عنوان مقاله [English]
The nonlinear propagation of electromagnetic waves in a plasma Bragg grating is considered. In a weakly relativistic regime, by means of the Maxwell’s equations along with a plasma fluid model, two coupled equations are found that govern the evolution of the envelopes of forward and backward propagating waves in a cold unmagnetized plasma undergoing an ambient density modulation in the form of gratings. Then, the nonlinear plane wave solutions with constant amplitude are obtained and the stability of them against a small perturbation is investigated. The dependence of the growth rate and instability window on relevant parameters of the system is addressed.
 D. Strickland, G. Mourou, Compression of amplified chirped optical pulse, Optics Communications 56 (1985) 219-221.
 G. Mourou, T. Tajima, S.V. Bulanov, Optics in relativistic regime, Review of Modern Physics 78 (2006) 309-371.
 An-Chun Tien, S. Backus, et. al., Short-pulse laser damage in transparent materials as a function of pulse durations, Physical Review Letters 82 (1999) 3883-3886.
 S. Suckewer, Ultra-intense laser: Beyound a pettawat, Nature Physics 7 (2011) 11-12.
 G. Mourou, J. Fisch, et. al., Exawat-Zettawat pulse generation and applications, Optics Communications 285 (2012) 720-724.
 C. Thaury, F. Quere, et. al., Plasma mirros for ultrahigh-intensity optics, Nature Physics 3 (2007) 424-429.
 P. Michel, L. Divol, D. Turnball, J.D. Moody, Dynamic control of the polarization of intense laser beams via optical wave mixing in plasmas, Physical Review Letters 113 (2014) 205001.
 Lu-Le Yu, Yao Zhao, et. al., Plasma optical modulator for intense lasers, Nature Communications 7 (2016) 11893.
 H.C. Wu, Z.M. Sheng, J. Zhang, Chirped pulse compression in nonuniform plasma gratings, Applied Physics Letters 87 (2005) 201502.
 H.C. Wu, Z.M. Sheng, Q.J. Zhang, J. Zhang, Manipulating ultrashort intense laser pulses by plasma Bragg gratings, Physics of Plasmas 12 (2005) 113103.
 S.X. Luan, Q.J. Zhang, Z.M. Sheng, The formation of relativistic electromagnetic solitons in plasma Bragg gratings induced by two counter-propagating laser pulses, Applied Physics B 93 (2008) 793-799.
M. Botton, A. Ron, Efficiency enhancement of a plasma filled backward wave oscillator by self-induced distributed feedback, Physical Review Letters 66 (1991) 2468-2471.
 Z.M. Sheng, J. Zhang, D. Umstadter, Plasma density gratings induced by intersecting laser pulses in underdense plasmas, Applied Physics B 77 (2003) 673-680.
 H.Y. Chen, Y. Yin, et. al., Moving electron density gratings induced in the beat-wave field of two counter-propagating laser pulses, Physics of Plasmas 17 (2010) 083112.
 M. Durand, A. Jarnac, et. al., Dynamics of plasma gratings in atomic and molecular gases, Physical Review E 86 (2012) 036405.
 G. Lehmann, K.H. Spatschek, Transient Plasma Photonic Crystals for High-Power Lasers, Physical Review Letters 116 (2016) 225002.
 G.P. Agrawal, Applications of nonlinear fiber optics 2nd Edition, Academic Press, New York, (2008).
 V.E. Zakharov, L.A. Ostrovsky, Modulational instability: the beginning, Physica D 238 (2009) 540-548.
 T.B. Benjamin, K. Hasselmann, Instability of periodic wavetrains in nonlinear dispersive systems, Proceedings of the Royal Society A 299 (1967) 59-75.
 L.A. Ostrovsky, Propagation of wave packets and space-time self-focusing in nonlinear medium, Soviet Physics JETP 24 (1967) 797-800.
 A. Hasegawa, Observation of self-trapping instability of a plasma cyclotron wave in a computer experiment, Physical Review Letters 24 (1970) 1165-1168.
 C.M. De Sterke, Theory of modulational instability in fiber Bragg gratings, Journal of the Optica Society of America B 15 (1998) 2660-2667.
 A. Yariv, P. Yeh, Photonics 6th Edition, Oxford Univerity Press, Oxford, (2007).
 J. Borhanian, Nonlinear birefringence in plasmas: Polarization dynamics, vector modulational instability and vector solitons, Physics of Plasmas 21 (2014) 062312.
 G.P. Agrawal, Nonlinear Fiber Optics 4th Edition, Academic Press, New York, (2007).
 M.R. Spiegel, S. Lipschutz, J. Liu, Mathematical handbook of formulas and table 3rd edition, Mc Graw-Hill, New York (2009).