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Generation of second harmonics of relativistically self-focused q-Gaussian laser beams in underdense plasma with axial density ramp

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Abstract

An investigation on frequency doubling of intense laser beams through the phenomenon of second harmonic generation (SHG) in underdense plasmas has been presented. In order to increase the efficiency of S.H.G the density profile of plasma has been considered in the shape of upward ramp. When laser beam with frequency \(\omega _0\) propagates through plasma, it makes the plasma electrons to oscillate at pump frequency. These oscillations of plasma electrons in the presence of thermal velocity generate a plasma wave at frequency \(\omega _0\). The generated plasma wave beats with the pump beam to double its frequency. Variational theory has been adopted to find semi analytical solution of the wave equation for the slowly varying envelope of the laser beam. By using hydrodynamic fluid model of plasma, nonlinear current density for SHG has been obtained. Emphasis are put on investigation of the effect of various laser and plasma parameters on propagation dynamics of pump beam and the power of generated second harmonics.

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References

  • Akhiezer, A.I., Polovin, R.V.: Theory of wave motion of an electron plasma. Sov. Phys. JETP 3, 696–705 (1956)

    MathSciNet  MATH  Google Scholar 

  • Albert, F., Thomas, A.G.R., Mangles, S.P.D., Banerjee, S., et al.: Laser wakefield accelerator based light sources: potential applications and requirements. Plasma Phys. Control. Fusion 56, 084015 (2014)

    Article  ADS  Google Scholar 

  • Anderson, D.: Stationary self-trapped laser beams in plasma. Phys. Scr. 18, 35–36 (1978)

    Article  ADS  Google Scholar 

  • Bobin, J.L.: High intensity laser plasma interaction. Phys. Rep. 122, 173–274 (1985)

    Article  ADS  Google Scholar 

  • Bohon, J., D’Mello, R., Ralston, C., Gupta, S., Chance, M.R.: Synchrotron X-ray footprinting on tour. J. Synchrotron Radiat. 21, 24–31 (2014)

    Article  Google Scholar 

  • Bokaei, B., Niknam, A.R.: Increasing the upper-limit intensity and temperature range for thermal self-focusing of a laser beam by using plasma density ramp-up. Phys. Plasmas 21, 032309 (2014)

    Article  ADS  Google Scholar 

  • Brunel, F.: Harmonic generation due to plasma effects in a gas undergoing multiphoton ionization in the high-intensity limit. JOSA B 7, 521–526 (1990)

    Article  ADS  Google Scholar 

  • Chen, Y., Fu, E., Yu, K., Song, M., Liu, Y., Wang, Y., Wang, H., Zhang, X.: Enhanced radiation tolerance in immiscible Cu/Fe multilayers with coherent and incoherent layer interfaces. J. Mater. Res. 30, 1300–1309 (2015)

    Article  ADS  Google Scholar 

  • Dobele, H.F.: Generation of coherent XUV radiation and its application to plasma diagnostics. Plasma Sources Sci. Technol. 4, 224–233 (1995)

    Article  ADS  Google Scholar 

  • Erokhin, N.S., Zakharov, V.E., Moiseev, S.S.: Second harmonic generation by an electromagnetic wave incident on inhomogeneous plasma. Sov. Phys. JETP 29, 101–104 (1969)

    ADS  Google Scholar 

  • Franken, E.P., Hill, A.E., Peters, C.W., Weinreich, G.: Generation of optical harmonics. Phys. Rev. Lett. 7, 118–121 (1961)

    Article  ADS  Google Scholar 

  • Gupta, N.: Self-action effects of quadruple-Gaussian laser beam in media possessing cubic-quintic nonlinearity. J. Electromagn. Waves Appl. 32, 2350–2366 (2018)

    Article  Google Scholar 

  • Li, D., Feng, J., Pacifici, D.: Nanoscale optical interferometry with incoherent light. Sci. Rep. 6, 1–8 (2016)

