Modulational instability of optically induced nematicon propagation

doi:10.1088/1674-1056/22/12/129401

Abstract We report the modulational instability (MI) analysis for the modulation equations governing the propagation of coherent polarized light through a nematic liquid crystal (NLC) slab, in the limit of low light intensity and local material response. The linear stability analysis of the nonlinear plane wave solutions is performed by considering both the wave vectors (k,l) of the basic states and wave vectors (K,L) of the perturbations as free parameters. We compute the MI gain, and the MI gain peak is reduced and the stable bandwidth is widened with the increase of the strength of the applied electric field. Further, we invoke the extended homogeneous balance method and Exp-function method aided with symbolic computation and obtain a series of periodic solitonic humps of nematicon profiles admitting the propagation of laser light in the NLC medium.

Keywords: solitons computational methods liquid crystals nonlinearity

Received: 01 February 2013
Revised: 30 May 2013
Accepted manuscript online:

PACS:	94.05.Fg	(Solitons and solitary waves)
	46.15.-x	(Computational methods in continuum mechanics)
	64.70.pp	(Liquid crystals)
	47.20.Ky	(Nonlinearity, bifurcation, and symmetry breaking)

Corresponding Authors: L. Kavitha
E-mail: louiskavitha@yahoo.co.in

Cite this article:

L. Kavitha, M. Venkatesh, S. Dhamayanthi, D. Gopi Modulational instability of optically induced nematicon propagation 2013 Chin. Phys. B 22 129401

