Advertisement

Evolution of the beam-width parameter of zeroth-order Bessel–Gaussian beams in collisional plasma with density ripple

  • L. Ouahid
  • L. Dalil-Essakali
  • A. BelafhalEmail author
Article
  • 36 Downloads

Abstract

In the present paper, we have investigated the self-focusing of zeroth-order Bessel–Gaussian beams in collisional plasma with density ripple. Based on Wentzel–Kramers–Brillouin and the paraxial ray approximations, the nonlinear differential equation governing the evolution of beam-width parameter is evaluated. The variation of beam-width parameter with propagation distance is examined for different values of ripple wave number and beam parameters. From our study, it is seen that stronger self-focusing is obtained when the density ripple is important. The results corresponding to Gaussian beams are deduced from this work as a particular case.

Keywords

Zeroth-order Bessel–Gaussian beams Wentzel–Kramers–Brillouin approximation Collisional plasma Density ripple 

Notes

References

  1. Aggarwal, M., Vij, S., Kant, N.: Propagation of cosh Gaussian laser beam in plasma with density ripple in relativistic-ponderomotive regime. Optik 125, 5081–5084 (2014)CrossRefADSGoogle Scholar
  2. Aggarwal, M., Kumar, H., Kant, N.: Propagation of Gaussian laser beam through magnetized cold plasma with increasing density ramp. Optik 127, 2212–2216 (2016)CrossRefADSGoogle Scholar
  3. Akhmanov, S.A., Sukhorukov, A.P., Khokhlov, R.V.: Self-focusing and diffraction of light in a nonlinear medium. Sov. Phys. Usp. 10, 609–636 (1968)CrossRefADSGoogle Scholar
  4. Arlt, J., Chávez, V.G., Sibbett, W., Dholakia, K.: Optical micromanipulation using a Bessel light beam. Opt. Commun. 197, 239–245 (2001)CrossRefADSGoogle Scholar
  5. Arora, V., Naik, P.A., Chakera, J.A., Bagchi, S., Tayyab, M., Gupta, P.D.: Study of 1–8 keV K-α X-ray emission from high intensity femtosecond laser produced plasma. AIP Adv. 4, 047106-1–047106-11 (2014)CrossRefADSGoogle Scholar
  6. Baranova, N.B., Zeldovich, B.Y., Scully, M.O.: Acceleration of charged particles by laser beams. J. Exp. Theor. Phys. 78, 249–258 (1994)ADSGoogle Scholar
  7. Belafhal, A., Dalil-Essakali, L.: Collins formula and propagation of Bessel-modulated Gaussian light beams through an ABCD optical system. Opt. Commun. 177, 181–188 (2000)CrossRefADSGoogle Scholar
  8. Cang, J., Zhang, Y.: Axial intensity distribution of truncated Bessel–Gauss beams in a turbulent atmosphere. Optik 121, 239–245 (2010)CrossRefADSGoogle Scholar
  9. Chen, F., Li, J., Belafhal, A., Chafiq, A., Sun, X.: Near-field spectral shift of a zero-order Bessel beam scattered from a spherical particle. Laser Phys. Lett. 15, 1–5 (2018)Google Scholar
  10. Dahiya, D., Sajal, V., Sharma, A.K.: Phase-matched second- and third-harmonic generation in plasmas with density ripple. Phys. Plasmas 14, 123104-1–123104-7 (2007)CrossRefADSGoogle Scholar
  11. Fahrbach, F.O., Simon, P., Rohrbach, A.: Microscopy with self-reconstructing beams. Nat. Photonics 4, 780–785 (2010)CrossRefADSGoogle Scholar
  12. Florjanczyk, M., Tremblay, R.: Guiding of atoms in a travelling-wave laser trap formed by the axicon. Opt. Commun. 73, 448–450 (1989)CrossRefADSGoogle Scholar
  13. Gori, F., Guattari, G.: Bessel–Gauss beams. Opt. Commun. 64, 491–495 (1987)CrossRefADSGoogle Scholar
  14. Gupta, D.N., Hur, M.S., Hwang, I., Suk, H.: Plasma density ramp for relativistic self-focusing of an intense laser. J. Opt. Soc. Am. B 24, 1155–1159 (2007)CrossRefADSGoogle Scholar
  15. Habibi, M., Ghamari, F.: Stationary self-focusing of intense laser beam in cold quantum plasma using ramp density profile. Phys. Plasmas 19, 103110-1–103110-6 (2012a)ADSGoogle Scholar
  16. Habibi, M., Ghamari, F.: Investigation of non-stationary self-focusing of intense laser pulse in cold quantum plasma using ramp density profile. Phys. Plasmas 19, 113109-1–113109-6 (2012b)ADSGoogle Scholar
  17. Hafeez, S., Shaikh, N.M., Baig, M.A.: Spectroscopic studies of Ca plasma generated by the fundamental, second, and third harmonics of a Nd:YAG laser. Laser Part. Beams 26, 41–50 (2008)CrossRefGoogle Scholar
