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Spatial frequency modulation of \(q\)-gaussian laser beams in a collisional plasma exhibiting an axial density ramp

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Abstract

This study investigates the phenomenon of spatial frequency chirping in q-Gaussian laser beams interacting nonlinearly with plasmas exhibiting an axial density ramp. The chirping, also known as phase anomaly, arises from the inherent uncertainty between a photon's position and momentum.The non-uniform intensity distribution of the laser beam leads to uneven heating of plasma electrons, causing a redistribution of charged particles due to which self focusing of laser beam takes place. The reduction in transverse dimensions subsequently spreads the transverse momentum of photons, modifying the axial phase of the laser beam. Employing variational theory, equations governing the evolution of the laser beam's radius and spatial frequency (axial phase) were derived and solved numerically. This allowed for analysis of how various laser and plasma parameters influence the changes in the laser beam's spatial frequency (axial phase).

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References

  1. L.G. Gouy, “Sur une propriete nouvelle des ondes lumineuses, “ C. R. Acad. Sci. ParisSer. 110, 1251 (1890)

    Google Scholar 

  2. R.W. Boyd, Intuitive explanation of the phase anomaly of focused light beams. J. Opt. Soc. Am. 70, 877 (1980)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. T.H. Maiman, Stimulated Optical Radiation in Ruby. Nature 187, 993 (1960)

    Article  Google Scholar 

  5. F. Gittes, C.F. Schmidt, Interference model for back-focal-plane displacement detection in optical tweezers. Opt. Lett. 23, 7 (1998)

    Article  ADS  Google Scholar 

  6. S.B. Pal, A. Haldar, R.K. Gupta, N. Ghosh, B. Roy, A. Banerjee, Probing the dynamics of an optically trapped particle by phase sensitive back focal plane interferometry. Opt. Express 20, 8317 (2012)

    Article  ADS  Google Scholar 

  7. L. Friedrich, A. Rohrbach, Phase anomalies in Bessel-Gauss beams. Opt. Lett. 37, 2019 (2012)

    Google Scholar 

  8. B.E. Saleh, M.C. Teich, S. Carrasco, J.T. Fourkas, Second-and third-harmonic generation with vector Gaussian beams. J. Opt. Soc. Am. B 23, 2134 (2006)

    Article  ADS  Google Scholar 

  9. Y.Q. Qin, C. Zhang, Y.Y. Zhu, Perfect quasi-phase matching for the third-harmonic generation using focused Gaussian beams. Opt. Lett. 33, 720 (2008)

    Article  ADS  Google Scholar 

  10. M.F. Erden, H.M. Ozaktas, Accumulated Gouy phase shift in Gaussian beampropagation through first-order optical systems. J. Opt. Soc. Am. A 14, 2190 (1997)

    Article  ADS  Google Scholar 

  11. C. Finot, D. Oron, E.R. Andresen, H. Rigneault, Spectral analog of the Gouy phase shift. Phys. Rev. Lett. 110, 143902 (2013)

    Article  ADS  Google Scholar 

  12. R.J. Gordon, V.J. Barge, Effect of the Gouy phase on the coherent phase control of chemical reactions. J. Chem. Phys. 127, 204302 (2007)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  14. J.R. Davies, R. Kodama, J.S. Green, K.L. Lancaster, K.U. Akli, F.N. Beg, S.N. Chen, D. Clark, R.R. Free-man, C.D. Gregory, H. Habara, R. Heathcote, D.S. Hey, K. Highbarger, P. Jaan-imagi, M.H. Key, K. Krushelnick, T. Ma, A. MacPhee, A.J. MacKinnon, H. Nakamura, R.B. Stephens, Storm M. M. Tampo, W. Theobald, L.V. Woerkom, R.L. Weber, M.S. Wei, N.C. Woolsey, P.A. NakatsutsumiNorreys, 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 

  15. N. Singh, N. Gupta, 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  18. S. Feng, H.G. Winful, “Physical origin of the Gouy phase shift, “ Opt. Lett. 26, 485 (2001)

    Google Scholar 

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Correspondence to Naveen Gupta.

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Gupta, N., Johari, R., K, A.A. et al. Spatial frequency modulation of \(q\)-gaussian laser beams in a collisional plasma exhibiting an axial density ramp. J Opt (2024). https://doi.org/10.1007/s12596-024-01846-6

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  • DOI: https://doi.org/10.1007/s12596-024-01846-6

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