Abstract
In this paper, a homogeneous, under-dense plasma channel was subjected to an interaction with a chirped super-Gaussian laser beam. We assume that the plasma already existed. The plasma electron velocity and density variance have been obtained in the relativistic regime. We derived the second harmonic efficiency that depends on normalized laser propagation distance in plasma by solving the wave equation under W–K–B (Wentzel–Kramers–Brillouin) approximation. The influence of different kinds of laser chirp parameters is examined on the second harmonic efficiency. The second harmonic efficiency has been plotted against the ratio of the plasma frequency to the initial laser frequency and normalized laser propagation distance in the plasma channel. The effects of positive and negative chirp parameters on second harmonic efficiency are compared with non-chirped laser pulses in the maximum value. The maximum value of second harmonic efficiency depends on the laser distance propagation and chirp parameter. Also, the positive chirp is more impressive than other kinds of chirping.
Similar content being viewed by others
Data availability
All figure have been drawn by Origin lab. Data will be available upon request, contact Sara Sohrabi at sarasohrabi60@gmail.com.
References
Bingham, R., de Angelis, U., Amin, M.R., Cairns, R.A., Mcnamara, B.: Relativistic Langmuir waves generated by ultra-short pulse lasers. Plasma Phys Controll Fus 34, 4 (1992)
Cros, B.: Laser-driven Plasma Wakefield: Propagation Effects. CERN, Geneva (2014)
Franken, P.A., Hill, A.E., Peters, C.W., Weinreich, G.: Generation of optical harmonics. Phys. Rev. Lett. 7, 118–119 (1961). https://doi.org/10.1103/PhysRevLett.7.118
Ghadimimehr, M., Jelvani, S., Safari, E.: Theoretical investigation of effective parameters on the second harmonic generation efficiency in AgGaSe2 crystal. Iran J Appl Phys 12, 76–84 (2022). https://doi.org/10.22051/IJAP.2022.39535.1264
Gill, T.S., Mahajan, R., Kaur, R., Gupta, S.: Relativistic self-focusing of super-Gaussian laser beam in plasma with transverse magnetic field. Laser Part. Beams 30, 509–516 (2012). https://doi.org/10.1017/S0263034612000444
Gill, T.S., Kaur, R., Mahajan, R.: Self-focusing of super-Gaussian laser beam in magnetized plasma under relativistic and ponderomotive regime. Optik. 126, 1683–1690 (2015). https://doi.org/10.1016/j.ijleo.2015.05.031
Gordon, D.F., Hafizi, B., Hubbard, R.F., Penano, J.R., Sprangle, P., Ting, A.: Asymmetric Self-Phase modulation and compression of short laser pulses in plasma channels. Phys Rev Lett. 90, 215001 (2003). https://doi.org/10.1103/PhysRevLett.90.215001
Gupta, N.: Second harmonic generation of q-Gaussian laser beam in plasma channel created by ignitor heater technique. Laser Part. Beams 37, 184–196 (2019). https://doi.org/10.1017/S0263034619000193
Gupta, N.: Optical second and third harmonic generation of laser beams in nonlinear media: a review. NLOQO. 53, 291–310 (2021)
Gupta, N., Kumar, S.: Generation of second harmonics of self-focused quadruple-Gaussian laser beams in collisional plasmas with density ramp. J Opt. 49(4), 455–468 (2020). https://doi.org/10.1007/s12596-020-00639-x
Gupta, N., Kumar, S.: Generation of second harmonics of relativistically self-focused q-Gaussian laser beams in underdense plasma with axial density ramp. Opt. Quant. Electron. 53, 193 (2021a). https://doi.org/10.1007/s11082-021-02827-w
Gupta, N., Kumar, S.: Generation of second harmonics of q-gaussian laser beams in collisionless plasma with axial density ramp. NLOQO. 54, 45–61 (2021b)
Gupta, N., Bhardwaj, S.B., Kumar, S., Choudhry, S., Khatri, R., Shishodia, S., Johari, R.: Second-harmonic generation of two cross-focused q-Gaussian laser beams by nonlinear frequency mixing in plasmas. J. Opt. (2022). https://doi.org/10.1007/s12596-022-00995-w
