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Nonlinear interaction of elliptical q-Gaussian laser beams with plasmas with axial density ramp: effect of ponderomotive force

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Abstract

Theoretical investigation on optical self action effects of intense q-Gaussian laser beams interacting with collisionless plasmas with axial density ramp has been presented. Emphasis are put on investigating the dynamics of beam width and axial phase of the laser beam. Effect of the ellipticity of the cross section of the laser beam also has been incorporated. Using variational theory based on Lagrangian formulation nonlinear partial differential equation (P.D.E) governing the evolution of beam amplitude has been reduced to a set of coupled ordinary differential equations for the beam widths of the laser beam along the transverse directions. The evolution equation for the axial phase of the laser beam has been obtained by the Fourier transform of the amplitude structure of the laser beam from coordinate space to \((k_x, k_y)\) space. The differential equations so obtained have been solved numerically to envision the effect of laser-plasma parameters on the propagation dynamics of the laser beam.

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References

  • Akhmanov, S.A., Sukhorukov, A.P., Khokhlov, R.V.: Self-focusing and diffraction of light in a nonlinear medium. Usp. Fiz. Nauk. 93, 609–636 (1967)

    Article  Google Scholar 

  • Anderson, D., Bonnedal, M.: Variational approach to nonlinear self-focusing of Gaussian laser beams. Phys. Fluids 22, 105–109 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  • Anderson, D., Bonnedal, M., Lisak, M.: Nonlinear propagation of elliptically shaped Gaussian laser beams. J. Plasma Phys. 23, 115–127 (1980)

    Article  ADS  Google Scholar 

  • Askaryan, G.A.: Effects of the gradient of strong electromagnetic beam on electrons and atoms. Soviet Phys. JETP 15, 1088–1092 (1962)

    Google Scholar 

  • Chiao, R.Y., Garmire, E., Townes, C.H.: Self-trapping of optical beams. Phys. Rev. Lett. 13, 479–482 (1965)

    Article  ADS  Google Scholar 

  • Cornolti, F., Lucchesi, M., Zambon, B.: Elliptic Gaussian beam selffocusing in nonlinear media. Opt. Commun. 75, 129–135 (1990)

    Article  ADS  Google Scholar 

  • Deutsch, C., Furukawa, H., Mima, K., Murakami, M., Nishihara, K.: Interaction physics of the fast ignitor concept. Phys. Rev. Lett. 77, 2483–2486 (1996)

    Article  ADS  Google Scholar 

  • El Sayed, A., El Badawy, N., Mohamed, S., El Halafawy, F.Z.: Self-focusing of powerful CO2-laser beams in collisional plasmas. J. Opt. Soc. Am. 72, 1393–1397 (1982)

    Article  ADS  Google Scholar 

  • Feit, M.D., Fleck, J.A.: Self-trapping of a laser beam in a cylindrical plasma column. Appl. Phys. Lett. 28, 121–124 (1976)

    Article  ADS  Google Scholar 

  • Feng, S., Winful, H.G.: Physical origin of the Gouy phase shift. Opt. Lett. 26, 485–487 (2001)

    Article  ADS  Google Scholar 

  • Gupta, N., Kumar, S.: Linear and nonlinear propagation characteristics of multi-Gaussian laser beams. Chin. Phys. B 29, 114210 (2020)

    Article  ADS  Google Scholar 

  • Gupta, N., Kumar, S.: Generation of second harmonics of q-Gaussian laser beams in collisional plasma with upward density ramp. Laser Phys. 30, 066003 (2020)

    Article  ADS  Google Scholar 

  • Gupta, D.N., Hur, M.S., Hwang, I., Suk, H., Sharma, A.K.: Plasma density ramp for relativistic self-focusing of an intense laser. J. Opt. Soc. Am. B 24, 1155–1159 (2007)

