Skip to main content Accessibility help

Effect of electron-ion recombination on self-focusing/defocusing of a laser pulse in tunnel ionized plasmas

  • Shikha Misra (a1), S. K. Mishra (a2), M. S. Sodha (a1) and V. K. Tripathi (a3)


A formalism for investigation of the propagation characteristics of various order short duration (pico second) Gaussian/dark hollow Gaussian laser pulse (DHGP) in a tunnel ionized plasma has been developed, which takes into account the electron-ion recombination. Utilizing the paraxial like approach, a nonlinear Schrödinger wave equation characterizing the beam spot size in space and time has been derived and solved numerically to investigate the transverse focusing (in space) and longitudinal compression (in time) of the laser pulse; the associated energy localization as the pulse advances in the plasma has also been analyzed. It is seen that in the absence of recombination the DHGP and Gaussian pulse undergo oscillatory and steady defocusing respectively. With the inclusion of recombination, the DHGP and Gaussian pulse both undergo periodic self-focusing for specific parameters. The DHGPs promise to be suitable for enhancement of energy transport inside the plasma.


Corresponding author

Address correspondence and reprint requests to: Shikha Misra, Centre of Energy Studies, Indian Institute of Technology Delhi, New Delhi 110016, India. E-mail:


Hide All
Akhmanov, S.A., Sukhorukov, A.P. & Khokhlov, R.V. (1968). Self-focusing and diffraction of light in a Nonlinear medium. Sov. Phys. Usp. 10, 609636.
Amendt, P., et al. (1991). X-ray lasing by optical-field-induced ionization. Phys. Rev. Lett. 66, 25892592.
Anand, S. (2009). Generation of Gaussian beam and its anomalous behaviour. Opt. Comm. 282, 13351339.
Annou, R., Tripathi, V.K. & Srivastava, M.P. (1996). Plasma channel formation by short pulse laser. Phys. Plasmas 3, 13561359.
Arlt, J. & Dholakia, K. (2000). Generation of high-order Bessel beams by use of an axicon. Opt. Comm. 177, 297301.
Biondi, M.A. & Brown, S.C. (1949). Measurement of electron and ion recombination, Technical Report 135, August 3, (Research laboratory of electronics)
Borisov, A.B., Borovisiky, A.V., Shiryaev, O.B., Korobkin, V.V., Prokhorov, A.M., Solem, J.C., Luk, T.S., Boyer, K. & Rhodes, C.K. (1992). Relativistic and charge-displacement self-channeling of intense ultrashort laser pulses in plasmas. Phys. Rev. A 45, 58305845.
Brandi, H.S., Manus, C., Mainfray, G., Lehner, T. & Bonnaud, G. (1993). Relativistic and ponderomotive self-focusing of a laser beam in a radially inhomogeneous plasma. I. Paraxial approximation. Phys. Fluids 5, 35393550.
Burnett, N.H. & Enright, G.D. (1990). Population inversion in the recombination of optically-ionized plasmas. IEEE J. Quant. Electron. 26, 17971808.
Cai, Y., Liu, X. & Lin, Q. (2003). Hollow Gaussian beam and their propagation properties. Opt. Lett. 28, 10841086.
Cai, Y. & Lin, Q. (2004). The elliptical Hermite–Gaussian beam and its propagation through paraxial systems. J. Opt. Soc. Am. A 21, 10581065.
Deng, S., Barnes, C.D., Clayton, C.E., O'Connell, C., Decker, F.J., Emma, P., Erdem, O., Huang, C., Hogan, M.J., Iverson, R., Johnson, D.K., Joshi, C., Katsouleas, T., Krejcik, P., Lu, W., Marsh, K., Mori, W.B., Mugglil, P., Siemann, R.H. & Walz, D. (2003). Proceeding of the Particle Accelerator conference.
Dufree III, C.G. & Milchburg, H.M. (1993). Light pipe for high intensity laser pulses. Phys. Rev. Lett. 71, 24092412.
Ganic, D., Gan, X. & Gu, M. (2003). Focusing of doughnut laser beams by a high numerical-aperture objective in free space. Opt. Express 11, 27472752.
Gildenburg, V.B., Kim, A.V., Krupnov, V.A., Semenov, V.E., Sergeev, A.M. & Zharova, N.A. (1993). Adiabatic frequency up-conversion of a powerful electromagnetic pulse producing gas ionization. IEEE Trans. Plasma Sci. 21 3444.
Gupta, D.N., Suk, H. & Ryu, C.M. (2005). Electron acceleration and electron-positron pair production by laser in tunnel ionized inhomogeneous plasma. Phys. Plasmas 12, 093110/1–6.
Gupta, R., Sharma, P., Rafat, M. & Sharma, R.P. (2011 a). Cross-focusing of two hollow Gaussian laser beams in plasmas. Laser Part. Beams 29, 227230.
Gupta, R., Rafat, M. & Sharma, R.P. (2011 b). Effect of relativistic self-focusing on plasma wave excitation by a hollow Gaussian beam. J. Plasma. Phys. 77, 777784.