Hora, H., Ghatak, A.K.: New electrostatic resonance driven by laser radiation at perpendicular incidence in super-dense plasmas. Phys. Rev. a. 31, 3473–3476 (1985). https://doi.org/10.1103/PhysRevA.31.3473
Hsieh, C.L., Pu, Y., Grange, R., Psaltis, D.: Second harmonic generation from nano crystals under linearly and circularly polarized excitation. Opt. Express 18, 11917–11932 (2010). https://doi.org/10.1364/OE.18.011917
Jha, P., Malviya, A., Upadhyay, A.K.: Propagation of chirped laser pulses in a plasma channel. Phys. Plasmas 16, 063106 (2009). https://doi.org/10.1063/1.3157247
Kant, N., Thakur, V.: Second harmonic generation by a chirped laser pulse in magnetized plasma. Optik 127, 4167–4172 (2016). https://doi.org/10.1016/j.ijleo.2015.12.165
Leemans, W.P., Nagler, B., Gonsalves, A.J., Toth, C.S., Nakamura, K., Geddes, C.G.R., Esarey, E., Schroeder, C.B., Hooker, S.M.: GeV electron beams from a centimeter-scale accelerator. Nat. Phys. 2, 696–699 (2006). https://doi.org/10.1038/nphys418
Li, G., Zhu, B., Wu, Y., Lu, F., Tan, F., Zhang, T., Yang, Y., Yu, M., Yan, Y., Fan, W., Gu, Y.: Simulation of a chirped femtosecond relativistic laser pulse interaction with under-dense plasma by using a hydrodynamic approach. Contrib Plasma Phys 59, e201900048 (2019). https://doi.org/10.1002/ctpp.201900048
Lisinski, S., Schaniel, D., Ratke, L., Woike, Th.: Second-harmonic generation by ferroelectric microparticles in aerogels. Chem. Mater. 18, 1534–1538 (2006). https://doi.org/10.1021/cm052784r
Liu, X., Umstadter, U., Ting, A., Esarey, E.: Harmonic generation by an intense laser pulse in neutral and ionized gases. IEEE Trans. Plasma Sci. 21, 90–94 (1993). https://doi.org/10.1109/27.221106
Malik, H.K., Devi, L.: Relativistic self-focusing and frequency shift of super-Gaussian laser beam in plasma. Results in Physics 17, 103070 (2020). https://doi.org/10.1016/j.rinp.2020.103070
Malik, H.K., Devi, L.: Self-defocusing of super-Gaussian laser beam in tunnel ionized plasmas. Optik. 222, 165357 (2020a). https://doi.org/10.1016/j.ijleo.2020.165357
Malik, H.K., Singh, D.: Terahertz emission during laser-plasma interaction: effect of electron temperature and collisions. J Theor Appl Phys 14, 359–365 (2020b). https://doi.org/10.1007/s40094-020-00392-3
Mulser, P., Bauer, D.: High power laser-matter interactions. Springer, Berlin (2010)
Niu, H.Y., He, X.T., Qiao, B., Zhou, C.T.: Resonant acceleration of electrons by intense circularly polarized Gaussian laser pulses. Laser and Particle Beams. 26, 51–60 (2008)
Parashar, J., Pandey, H.D.: Second-harmonic generation of laser radiation in a plasma with a density ripple. IEEE Trans. Plasma Sci. 20, 996–999 (1992). https://doi.org/10.1109/27.199564
Pathak, V.B., Vieira, J., Silva, L.O.: Effect of the frequency chirp on laser wakefield acceleration. New J. Phys. 14, 023057 (2012). https://doi.org/10.1088/1367-2630/14/2/023057
Pathak, N., Agarwal, P.C., Gill, T.S., Kaur, S.: Dynamics of resonant self-focusing on second harmonic generation of Gaussian laser beam in a rippled density plasma. Contrib. Plasma Phys. 6, (2021). https://doi.org/10.1002/ctpp.202100031
Roth, M., Blazevic, A., Geissel, M., Schlegel, T., Cowan, T.E., Allen, M., Gauthier, J.C., Audebert, P., Fuchs, J., Meyerter-Vehn, J.: Energetic ions generated by laser pulses: a detailed study on target properties. Phys. Rev. Spec. Top. Accel. Beams. 5, 061301 (2002). https://doi.org/10.1103/PhysRevSTAB.5.061301
Rousse, A., Phuoc, K.T., Albert, F.: Collimated and ultrafast X-ray beams from laser-plasma interactions progress in ultrafast intense laser science II. Springer Ser Chem Phys 85, 215–230 (2007). https://doi.org/10.1007/978-3-540-38156-3_11
Schroeder, C.B., Esarey, E., Shadwick, B.A., Leemans, W.P.: Raman forward scattering of chirped laser pulses. Phys. Plasmas 10(1), 285–295 (2003). https://doi.org/10.1063/1.1528901