[1]	Dodd R K, Eilbeck J C, Dibbon J D and Morris H C 1982 Solitons and Nonlinear Wave Equation (New York: Academic Press)
[2]	Drazin P G and Johnson R S 1989 Solitons: An Introduction (New York: Cambridge University Press)
[3]	Stegeman G I, Christodoulides D N and Sege M 2000 IEEE J. Sel. Top. Quantum Electron 6 1419
[4]	Kivshar Y S and Agrawal G P 2003 Optical Solitons: From Fibers to Photonic Crystals (New York: Academic)
[5]	Peccianti M, Dyadyusha A, Kaczmarek M and Assanto G 2006 Nat. Phys. 2 737
[6]	Shalaby M and Barthelemy A 1991 Opt. Lett. 16 1472
[7]	Shen Y R 2002 The Principle of Nonlinear Optics (New York: Wiley)
[8]	Khoo I C 1995 Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (New York: Wiley)
[9]	Daniel M, Gnanasekaran K and Kavitha L 2008 Physica D 237 3135
[10]	Assanto G and Peccianti M 2003 IEEE J. Quantum Electron 39 13
[11]	Mclaughlin D W, Muraki D J, Shelley M J and Wang X 1995 Physica D 88 55
[12]	McLaughlin D W, David J M and Michael J S 1996 Physica D 97 471
[13]	Conti C, Peccianti M and Assanto G 2003 Phys. Rev. Lett. 91 073901
[14]	Catherine G R, Antonmaria A M, Marchant T R, Noel F S and Annette L W 2008 Physica D 237 1088
[15]	Collet J H, Litaize D, van Camenhout J, Jesshope C, Desmulliez M, Thienpont H, Goodman J W and Louri A 2000 Appl. Opt. 39 671
[16]	Pinkston T M and Goodman J W 1994 Appl. Opt. 33 1434
[17]	Yang L, Liu J and Wang K 2001 Phys. Lett. A 278 267
[18]	de Gennes P G and Prost J 1974 The Physics of Liquid Crystals (Oxford: Clarendon Press)
[19]	Snyder A and Mitchell D 1997 Science 276 1538
[20]	Reyes J A and Palffy-Muhoray P 1998 Phys. Rev. E 58 5855
[21]	Sarkissian H, Tsai C, Zeldovich B and Tabirian N 2005 "Beam Clean Up and Combining Using Orientational Stimulated Scattering in Liquid Crystal", Conference on Laser and Electro-Optics: Application of LY3 Nonlinearities, Optical Society of America, 2005, p. 505
[22]	Warenghem M, Blach J F, Henninot J F 2006 Mol. Cryst. Liq. Cryst. 454 297
[23]	Reinbert C G, Minzoni A A, Smyth N F and Worthy A L 2006 J. Opt. Soc. Am. B 23 2551
[24]	Reinbert C G, Minzoni A A and Smyth N F 2006 J. Opt. Soc. Am. B 23 294
[25]	Fratalocchi A and Assanto G 2005 Phys. Rev. E 72 066608
[26]	Krolikowski W, Bang O, Nikolov N, Neshev D, Wyller J, Ramussen J and Edmundson D 2004 J. Opt. B 6 S288
[27]	Wyller J, Krlikowski W Z, Bang O, Petersen D E and Rasmussen J J 2007 Physica D 227 8
[28]	Griffiths S D, Grimshaw R H J and Khusnutdinova K R 2006 Physica D 214 1
[29]	Li S C and Duan W S 2009 Chin. Phys. B 18 4177
[30]	Zhang B Z, Cui H and She W L 2009 Chin. Phys. B 18 209
[31]	Xue J K, Duan W S and Lang H 2002 Chin. Phys. 11 1184
[32]	El-Labany S K, Abdel Krim M S, El-Warraki S A and El-Taibany W F 2003 Chin. Phys. 12 759
[33]	El-Wakil S A, Abulwafa E M, Elhanbaly A and Abdou M A 2007 Chaos, Solitons and Fractals 33 1512
[34]	El-Wakil S A, El-labany S K, Zahran M A and Sabry R 2002 Phys. Lett. A 299 179
[35]	Kavitha L, Sathishkumar P and Gopi D 2009 Phys. Scr. 79 015402
[36]	Zhu J M 2005 Chin. Phys. 14 1290
[37]	He J H 2005 Chaos, Solitons and Fractals 26 695
[38]	Zhang J L, Wang Y M, Wang M L and Fang Z D 2003 Chin. Phys. 12 245
[39]	He J H 2007 J. Comput. Appl. Math. 207 03
[40]	Lin Q, Wu Y H and Loxton R 2009 J. Phys. A: Math. Theor. 42 045207
[41]	Yan Z 2003 J. Phys. A: Math. Gen. 36 1961
[42]	Kavitha L, Saravanan M, Srividya B and Gopi D 2011 Phys. Rev. E 84 066608
[43]	Zhang S 2007 J. Phys. A: Math. Theor. 40 227
[44]	Lin X Y and Shi T J 2007 Chin. Phys. 16 310
[45]	Malfliet W 1992 Am. J. Phys. 60 650
[46]	Malfliet W and Hereman W 1996 Phys. Scr. 54 563
[47]	Fan E 2006 Phys. Lett. A 277 212
[48]	Yusufoglu E and Bekir A 2008 Chaos, Solitons and Fractals 38 1126
[49]	Soliman A A 2006 Physica A 361 394
[50]	Kavitha L, Sathishkumar P and Gopi D 2010 Commun. Nonlinear Sci. Numer. Simul. 15 3900
[51]	Kavitha L, Prabhu A and Gopi D 2009 Chaos, Solitons and Fractals 42 2322
[52]	Kavitha L, Srividya B, Akila N and Gopi D 2010 Nonlinear Sci. Lett. A 1 95
[53]	Kavitha L, Srividya B and Gopi D 2010 J. Magn. Magn. Mater. 322 1793
[54]	Kavitha L, Akila N, Prabhu A, Kuzmanovska-Barandovska O and Gopi D 2011 Math. Comput. Modelling 53 1095
[55]	Kavitha L, Jayanthi S, Muniyappan A and Gopi D 2011 Phys. Scr. 84 035803
[56]	Kavitha L, Venkatesh M, Jayanthi S and Gopi D 2012 Phys. Scr. 86 025403
[57]	Darvishi M, Najafi M T, Kavitha L and Venkatesh M 2012 Commun. Theor. Phys. 58 785
[58]	Wang M L 1995 Phys. Lett. A 199 169
[59]	Wang M L 1996 Phys. Lett. A 216 67
[60]	Fan E G 2000 Phys. Lett. A 265 353
[61]	Peccianti M, Conti C, Assanto A, De Luca D and Umeton C 2002 Appl. Phys. Lett. 81 3335
[62]	Henninot J, Debailleul, Asquini R, d’Alessandro A and Warenghem M 2004 J. Opt. A: Pure Appl. Opt. 6 315
[63]	Beeckman J, Neyts K, Hutsebaut X and Haelterman M 2006 Opto-Electronics Rev. 14 263
[64]	He J H and Wu X H 2006 Chaos, Solitons and Fractals 30 700
[65]	He J H 2008 Int. J. Mod. Phys. B 22 3487
[66]	He J H 2006 "Non-perturbative Methods for Strongly Nonlinear Problems", Dissertation de-verlag im Internet gmbh, Berlin, Germany
[67]	Wu X H and He J H 2007 Comput. Math. Appl. 54 966
[68]	Bekir A and Boz A 2007 Int. J. Nonlinear Sci. Numer. Simul. 8 505
[69]	Marinakis V 2008 Z. Naturforsch 63a 653
[70]	Zhang S and Zhang H Q 2009 Phys. Lett. A 373 2501
[71]	Zhu S D 2007 Int. J. Nonlinear Sci. Numer. Simul. 8 461
[72]	Zhu S D 2007 Int. J. Nonlinear Sci. Numer. Simul. 8 465
[73]	He J H 2012 Abstract and Applied Analysis 916793ewline DOI:10.1155/2012/916793
[74]	Kavitha L, Srividya B and Gopi D 2011 Comput. Math. Appl. 62 4691

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