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Optical guiding of intense Hermite–Gaussian laser beam in preformed plasma channel and second harmonic generation


This work presents the scheme of optical channeling of the intense Hermite Gaussian laser beam and second-harmonic generation in plasma having the preformed plasma channel, where relativistic nonlinearity is operative. Excitation of the electron plasma wave at the incident beam frequency leads its coupling with the latter produces the second harmonics of the beam. For the formulation of differential equations for the beam waists of the Hermite Gaussian laser beam propagating through the channel, the method of moments has been used. The solutions of the coupled differential equations are found using Runge Kutta fourth-order numerical method. Perturbation theory has been applied to find the equation governing the excitation of electron plasma wave and hence the source term for the second-harmonic yield. It has been observed that the preformed plasma channel helps to optically guide the laser beam and enhances the efficiency of second-harmonic generation of various modes of the Hermite Gaussian laser beam in plasma.

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  1. Basov, N.G., Bychenkov, V.Y., Krokhin, O.N., Osipov, M.V., Rupasov, A.A., Silin, V.P., Sklizkov, G.V., Starodub, A.N., Tikhonchuk, V.T., Shikanov, A.S.: Second harmonic generation in a laser plasma (review). Soviet J. Quant. Electron. 9, 1081–1102 (1979)

    ADS  Article  Google Scholar 

  2. Clayton, C.E., Ralph, J.E., Albert, F., Fonseca, R.A., Glenzer, S.H., Joshi, C., Lu, W., Marsh, K.A., Martins, S.F., Mori, W.B., Pak, A., Tsung, F.S., Pollock, B.B., Ross, J.S., Silva, L.O., Froula, D.H.: Self-guided laser wakefield acceleration beyond 1 GeV using ionization-induced injection. Phys. Rev. Lett. 105, 105003 (2010)

    ADS  Article  Google Scholar 

  3. Durfee, C.G., Lynch, J., Milchberg, H.M.: Development of a plasma waveguide for high-intensity laser pulses. Phys. Rev. E 51, 2368–2389 (1995)

    ADS  Article  Google Scholar 

  4. Ehrlich, Y., Cohen, C., Zigler, A.: Guiding of high intensity laser pulses in straight and curved plasma channel experiments. Phys. Rev. Lett. 77, 4186–4189 (1996)

    ADS  Article  Google Scholar 

  5. Esarey, E., Sprangle, P.: Self-focusing and guiding of short laser pulses in ionizing gases and plasmas. IEEE J. Quant. Electron. 33(11), 1879–1914 (1997)

    ADS  Article  Google Scholar 

  6. Gibbon, P.: High-order harmonic generation in plasma. IEEE J. Quant. Electron. 33, 1915–1924 (1997)

    ADS  Article  Google Scholar 

  7. Gupta, N., Singh, N., Singh, A.: Second harmonic generation of \(q\)-Gaussian laser beam in preformed collisional plasma channel with nonliner absorption nonlinear absorption. Phys. Plasmas 22, 113106 (2015)

    ADS  Article  Google Scholar 

  8. Kant, N., Thakur, V.: Enhanced self-focusing of Laguerre–Gaussian laser beam in relativistic plasma under exponential plasma density transition. Chin. J. Phys. 70, 182–187 (2021a)

    MathSciNet  Article  Google Scholar 

  9. Kant, N., Thakur, V.: Influence of linear absorption and density ramp on self-focusing of the Hermite–Gaussian chirped pulse laser in plasma. Opt. Quant. Electron. 53(12), 1–10 (2021b)

    Google Scholar 

  10. Kant, N., Singh, A., Thakur, V.: Second-harmonic generation by a chirped laser pulse with the exponential density ramp profile in the presence of a planar magnetostatic wiggler. Laser Part. Beams 37, 442–447 (2019)

    ADS  Article  Google Scholar 

  11. Lam, J.F., Lippmann, B., Tappert, F.: Self-trapped laser beams in plasma. Phys. Fluids 20, 1176–1179 (1977)

    ADS  Article  Google Scholar 

  12. Nakano, H., Nishikawa, T., Uesugi, N.: Soft x-ray pulse generation from femtosecond laser-produced plasma with reduced debris using a metal-doped glass target. Appl. Phys. Lett. 70, 16–18 (1997)

    ADS  Article  Google Scholar 

  13. Salih, H.A., Tripathi, V.K., Pandey, B.K.: Second-harmonic generation of a Gaussian laser beam in a self created magnetized plasma channel. IEEE Trans. Plasma Sci. 31, 324–328 (2003)

    ADS  Article  Google Scholar 

  14. Sharma, V., Thakur, V., Kant, N.: Second harmonic generation of cosh-Gaussian laser beam in magnetized plasma. Opt. Quant. Electron. 52, 1–9 (2020).

    Article  Google Scholar 

  15. Sharma, V., Thakur, V., Singh, A., Kant, N.: Second harmonic generation of a self-focused Hermite–Gaussian laser in plasma. Chin. J. Phys. 71, 312–318 (2021)

    MathSciNet  Article  Google Scholar 

  16. 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)

    ADS  Article  Google Scholar 

  17. Spence, D.J., Butler, A., Hooker, S.M.: First demonstration of guiding of high-intensity laser pulses in a hydrogen-filled capillary discharge waveguide. J. Phys. B: At. Mol. Opt. Phys. 34, 4103–4112 (2001)

    ADS  Article  Google Scholar 

  18. Sprangle, P., Esarey, E., Ting, A., Joyce, G.: Laser wakefield accelration and relativistic optical guiding. Appl. Phys. Lett. 53, 2146–2148 (1988)

    ADS  Article  Google Scholar 

  19. Upadhyay, A.K., Raj, G., Mishra, R.K., Jha, P.: Propagation of sinusoidal pulse laser beam in a plasma channel. Phys. Plasmas 14, 113105 (2007)

    ADS  Article  Google Scholar 

  20. Wadhwa, J., Singh, A.: Generation of second harmonics of intense Hermite–Gaussian laser beam in relativistic plasma. Laser Part. Beams 37, 79–85 (2019)

    ADS  Article  Google Scholar 

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The authors are thankful to the Ministry of Human Resources and Development (MHRD) of India for providing the necessary funds to carry out the research work.

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Correspondence to Arvinder Singh.

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Wadhwa, J., Singh, A. Optical guiding of intense Hermite–Gaussian laser beam in preformed plasma channel and second harmonic generation. Opt Quant Electron 53, 428 (2021).

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  • Hermite–Gaussian laser beam
  • Preformed plasma channel
  • Relativistic plasma
  • Second harmonic generation