    Article  ADS  Google Scholar 

  • Gupta, D.N., Islam, M.R., Jang, D.G., Suk, H., Jaroszynski, D.A.: Self-focusing of a high-intensity laser in a collisional plasma under weak relativistic-ponderomotive nonlinearity. Phys. Plasmas 20, 123103 (2013)

    Article  ADS  Google Scholar 

  • Habibi, M., Ghamari, F.: Significant enhancement in self-focusing of high-power laser beam through dense plasmas by ramp density profile. J. Opt. Soc. Am. B 32, 1429–1434 (2015)

    Article  ADS  Google Scholar 

  • Hariharan, P., Robinson, P.A.: The gouy phase shift as a geometrical quantum effect. J. Mod. Opt. 43, 219–221 (1996)

    ADS  MathSciNet  MATH  Google Scholar 

  • Hora, H.: Theory of relativistic self-focusing of laser radiation in plasmas. J. Opt. Soc. Am. 65, 882–886 (1975)

    Article  ADS  Google Scholar 

  • Kelley, P.L.: Self-focusing of optical beams. Phys. Rev. Lett. 15, 1005–1008 (1966)

    Article  ADS  Google Scholar 

  • Khalkhal, E., Tavirani, M.R., Zali, M.R., Akbari, Z.: The evaluation of laser application in surgery: a review article. J. Lasers Med. Sci. 10, S104–S111 (2019)

    Article  Google Scholar 

  • Konar, S., Sengupta, A.: Propagation of an elliptic Gaussian laser beam in a medium with saturable nonlinearity. J. Opt. Soc. Am. B 11, 1644–1646 (1994)

    Article  ADS  Google Scholar 

  • Kumar, H., Aggarwal, M., Richa, Gill, T.S.: Self-focusing of an elliptic-Gaussian laser beam in relativistic ponderomotive plasma using a ramp density profile. J. Opt. Soc. Am. B 35, 1635–1641 (2018)

    Article  ADS  Google Scholar 

  • Kurniawan, K.H., Tjia, M., Kagawa, K.: Review of laser-induced plasma, its mechanism, and application to quantitative analysis of hydrogen and deuterium. Appl. Spectrosc. Rev. 49, 323–434 (2014)

    Article  ADS  Google Scholar 

  • Leduc, M., Dugue, J., Simone, J.: Laser cooling, trapping, and Bose–Einstein condensation of atoms and molecules. Phys. Today 71, 37–42 (2018)

    Google Scholar 

  • Maiman, T.H.: Stimulated optical radiation in Ruby. Nature 187, 493–494 (1960)

    Article  ADS  Google Scholar 

  • Nakatsutsumi, M., Davies, J.R., Kodama, R., Green, J.S., Lancaster, K.L., Akli, K.U., Beg, F.N., Chen, S.N., Clark, D., Freeman, R.R., Gregory, C.D., Habara, H., Heathcote, R., Hey, D.S., Highbarger, K., Jaanimagi, P., Key, M.H., Krushelnick, K., Ma, T., MacPhee, A., MacKinnon, A.J., Nakamura, H., Stephens, R.B., Storm, M., Tampo, M., Theobald, W., Van Woerkom, L., Weber, R.L., Wei, M.S., Woolsey, N.C., Norreys, P.A.: Space and time resolved measurements of the heating of solids to ten million kelvin by a petawatt laser. New J. Phys. 10, 043046 (2008)

    Article  Google Scholar 

  • Patel, P.K., Key, M.H., Mackinnon, A.J., Berry, R., Borghesi, M., Chambers, D.M., Chen, H., Clarke, R., Damian, C., Eagleton, R., Freeman, R., Glenzer, S., Gregori, G., Heathcote, R., Hey, D., Izumi, N., Kar, S., King, J., Nikroo, A., Niles, A., Park, H.S., Pasley, J., Patel, N., Shepherd, R., Snavely, R.A., Steinman, D., Stoeckl, C., Storm, M., Theobald, W., Town, R., Van Maren, R., Wilks, S.C., Zhang, B.: Integrated laser-target interaction experiments on the RAL petawatt laser. Plasma Phys. Control. Fusion 47, B833–B840 (2005)