Schroeder, C.B., Esarey, E., Geddes, C.G.R., Tóth, C., Leemans, W.P.: Design considerations for a laser-plasma linear collider. AIP Conf. Proc. 1086(1), 208–214 (2009). https://doi.org/10.1063/1.3080906
Sharma, V., Thakur, V., Kant, N.: Third harmonic generation of a relativistic self-focusing laser in plasma in the presence of wiggler magnetic field. High Energy Density Phys. 32, 51–55 (2019). https://doi.org/10.1016/j.hedp.2019.04.007
Sharma, V., Thakur, V., Kant, N.: Second harmonic generation of cosh-Gaussian laser beam in magnetized plasma. Opt. Quant. Electron. 52, 444 (2020). https://doi.org/10.1007/s11082-020-02559-3
Sharma, V., Thakur, V., Singh, A., Kant, N.: Third harmonic generation of a relativistic self-focusing laser in plasma under exponential density ramp. Z. Naturforsch. 77(4), 323–328 (2022). https://doi.org/10.1515/zna-2021-0266
Singh, A., Gupta, N.: Higher harmonic generation by self-focused q-Gaussian laser beam in preformed collisionless plasma channel. Laser Part Beams 32, 621–629 (2014). https://doi.org/10.1017/S0263034614000639
Singh, A., Gupta, N.: Second-harmonic generation by relativistic self-focusing of cosh-Gaussian laser beam in underdense plasma. Laser Part. Beams 34, 1–10 (2016). https://doi.org/10.1017/S0263034615000749
Singh, N., Gupta, N., Singh, A.: Second harmonic generation of Cosh-Gaussian laser beam in collisional plasma with nonlinear absorption. Opt. Commun. 381, 180–188 (2016). https://doi.org/10.1016/j.optcom.2016.06.047
Sprangle, P., Esarey, E., Ting, A.: Nonlinear theory of intense laser-plasma interaction. Phys. Rev. Lett. 64, 2011–2014 (1990). https://doi.org/10.1103/PhysRevLett.64.2011
Thakur, V., Vij, S., Sharma, V., Kant, N.: Influence of exponential density ramp on second harmonic generation by a short pulse laser in magnetized plasma. Optik 171, 523–528 (2018). https://doi.org/10.1016/j.ijleo.2018.06.086
Varaki, M.A., Kant, N.: Magnetic field-assisted wakefield generation and electron acceleration by Gaussian and super-Gaussian laser pulses in plasma. Mod. Phys. Lett. B 36, 2150604 (2022). https://doi.org/10.1142/S0217984921506041
Vij, S., Aggarwal, M., Kant, N.: Phase-matched relativistic second harmonic generation in clusters with density ripple. Opt Commun 383, 349–354 (2017)
Willingale, L., Mangles, S.P.D., Nilson, P.M., Clarke, R.J., Dangor, A.E., Kaluza, M.C., Karsch, S., Lancaster, K.L., Mori, W.B., Najmudin, Z.: Collimated multi-MeV ion beams from high-intensity laser interactions with under-dense Plasma. Phys. Rev. Lett. 96, 245002 (2006). https://doi.org/10.1103/PhysRevLett.96.245002
Zare, S.: The effect of chirp parameter on laser propagation in collisional quantum plasma. Results in Optics. 9, 100284 (2022). https://doi.org/10.1016/j.rio.2022.100284
Funding
The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.
Author information
Authors and Affiliations
Contributions
Solving the problem and analysis were performed by SJ, KS and SS. Bibliography was done by SS. The first draft of the manuscript was written by SS. SJ and KS assign the problem, contribute to the writing, and supervise the work. LFM contribute to solving some mathematics problems and advise the work. All authors have read and agreed to the published version of the manuscript.
Corresponding author
Ethics declarations
Competing interests
All authors certify that they have no competing interests as defined by Springer, or other interests that might be perceived to influence the results and/or discussion reported in this paper.
Ethical approval
This work does not apply to both human and/or animal studies.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sohrabi, S., Jelvani, S., Samavati, K. et al. Effect of chirp parameter on the second harmonic efficiency in relativistic super-Gaussian laser-plasma interaction. Opt Quant Electron 55, 942 (2023). https://doi.org/10.1007/s11082-023-05218-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-023-05218-5