    Article  Google Scholar 

  • Liu, C.S., Tripathi, V.K.: Third harmonic generation of a short pulse laser in a plasma density ripple created by a machining beam. Phys. Plasmas 15, 023106 (2008)

    Article  ADS  Google Scholar 

  • Malka, V., Modena, A., Najmudin, Z., Dangor, A.E., Clayton, C.E., Marsh, K.A., Joshi, C., Danson, C., Neely, D., Walsh, F.N.: Second harmonic generation and its interaction with relativistic plasma waves driven by forward Raman instability in underdense plasmas. Phys. Plasmas 4, 1127–1131 (1997)

    Article  ADS  Google Scholar 

  • McNeil, B.W., Thompson, N.R.: X-ray free-electron lasers. Nat. Photonics 4, 814–821 (2010)

    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.M., Tampo, T.W., Woerkom, L.V., 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 

  • Orlando, G., Wang, C.M., Ho, T.S., Chu, S.I.: High-order harmonic generation in disordered semiconductors. J. Opt. Soc. Am. B 35, 680–688 (2018)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • Patel, P.K., Key, M.H., Mackinnon, A.J., Berry, R., Borghesi, M., Chambers, D.M., Chen, H., Clarke, 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., Maren, R.V., Wilks, S.C., Zhang, B.: Integrated laser target interaction experiments on the RAL petawatt laser. Plasma Phys. Cont. Fusion 47, 833 (2005)

  • Purohit, G.: Second harmonic generation by self-focusing of intense hollow Gaussian laser beam in collisionless plasma. Phys. Plasmas 23, 013103 (2016)

    Article  ADS  Google Scholar 

  • Quiney, H.M.: Coherent diffractive imaging using short wavelength light sources. J. Mod. Opt. 57, 1109 (2010)

    Article  ADS  MathSciNet  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, K.P., Gupta, D.N., Yadav, S., Tripathi, V.K.: Relativistic second-harmonic generation of a laser from underdense plasmas. Phys. Plasmas 12, 013101 (2005)

    Article  ADS  Google Scholar 

  • Singh, R.P., Gupta, S.L., Thareja, R.K.: Third harmonic generation in air ambient and laser ablated carbon plasma. Phys. Plasmas 22, 123302 (2015)

    Article  ADS  Google Scholar 

  • Slaih, H.A., Sharma, R.P.: Plasma wave and second-harmonic generation of intense laser beams due to relativistic effects. Phys. Plasmas 11, 3186–3190 (2004)

    Article  ADS  Google Scholar 

  • Solak, H.H.: Nanolithography with coherent extreme ultraviolet light. J. Phys. D Appl. Phys. 39, R171–R188 (2006)

    Article  ADS  Google Scholar 

  • Teubner, U., Gibbon, P.: High-order harmonics from laser-irradiated plasma surfaces. Rev. Mod. Phys. 81, 445–479 (2009)

    Article  ADS  Google Scholar 

  • Tsallis, C.: Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479–487 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  • Tyagi, Y., Tripathi, D., Kumar, A.: Bernstein wave aided laser third harmonic generation in a plasma. Phys. Plasmas 23, 093115 (2016)

    Article  ADS  Google Scholar 

  • Vampa, G., Brabec, T.: Merge of high harmonic generation from gases and solids and its implications for attosecond science. J. Phys. B 50, 083001 (2017)

    Article  ADS  Google Scholar 

  • Wilks, S.C., Dawson, J.M., Mori, W.B., Katsouleas, T., Jones, M.E.: Photon accelerator. Phys. Rev. Lett. 62, 2600–2603 (1989)

    Article  ADS  Google Scholar 

  • Winterfeldt, C., Spielmann, C., Gerber, G.: Colloquium: optimal control of high-harmonic generation. Rev. Mod. Phys. 80, 117–140 (2008)

    Article  ADS  Google Scholar 

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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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Correspondence to Naveen Gupta.

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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 (2021). https://doi.org/10.1007/s11082-021-02827-w

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