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Relativistic effects on propagation of q-Gaussian laser beam in a rippled density plasma: Application of higher order corrections

  • M. Kaur (a1), P. C. Agarwal (a2), S. Kaur (a1) and T. S. Gill (a1)


A nonparaxial investigation for propagation characteristics of q-Gaussian laser beam in rippled density plasma is studied by considering the relativistic nonlinearity. The field distribution in the medium is expressed in terms of q parameter and beam width parameter f. Nonlinear parabolic partial differential equation governing the evolution of complex envelope in slowly varying approximation is solved in a modulated density profile. Analytical theory of self-focusing including higher order terms in the expansion of dielectric function up to fourth order is developed and the variation of beam width parameter f with the distance of propagation for different parameters is studied. One may note that increased value of density ripple, laser intensity and depth of modulation, increases self-focusing whereas a lower value of q shows strong self-focusing. A comparative study between paraxial and nonparaxial study has also conducted. This study is useful for research in high energy density physics.


Corresponding author

Author for correspondence: S. Kaur, Department of Physics, Guru Nanak Dev University, Amritsar, 143005, Punjab, India. E-mail:


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Abari, ME, Sedaghat, M and Hosseinnejad, MT (2017) Self-focusing of a high intensity laser pulse by a magnetized plasma lens in sub-relativistic regime. Journal of Theoretical and Applied Physics 11, 143150.
Aggarwal, M, Vij, S and Kant, N (2014) Propagation of cosh Gaussian laser beam in plasma with density ripple in relativistic – ponderomotive regime. Optik 125, 50815084.
Akhmanov, SA, Sukhorukov, AP and Khokhlov, RV (1966) Self- focusing and self-trapping of intense light beams in a nonlinear medium. Soviet Physics JETP 23, 10251033.
Anderson, D and Bonnedal, M (1979) Variational approach to nonlinear self focusing of gaussian laser beams. Physics of Fluids 22, 105109.
Askar'yan, G (1962) Effect of the gradient of a strong electromagnetic beam on electron and atoms. Journal of Experimental and Theoretical Physics 42, 15671570.
Bokaei, B and Niknam, AR (2014) Weakly relativistic and ponderomotive effects on self focusing and self-compression of laser pulses in near critical plasmas. Physics of Plasmas 21, 103107.
Bonabi, RS, Habibi, M and Yazdani, E (2009) Improving the relativistic self focusing of intense laser beam in plasma using density transition. Physics of Plasmas 16, 083105.
Davies, JR (2010) Private communication.
Faisal, M, Mishra, SK, Verma, MP and Sodha, MS (2007) Ring formation in self-focusing of electromagnetic beams in plasmas. Physics of Plasmas 14, 103103.
Firth, WJ (1977) Propagation of laser beams through inhomogeneous media. Optics Communications 22, 226230.
Ghoranneviss, M, Malekynia, B, Hora, H, Miley, GH and He, X (2008) Inhibition factor reduces fast ignition threshold for laser fusion using nonlinear force driven block acceleration. Laser and Particle Beams 26, 105111.
Gill, TS, Kaur, R and Mahajan, R (2010a) Propagation of high power electromagnetic beam in relativistic magnetoplasma: Higher order paraxial ray theory. Physics of Plasmas 17, 093101.
Gill, TS, Kaur, R and Mahajan, R (2015) Self-focusing of super-Gaussian laser beam in magnetized plasma under relativistic and ponderomotive regime. Optik 126, 16831690.
Gill, TS, Mahajan, R and Kaur, R (2010b) Relativistic and ponderomotive effects on evolution of dark hollow Gaussian electromagnetic beams in a plasma. Laser and Particle Beams 28, 521529.
Gill, TS, Mahajan, R, Kaur, R and Gupta, S (2012) Relativistic self-focusing of super Gaussian laser beam in plasma with transverse magnetic field. Laser and Particle Beams 30, 509516.
Gupta, DN, Hur, MS, Hwang, I, Suk, H and Sharma, AK (2007) Plasma density ramp for relativistic self-focusing of an intense laser. Journal of the Optical Society of America B 24, 11551159.
Hoffmann, DHH, Blazevic, A, Ni, P, Rosmej, O, Roth, M, Tahir, NA, Tauschwitz, A, Udera, S, Vanentsov, D, Weyrich, K and Maron, Y (2005) Present and future perspectives for high energy density physics with intense heavy ion and laser beams. Laser and Particle Beams 23, 4753.
Hora, H (1975) Theory of relativistic self focusing of laser radiation in plasmas. Journal of the Optical Society of America 65, 882886.
Kaur, R, Gill, TS and Mahajan, R (2017a) Relativistic effects on evolution of a q Gaussian laser beam in magnetoplasma: application of higher order corrections. Physics of Plasmas 24, 053105.
Kaur, S, Kaur, M, Kaur, R and Gill, TS (2017b) Propagation characteristics of Hermite-cosh-Gaussian laser beam in a rippled density plasmas. Laser and Particle Beams 35, 100107.
Kaur, S and Sharma, AK (2008) Resonant third harmonic generation in a laser produced thin foil plasma. Physics of Plasmas 15, 102705.