  18. Herman, R.M., Wiggins, T.A.: Production and uses of diffractionless beams. J. Opt. Soc. Am. A 8, 932–942 (1991)CrossRefADSGoogle Scholar
  19. Hricha, Z., Dalil-Essakali, L., Belafhal, A.: Axial intensity distribution and focal shifts of focused partially coherent conical Bessel–Gauss beams. Opt. Quantum Electron. 35, 101–110 (2003)CrossRefGoogle Scholar
  20. Kant, N., Wani, M.A.: Density transition based self-focusing of cosh-Gaussian laser beam in plasma with linear absorption. Commun. Theor. Phys. 64, 103–107 (2015)MathSciNetCrossRefGoogle Scholar
  21. Kant, N., Wani, M.A., Kumar, A.: Self-focusing of Hermite–Gaussian laser beams in plasma density ramp. Opt. Commun. 285, 4483–4487 (2012)CrossRefADSGoogle Scholar
  22. Kaur, S., Sharma, A.K.: Nonlinear propagation of a short-pulse laser in a plasma with density ripple. Korean Phys. Soc. 53, 3768–3771 (2008)CrossRefADSGoogle Scholar
  23. Kaur, S., Sharma, A.K.: Self-focusing of a laser pulse in plasma with periodic density ripple. Laser Part. Beams 27, 193–199 (2009)CrossRefADSGoogle Scholar
  24. Kaur, S., Kaur, M., Kaur, R., Gill, T.S.: Propagation characteristics of Hermite-cosh-Gaussian laser beam in a rippled density plasmas. Laser Part. Beams 35(1), 100–107 (2017)CrossRefADSGoogle Scholar
  25. Kuo, C.C., Pai, C.H., Lin, M.W., Lee, K.H., Lin, J.Y., Wang, J., Chen, S.Y.: Enhancement of relativistic harmonic generation by an optically preformed periodic plasma waveguide. Phys. Rev. Lett. 98, 033901-1–033901-4 (2007)CrossRefADSGoogle Scholar
  26. Lin, M.W., Chen, Y.M., Pai, C.H., Kuo, C.C., Lee, K.H., Wang, J., Chen, S.Y.: Programmable fabrication of spatial structures in a gas jet by laser machining with a spatial light modulator. Phys. Plasmas 13, 110701-1–110701-4 (2006)ADSGoogle Scholar
  27. 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, 023106-1–023106-4 (2008)ADSGoogle Scholar
  28. Lu, B., Huang, W.: Focal shift in unapertured Bessel–Gauss beams. Opt. Commun. 109, 43–46 (1994)CrossRefADSGoogle Scholar
  29. Michel, P., Divol, L., Dewald, E.L., Milovich, J.L., Hohenberger, M., Jones, O.S., Hopkins, L.B., Berger, R.L., Kruer, W.L., Moody, J.D.: Multi-beam stimulated raman scattering in inertial confinement fusion conditions. Phys. Rev. Lett. 115, 055003-1–055003-5 (2015)CrossRefADSGoogle Scholar
  30. Mitri, F.G.: Nonparaxial Bessel and Bessel–Gauss pincers light-sheets. Phys. Lett. A 190, 1–5 (2016)MathSciNetGoogle Scholar
  31. Nanda, V., Kant, N.: Enhanced relativistic self-focusing of Hermite-cosh-Gaussian laser beam in plasma under density transition. Phys. Plasmas 21, 042101-1–042101-6 (2014)ADSGoogle Scholar
  32. Nanda, V., Kant, N., Wani, M.A.: Self-focusing of a Hermite-cosh Gaussian laser beam in a magnetoplasma with ramp density profile. Phys. Plasmas 20, 113109-1–113109-7 (2013)CrossRefADSGoogle Scholar
  33. Navare, S.T., Takale, M.V., Patil, S.D., Dongare, M.B.: Impact of linear absorption on self-focusing of Gaussian laser beam in collisional plasma. Opt. Lasers Eng. 50, 1316–1320 (2012)CrossRefGoogle Scholar
  34. Ouahid, L., Dalil-Essakali, L., Belafhal, A.: Relativistic self-focusing of finite Airy–Gaussian beams in collisionless plasma using the Wentzel–Kramers–Brillouin approximation. Optik 154, 58–66 (2018a)CrossRefADSGoogle Scholar
  35. Ouahid, L., Dalil-Essakali, L., Belafhal, A.: Effect of light absorption and temperature on self-focusing of finite Airy–Gaussian beams in a plasma with relativistic and ponderomotive regime. Opt. Quantum Electron 50(216), 1–17 (2018b)Google Scholar
  36. 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)CrossRefADSGoogle Scholar
  37. 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, 083101-1–083101-5 (2013)ADSGoogle Scholar
  38. Patil, S.D., Takale, M.V.: Ponderomotive and weakly relativistic self-focusing of Gaussian laser beam in plasma: effect of light absorption. AIP Conf. Proc. 1728, 020129–1–020129-4 (2016)Google Scholar
  39. Patil, S.D., Takale, M.V., Gill, T.S.: Effect of light absorption on relativistic self-focusing of Gaussian laser beam in plasma. Eur. Phys. J. D 69, 163.1–163.4 (2015)CrossRefGoogle Scholar