    Article  Google Scholar 

  • Pathak, N., Agarwal, P.C., Gill, T.S., Kaur, S.: Characteristics of spatiotemporal dynamics of a quadruple Gaussian laser beam in a relativistic ponderomotive magnetized plasma. J. Opt. Soc. Am. B 37, 2892–2900 (2020)

    Article  ADS  Google Scholar 

  • Patil, S.D., Takale, M.V.: Self-focusing of Gaussian laser beam in weakly relativistic and ponderomotive regime using upward ramp of plasma density. Phys. Plasmas 20, 083101 (2013)

    Article  ADS  Google Scholar 

  • Purohit, G., Gaur, B., Rawat, P.: Propagation of two intense cosh-Gaussian laser beams in plasma in the relativistic-ponderomotive regime. J. Opt. Soc. Am. B 33, 1716–1722 (2016)

    Article  ADS  Google Scholar 

  • Roso, N.A., Moreira, R.C., Oliveira, J.B.: High power laser weapons and operational implications. J. Aerosp. Technol. Manag. 6, 231–236 (2014)

    Article  Google Scholar 

  • Sharma, A., Kourakis, I.: Spatial evolution of a q-Gaussian laser beam in relativistic plasma. Laser Part. Beams 28, 479–489 (2010)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • Singh, T., Kaul, S.S.: Self-focusing and self-phase modulation of elliptic Gaussian laser beam in a graded Kerr-medium. Indian J. Pure Appl. Phys. 37, 794–797 (1999)

    Google Scholar 

  • Singh, A., Walia, K.: Self-focusing of Gaussian laser beam through collisionless plasmas and its effect on second harmonic generation. J. Fusion Energy 30, 555–560 (2011)

    Article  ADS  Google Scholar 

  • Sodha, M.S., Ghatak, A.K., Tripathi, V.K.: In: Wolf, E. (ed.) Progress in Optics, vol. 13, p. 169–175. North Holland, Amsterdam (1976)

  • Spiers, B.T., Hill, M.P., Brown, C., Ceurvorst, L., Ratan, N., Savin, A.F., Allan, P., Floyd, E., Fyrth, J., Hobbs, L., James, S., Luis, J., Ramsay, M., Sircombe, N., Skidmore, J., Aboushelbaya, R., Mayr, M.W., Paddock, R., Wang, R.H.W., Norreys, P.A.: Whole-beam self-focusing in fusion-relevant plasma. Philos. Trans. R. Soc. A. 379, 20200159 (2021)

    Article  ADS  Google Scholar 

  • Tajima, T., Dawson, J.M.: Laser electron accelerator. Phys. Rev. 43, 267–270 (1979)

    ADS  Google Scholar 

  • Tsallis, C.: Nonadditive entropy and nonextensive statistical mechanics—an overview after 20 years. Braz. J. Phys. 39, 337–356 (2009)

    Article  ADS  Google Scholar 

  • Wang, Y., Liang, Y., Yao, J., Yuan, C., Zhou, Z.: Nonlinear propagation characteristics of multi-Gaussian beams in collisionless plasmas. J. Opt. Soc. Am. B 35, 3088–3093 (2018)

    Article  ADS  Google Scholar 

  • Yadav, M., Gupta, D.N., Sharma, S.C.: Electron plasma wave excitation by a q-Gaussian laser beam and subsequent electron acceleration. Phys. Plasmas 27, 093106 (2020)

    Article  Google Scholar 

Download references

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  1. Lovely Professional University, Phagwara, India

    Naveen Gupta & Sandeep Kumar

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  1. Naveen Gupta
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  2. Sandeep Kumar
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Gupta, N., Kumar, S. Nonlinear interaction of elliptical q-Gaussian laser beams with plasmas with axial density ramp: effect of ponderomotive force. Opt Quant Electron 53, 253 (2021). https://doi.org/10.1007/s11082-021-02905-z

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