Kaur, S and Sharma, AK (2009) Self focusing of a laser pulse in plasma with periodic density ripple. Laser and Particle Beams 27, 193199.
Kruglov, VI and Vlasov, RA (1985) Spiral self-trapping propagation of optical beams in media with cubic non linearity. Physics Letters 111A, 401404.
Kuo, CC, Pai, CH, Lin, MW, Lee, KH, Lin, JY, Wang, J and Chen, SY (2007) Enhancement of relativistic harmonic generation by an optically preformed periodic plasma waveguide. Physical Review Letters 98, 033901.
Lam, JF, Lippmann, B and Tappert, F (1975) Moment theory of self- trapped laser beams with nonlinear saturation. Optics Communications 15, 419421.
Lin, MW, Chen, YM, Pai, CH, Kuo, CC, Lee, KH, Wang, J, Chen, SY and Lin, JY (2006) Programmable fabrication of spatial structure in a gas jet by laser machining with a spatial light modulator. Physics of Plasmas 13, 110701.
Litvak, AG (1966) Self focusing of powerful light beams by thermal effects. Journal of Experimental and Theoretical Physics 4, 230.
Liu, CS and Tripathi, VK (2000) Laser frequency upshift, self-defocusing and ring formation in tunnel ionizing gases and plasmas. Physics of Plasmas 7, 4360.
Liu, CS and Tripathi, VK (2008) Third harmonic generation of a short pulse laser in a plasma density ripple created by a machining beam. Physics of Plasmas 15, 023106.
Miller, CL, Welch, DR, Rose, DV, Campbell, RB, Oliver, BV, Webb, TJ and Flicker, DG (2012) Simulations of dynamic laser/plasma X-ray production. IEEE Transactions on Plasma Science 40, 26582666.
Misra, S and Mishra, SK (2009) Ring formation in electromagnetic beams propagating in a magnetoplasma. Journal of Plasma Physics 75, 769.
Nakatsutsumi, M, Davies, JR, Kodama, R, Green, JS, Lancaster, KL, Akli, KU, Beg, FN, Chen, SN, Clark, D, Freeman, RR, Gregory, CD, Habara, H, Heathcote, R, Hey, DS, Highbarger, K, Jaanimagi, P, Key, MH, Krushelnick, K, Ma, T, Macphee, A, Mackinnon, AJ, Nakamura, H, Stephens, RB, Storm, M, Tampo, M, Theobald, W, Woerkom, LV, Weber, RL, Wei, MSF, Woolsey, NC and Norreys, PA (2008) Space and time resolved measurements of the heating of solids to ten million kelvin by a petawatt laser. New Journal of Physics 10, 043046.
Patil, SD, Navare, ST, Takale, MV and Dongare, MB (2009) Self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption. Optics and Lasers in Engineering 47, 604606.
Salih, HA, Tripathi, VK and Pandey, BK (2003) Second-harmonic generation of a Gaussian laser beam in a self created magnetized plasma channel. IEEE Transactions on Plasma Science 31, 324328.
Sharma, A and Kourakis, I (2010) Spatial evolution of a q-Gaussian laser beam in relativistic plasma. Laser and Particle Beams 28, 479489.
Singh, A and Gupta, N (2015) Second harmonic generation by relativistic self- focusing of q-Gaussian laser beam in preformed parabolic channel. Physics of Plasmas 22, 013102.
Singh, A and Walia, A (2010) Relativistic self-focusing and self-channeling of Gaussian laser beam in plasma. Applied Physics B: Photophysics and Laser Chemistry 101, 617622.
Singh, A and Walia, A (2013) Self-focusing of Gaussian laser beam in collisionless plasma and its effect on stimulated Brillouin scattering process. Optics Communications 290, 175182.
Sodha, MS and Faisal, M (2008) Propagation of high power electromagnetic beams in overdense plasmas: higher order paraxial theory. Physics of Plasmas 15, 033102.
Sodha, MS, Ghatak, AK and Tripathi, VK (1976) V self –focusing of laser beams in plasmas and semiconductors. Progress in Optics 13, 169265.
Sodha, MS, Mishra, SK and Misra, S (2009) Focusing of dark hollow Gaussian electromagnetic beams in a plasma. Laser and Particle Beams 27, 5768.
Sprangle, P, Hafizi, B and Penano, JR (2000) Laser pulse modulation instabilities in plasma channels. Physics Review E 61, 43814393.
Suk, H, Barov, N, Rosenzweig, JB and Esarey, E (2001) Trapping of background plasma electrons in a beam-driven plasma wake field using a downward density transition. AIP Conference Proceedings 569, 630639.
Wang, L, Hong, XR, Sun, JA, Tang, RA, Yang, Y, Zhou, WJ, Tian, JM and Duan, WS (2017) Effects of relativistic and channel focusing on q-Gaussian laser beam propagating in a preformed parabolic plasma channel. Physics Letters A 381, 20652071.
Xie, BS, Aimidula, A, Niu, JS, Liu, J and Yu, MY (2009) Electron acceleration in the wakefield of asymmetric laser pulses. Laser and Particle Beams 27, 2732.
Yin, J, Gao, W and Zhu, Y (2003) Generation of dark hollow beams and their applications. Progress in Optics 45, 119.
York, AG, Milchberg, HM, Palastro, JP and Antonsen, TM (2008) Direct acceleration of electrons in a corrugated plasma waveguide. Physical Review Letters 100, 195001.
Zhang, P, He, JT, Chen, DB, Li, ZH, Zhang, Y, Lang, W, Li, ZH, Feng, BH, Zhang, DX, Tang, XW and Zhang, J (1998) X-ray emission from ultra intense-ultra short laser irradiation. Physical Review E 57, 37463752.



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