Gurevich, A.V. (1978). Nonlinear Phenomena in the Ionosphere. New York: Springer.
Hefferon, G., Sharma, A. & Kourakis, I. (2010). Electromagnetic pulse compression and energy localization in quantum plasmas. Phys. Lett. A 374, 43364342.
Herman, R.M. & Wiggins, T.A. (1991). Production and uses of diffraction less beams. J. Opt. Sot. Am. A 8, 932942.
Joshi, C., et al. (1984). Ultrahigh gradient particle acceleration by intense laser-driven plasma density waves. Nature (London) 311, 525529.
Keldysh, L.V. (1965). Ionization in the field of a strong electromagnetic wave. Sov. Phys. JETP 20, 13071314.
Landau, L.D. & Lifshitz, E.M. (1978). Quantum Mechanics. London: Pergamum.
Lee, H.S., Atewart, B.W., Choi, K. & Fenichel, H. (1994). Holographic non-diverging hollow beams. Phys. Rev. A 49, 49224927.
Leemans, W.P., Clayton, C.E., Mori, W.B., Marsh, K.A., Kaw, P.K., Dyson, A. & Joshi, C. (1992). Experiments and simulations of tunnel-ionized plasmas. Phys. Rev. A. 46, 10911105.
Liu, C.S. & Tripathi, V.K. (1994). Laser guiding in an axially nonuniform plasma channel. Phys. Plasmas 1, 31003103.
Liu, C.S. & Tripathi, V.K. (2000). Ring formation in self-focusing of electromagnetic beams in plasmas. Phys. Plasmas 7, 43604363.
Mei, Z. & Zhao, D. (2005). Controllable dark-hollow beams and their propagation characteristics. J. Opt. Soc. Am. A 22, 18981902.
Misra, S. & Mishra, S.K. (2009). Focusing of dark hollow Gaussian electromagnetic beams in a plasma with relativistic-ponderomotive regime. Prog. Electromagn. Res. B 16, 291309.
Parashar, J., Pandey, H.D. & Tripathi, V.K. (1997). Two dimensional effects in a tunnel ionized plasma. Phys. Plasmas 4, 30403042.
Paterson, C. & Smith, R. (1996). Higher-order Bessel waves produced by axicon-type computer-generated holograms. Opt. Comm. 124, 121130.
Sharma, A., Borhanian, J. & Kourakis, I. (2009). Electromagnetic beam profile dynamics in collisional plasmas. J. Phys. A: Math. Theor. 42, 4655011–12.
Sharma, A. & Kourakis, I. (2009). Relativistic laser pulse compression in plasmas with a linear axial density gradient. Plasmas Phys. Contr. Fusion 52, 065002/1–13.
Sharma, A., Kourakis, I. & Shukla, P.K. (2010). Spatiotemporal evolution of high-power relativistic laser pulses in electron-positron-ion plasmas. Phys. Rev. E 82, 016402/1–7.
Sodha, M.S., Ghatak, A.K. & Tripathi, V.K. (1974). Self Focusing of Laser Beams in Dielectrics, Semiconductors and Plasmas. Delhi: Tata-McGraw-Hill.
Sodha, M.S., Mishra, S.K. & Misra, S. (2009 a). Focusing of dark hollow Gaussian electromagnetic beams in a plasma. Laser Part. Beams 27, 5768.
Sodha, M.S., Mishra, S.K. & Misra, S. (2009 b). Focusing of dark hollow Gaussian electromagnetic beam in a magneto-plasma. J. Plasma Phys. 75, 731748.
Soding, J., Grimm, R. & Ovchinnikov, Yu.V. (1995). Gravitational laser trap for atoms with evanescent wave cooling. Opt. Comm. 119, 652662.
Tajima, T. & Dawson, J.M. (1979). Laser electron accelerator. Phys. Rev. Lett. 43, 267270.
Tikhonenko, V. & Akhmediev, N.N. (1996). Excitation of vortex solitons in a Gaussian beam configuration. Opt. Comm. 126, 108112.
Verma, U. & Sharma, A.K. (2011). Laser focusing and multiple ionization of Ar in a hydrogen plasma channel created by a pre-pulse. Laser Part. Beams 29, 219225.
Wang, X. & Littman, M.G. (1993). Laser cavity for generation of variable radius rings of light. Opt. Lett. 18, 767770.
Xu, X., Wang, Y. & Jhe, W. (2002). Theory of atom guidance in a hollow laser beam: Dressed atom approach. J. Opt. Soc. Am. B 17, 10391050.
Yin, J., Gao, W. & Zhu, Y. (2003). Propagation of various dark hollow beams in a turbulent atmosphere. Progr. Opt. 44, 119204.
Yin, J., Noh, H., Lee, K., Kim, K., Wang, Yu. & Jhe, W. (1997). Generation of a dark hollow beam by a small hollow fibre. Opt. Comm. 138, 287292.
York, A.G., Milchberg, H.M., Palastro, J.P. & Antonsen, T.M. (2008). Direct acceleration of electrons in a corrugated plasma waveguide. Phys. Rev. Lett. 100 195001–7
Zhu, K., Tang, H., Sun, X., Wang, X. & Liu, T. (2002). Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams. Opt. Comm. 207, 2934.


Effect of electron-ion recombination on self-focusing/defocusing of a laser pulse in tunnel ionized plasmas

  • Shikha Misra (a1), S. K. Mishra (a2), M. S. Sodha (a1) and V. K. Tripathi (a3)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed