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Second-harmonic generation of two cross-focused q-Gaussian laser beams by nonlinear frequency mixing in plasmas

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Abstract

A scheme for second-harmonic generation (SHG) of a pair of q-Gaussian laser beams interacting nonlinearly with underdense plasma has been proposed. Due to the relativistic increase in electron mass under the intense fields of the laser beam, the resulting optical nonlinearity of plasma leads cross-focusing of the laser beams. The resulting nonlinear coupling between the two laser beams makes the oscillations of plasma electrons to contain a frequency component equal to the sum of frequencies of the pump beams. This results in a nonlinear current density at frequency equal to the sum of frequencies of the pump beams. If the frequencies of the pump beams are equal, then the resulting nonlinear current generates a new radiation at frequency twice the frequencies of the pump beams— a phenomenon known as SHG. Starting from nonlinear Schrodinger wave equation a set of coupled differential equations governing the evolution of beam widths of the laser beams and power of generated second-harmonic radiation with longitudinal distance has been obtained with the help of variational theory. The equations so obtained have been solved numerically to envision the effect of laser as well as plasma parameters on the power of generated second-harmonic radiation.

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References

  1. T.H. Maiman, Stimulated optical radiation in Ruby. Nature 187, 493 (1960)

    Article  ADS  Google Scholar 

  2. S.E. Miller, Communication by laser. Sci. Am. 214, 19 (1966)

    Article  ADS  Google Scholar 

  3. T. Fortier, E. Baumann, 20 years of developments in optical frequency comb technology and applications. Commun. Phys. 2, 153 (2019)

    Article  Google Scholar 

  4. M. Giunta, W. Hansel, M. Fischer, M. Lezius, T. Udem, R. Holzwarth, Real-time phase tracking for wide-band optical frequency measurements at the 20th decimal place. Nat. Photonics 14, 44 (2020)

    Article  CAS  ADS  Google Scholar 

  5. S. Mak, D. Yip, The measurement of the speed of light using a laser pointer. Phys. Educ. 35, 95 (2000)

    Article  ADS  Google Scholar 

  6. D.K. Mao, X.B. Deng, H.Q. Luo, Y.Y. Xu, M.K. Zhou, X.C. Duan, Z.K. Hu, A dual-magneto-optical-trap atom gravity gradiometer for determining the Newtonian gravitational constant. Rev. Sci. Inst. 92, 053202 (2021)

    Article  CAS  ADS  Google Scholar 

  7. E. Khalkhal, M.R. Tavirani, M.R. Zali, Z. Akbari, The evaluation of laser application in surgery: a review article. J. lasers in med. Sci. 10, S104 (2019)

    Article  Google Scholar 

  8. E. Esarey, C.B. Schroeder, W.P. Leemans, Physics of laser-driven plasma-based electron accelerators. Rev. Mod. Phys. 81, 1229 (2009)

    Article  CAS  ADS  Google Scholar 

  9. N. Gupta, S.B. Bhardwaj, Relativistic effects on electron acceleration by elliptical q-Gaussian laser beam driven electron plasma wave. Opt. Quant. Electron. 53, 700 (2021)

    Article  CAS  Google Scholar 

  10. N. Gupta, Hot electron generation by self focused quadruple gaussian laser beams during inertial confinement fusion. Nonlinear Opt. Quan. Opt. 55, 63 (2022)

    CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. N. Gupta, Optical second and third harmonic generation of laser beams in nonlinear media: a review. Nonlinear Opt. Quant. Opt. 53, 291 (2021)

    CAS  Google Scholar 

  13. A. Singh, N. Gupta, Higher harmonic generation by self-focused q-Gaussian laser beam in preformed collisionless plasma channel. Laser Part. Beams 32, 621 (2014)

    Article  CAS  ADS  Google Scholar 

  14. N. Gupta, Second harmonic generation of q-Gaussian laser beam in plasma channel created by ignitor heater technique. Laser Part. Beams 37, 184 (2019)

    Article  CAS  ADS  Google Scholar 

  15. N. Gupta, S. Kumar, Generation of second harmonics of self-focused quadruple-Gaussian laser beams in collisional plasmas with density ramp. J. Opt. 49, 455 (2020)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. A. Singh, N. Gupta, Second harmonic generation by relativistic self-focusing of q-Gaussian laser beam in preformed parabolic plasma channel. Phys. Plasmas 22, 013102 (2015)

    Article  ADS  Google Scholar 

  18. A. Sharma, I. Kourakis, Spatial evolution of a q-Gaussian laser beam in relativistic plasma. Laser Part. Beams 28, 470 (2010)

    Article  ADS  Google Scholar 

  19. N. Gupta, S. Kumar, S.B. Bhardwaj, Stimulated Raman scattering of self-focused elliptical q-Gaussian laser beam in plasma with axial density ramp: effect of ponderomotive force. J. Opt. (2021). https://doi.org/10.1007/s12596-021-00822-8

    Article  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  22. D. Anderson, M. Bonnedal, M. Lisak, Self-trapped cylindrical laser beams. Phys. Fluids 22, 1838 (1979)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Lovely Professional University, Phagwara, India

    Naveen Gupta, Sanjeev Kumar, Suman Choudhry, Rishabh Khatri, Siddhanth Shishodia & Rohit Johari

  2. SUS Govt College, Matak-Majri, Indri, Karnal, India

    S. B. Bhardwaj

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  1. Naveen Gupta
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  2. S. B. Bhardwaj
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  3. Sanjeev Kumar
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  4. Suman Choudhry
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  6. Siddhanth Shishodia
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  7. Rohit Johari
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Correspondence to Naveen Gupta.

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Gupta, N., Bhardwaj, S.B., Kumar, S. et al. Second-harmonic generation of two cross-focused q-Gaussian laser beams by nonlinear frequency mixing in plasmas. J Opt 53, 18–29 (2024). https://doi.org/10.1007/s12596-022-00995-w

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