  40. Patil, S.D., Takale, M.V., Fulari, V.J., Gill, T.S.: Sensitiveness of light absorption for self-focusing at laser-plasma interaction with weakly relativistic and ponderomotive regime. Laser Part. Beams 34, 669–674 (2016)CrossRefADSGoogle Scholar
  41. Purohit, G., Chauhan, P.K., Sharma, R.P.: Excitation of an upper hybrid wave by a high power laser beam in plasma. Laser Part. Beams 26, 61–67 (2008)CrossRefGoogle Scholar
  42. Saad, F., Belafhal, A.: Conical refraction with Bessel–Gaussian beam modulated by Bessel gratings using biaxial crystals. Optik 127, 10868–10874 (2016)CrossRefADSGoogle Scholar
  43. Sabaeian, M., Nadgaran, H.: Bessel–Gauss beams: investigations of thermal effects on their generation. Opt. Commun. 281, 672–678 (2008)CrossRefADSGoogle Scholar
  44. Singh, M., Singh, R.K., Sharma, R.P.: THz generation by cosh-Gaussian lasers in rippled density plasma. Eerophys. Lett. 104, 35002-1–35002-5 (2013)ADSGoogle Scholar
  45. Sodha, M.S., Ghatak, A.K., Tripathi, V.K.: Self-focusing of laser beams in plasmas and semiconductors. Prog. Opt. 13, 169–265 (1976)CrossRefADSGoogle Scholar
  46. Tajima, T., Dawson, J.M.: Laser electron accelerator. Phys. Rev. Lett. 43, 267–270 (1979)CrossRefADSGoogle Scholar
  47. Urunkar, T.U., Valkunde, A.T., Vhanmore, B.D., Gavade, K.M., Patil, S.D., Takale, M.V.: On the exploration of effect of critical beam power on the propagation of Gaussian laser beam in collisionless magnetized plasma. AIP Conf. Proc. 1953(1), 140087-1–140087-4 (2018).  https://doi.org/10.1063/1.5033262 CrossRefGoogle Scholar
  48. Valkunde, A.T., Patil, S.D., Vhanmore, B.D., Urunkar, T.U., Gavade, K.M., Takale, M.V., Fulari, V.J.: Analytical investigation on domain of decentered parameter for self-focusing of Hermite-cosh-Gaussian laser beam in collisional plasma. Phys. Plasmas 25, 033103.1–033103.6 (2018a)CrossRefGoogle Scholar
  49. Valkunde, A.T., Patil, S.D., Takale, M.V., Vhanmore, B.D., Urunkar, T.U., Gavade, K.M., Gupta, D.N.: Exponential density transition based self-focusing of Gaussian laser beam in collisional plasma. Optik 158, 1034–1039 (2018b)CrossRefADSGoogle Scholar
  50. Vhanmore, B.D., Patil, S.D., Valkunde, A.T., Urunkar, T.U., Gavade, K.M., Takale, M.V.: Self-focusing of asymmetric cosh-Gaussian laser beams propagating through collisionless magnetized plasma. Laser Part. Beams 35, 670–676 (2017)CrossRefADSGoogle Scholar
  51. Wani, M.A., Kant, N.: Nonlinear propagation of Gaussian laser beam in an inhomogeneous plasma under plasma density ramp. Optik 127, 6710–6714 (2016)CrossRefADSGoogle Scholar
  52. Wani, M.A., Kant, N.: Self-focusing of a laser beam in the rippled density magnetoplasma. Optik 128, 1–7 (2017)CrossRefADSGoogle Scholar
  53. Wulle, T., Herminghaus, S.: Nonlinear optics of Bessel beams. Phys. Rev. Lett. 70, 1401–1404 (1993)CrossRefADSGoogle Scholar
  54. Yang, Y., Li, Y.: Spectral shifts and spectral switches of a pulsed Bessel–Gauss beam from a circular aperture in the far field. Opt. Laser Technol. 39, 1478–1484 (2007)CrossRefADSGoogle Scholar
  55. Zhang, Q., Cheng, X., Chen, H., He, B., Ren, Z., Zhang, Y., Bai, J.: Enhancement of phase conjugation degenerate four-wave mixing using a Bessel beam. Photonics Res. 6, 162–167 (2018)CrossRefGoogle Scholar
  56. Zhanga, Z., Zenga, X., Miaoa, Y., Fanc, Y., Gaoa, X.: Focusing properties of vector Bessel–Gauss beam with multiple-annular phase wavefront. Optik 157, 240–247 (2018)CrossRefADSGoogle Scholar
  57. Zhao, D., Wang, S.: Comparison of transformation characteristics of linearly polarized and azimuthally polarized Bessel–Gauss beams. Opt. Commun. 131, 8–12 (1996)CrossRefADSGoogle Scholar
  58. Zhao, C., Huang, K., Lu, X.: Propagation properties of Bessel and Bessel–Gaussian beams in a fractional Fourier transform optical system. Opt. Laser Technol. 42, 280–284 (2010)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratory LPNAMME, Laser Physics Group, Department of Physics, Faculty of Sciences, Chouaïb Doukkali UniversityEl JadidaMorocco

Personalised recommendations