D. Sangwan, P. A. Sóderstróm, D. Stutman, G. Suliman, O. Tesileanu, L. Tudor, N. Tsoneva, C. A. Ur, D. Ursescu, N. V. Zamfir. Matter Radiat. Extremes, 5, 024402(2020).
[6] B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, M. D. Perry. Phys. Rev. B, 53, 1749(1996).
[7] C. Thaury, F. Quéré, J. P. Geindre, A. Levy, T. Ceccotti, P. Monot, M. Bougeard, F. Réau, P. d’Oliveira, P. Audebert, R. Marjoribanks, P. H. Martin. Nat. Phys., 3, 424(2007).
[8] M. Nakatsutsumi, A. Kon, S. Buffechoux, P. Audebert, J. Fuchs, R. Kodama. Opt. Lett., 35, 2314(2010).
[9] V. M. Malkin, G. Shvets, N. J. Fisch. Phys. Rev. Lett., 82, 4448(1999).
[10] R. M. G. M. Trines, F. Fiúza, R. Bingham, R. A. Fonseca, L. O. Silva, R. A. Cairns, P. A. Norreys. Nat. Phys., 7, 87(2011).
[11] A. A. Andreev, C. Riconda, V. T. Tikhonchuk, S. Weber. Phys. Plasmas, 13, 053110(2006).
[12] M. R. Edwards, J. M. Mikhailova, N. J. Fisch. Phys. Rev. E, 96, 023209(2017).
[13] S. Weng, Q. Zhao, Z. Sheng, W. Yu, S. Luan, M. Chen, L. Yu, M. Murakami, W. B. Mori, J. Zhang. Optica, 4, 1086(2017).
[14] Y. Shi, H. Qin, N. J. Fisch. Phys. Rev. E, 95, 023211(2017).
[15] X. L. Zheng, S. M. Weng, H. H. Ma, Y. X. Wang, M. Chen, P. McKenna, Z. M. Sheng. Opt. Express, 27, 23529(2019).
[16] Z. Li, Z. Wu, Y. Zuo, X. Zeng, X. Wang, X. Wang, J. Mu, B. Hu, J. Su. Phys. Plasmas, 28, 013107(2021).
[17] I. Y. Dodin, N. J. Fisch. Phys. Rev. Lett., 88, 165001(2002).
[18] G. Lehmann, K. H. Spatschek. Phys. Rev. E, 100, 033205(2019).
[19] M. R. Edwards, V. R. Munirov, A. Singh, N. M. Fasano, E. Kur, N. Lemos, J. M. Mikhailova, J. S. Wurtele, P. Michel. Phys. Rev. Lett., 128, 065003(2022).
[20] G. Lehmann, K. H. Spatschek. Phys. Rev. E, 97, 063201(2018).
[21] H. C. Wu, Z. M. Sheng, J. Zhang. Appl. Phys. Lett., 87, 201502(2005).
[22] S. Monchocé, S. Kahaly, A. Leblanc, L. Videau, P. Combis, F. Réau, D. Garzella, P. D’Oliveira, P. Martin, F. Quéré. Phys. Rev. Lett., 112, 145008(2014).
[23] P. Michel, L. Divol, D. Turnbull, J. D. Moody. Phys. Rev. Lett., 113, 205001(2014).
[24] D. Turnbull, P. Michel, T. Chapman, E. Tubman, B. B. Pollock, C. Y. Chen, C. Goyon, J. S. Ross, L. Divol, N. Woolsey, J. D. Moody. Phys. Rev. Lett., 116, 205001(2016).
[25] G. Lehmann, K. H. Spatschek. Phys. Rev. Lett., 116, 225002(2016).
[26] S. H. Glenzer, B. J. MacGowan, P. Michel, N. B. Meezan, L. J. Suter, S. N. Dixit, J. L. Kline, G. A. Kyrala, D. K. Bradley, D. A. Callahan, E. L. Dewald, L. Divol, E. Dzenitis, M. J. Edwards, A. V. Hamza, C. A. Haynam, D. E. Hinkel, D. H. Kalantar, J. D. Kilkenny, O. L. Landen, J. D. Lindl, S. LePape, J. D. Moody, A. Nikroo, T. Parham, M. B. Schneider, R. P. J. Town, P. Wegner, K. Widmann, P. Whitman, B. K. F. Young, B. Van Wonterghem, L. J. Atherton, E. I. Moses. Science, 327, 1228(2010).
[27] P. Michel, L. Divol, E. A. Williams, S. Weber, C. A. Thomas, D. A. Callahan, S. W. Haan, J. D. Salmonson, S. Dixit, D. E. Hinkel, M. J. Edwards, B. J. Macgowan, J. D. Lindl, S. H. Glenzer, L. J. Suter. Phys. Rev. Lett., 102, 025004(2009).
[28] W. L. Kruer, S. C. Wilks, B. B. Afeyan, R. K. Kirkwood. Phys. Plasmas, 3, 382(1996).
[29] I. Barth, N. J. Fisch. Phys. Plasmas, 23, 102106(2016).
[30] H. H. Ma, X. F. Li, S. M. Weng, S. H. Yew, S. Kawata, P. Gibbon, Z. M. Sheng, J. Zhang. Matter Radiat. Extremes, 6, 055902(2021).
[31] Z. M. Sheng, J. Zhang, D. Umstadter. Appl. Phys. B, 77, 673(2003).
[32] H. H. Ma, S. M. Weng, P. Li, X. F. Li, Y. X. Wang, S. H. Yew, M. Chen, P. McKenna, Z. M. Sheng. Phys. Plasmas, 27, 073105(2020).
[33] H. Peng, C. Riconda, M. Grech, J. Q. Su, S. Weber. Phys. Rev. E, 100, 061201(2019).
[34] R. A. Fonseca, L. O. Silva, F. S. Tsung, V. K. Decyk, W. Lu, C. Ren, W. B. Mori, S. Deng, S. Lee, T. Katsouleas, J. C. Adam. Lect. Notes Comput. Sci., 2331, 342(2002).
[35] J. Tinbergen. Astronomical Polarimetry(1996).
[36] S. Atzeni, J. Meyer-ter-Vehn. The Physics of Inertial Fusion(2004).
[37] C. S. Liu. High-Power Laser-Plasma Interaction(2019).
[38] D. S. Montgomery. Phys. Plasmas, 23, 055601(2016).
Set citation alerts for the article
Please enter your email address