Nonlinear refractive index induced collision and propagation of nematicons

Journal of Molecular Liquids 197 (2014) 142–151

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Nonlinear refractive index induced collision and propagation of nematicons L. Kavitha a,b,1, M. Venkatesh c,d, S. Dhamayanthi c, D. Gopi e,f a

Department of Physics, School of Basic and Applied Sciences, Central University of Tamilnadu, Thiruvarur 610 101, Tamilnadu, India The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy Department of Physics, Periyar University, Salem 636 011, Tamilnadu, India d Department of Physics, K.S.R. College of Arts and Science (Autonomous), Thiruchengode – 637 215, Tamil Nadu, India e Department of Chemistry, Periyar University, Salem 636 011, Tamilnadu, India f Center for Nanoscience and Nanotechnology, Periyar University, Salem 636 011, Tamilnadu, India b c

a r t i c l e

i n f o

Article history: Received 27 December 2013 Received in revised form 28 April 2014 Accepted 30 April 2014 Available online 16 May 2014 Keywords: Soliton Optical soliton Symbolic computation Switching phenomena

a b s t r a c t Nematic liquid crystals (NLCs) have proved to be excellent materials for nonlinear optics and its applications because of their large nonresonant nonlinearity and their extended spectral transparency. We demonstrate the exemplary collision scenario of both optical solitons and nematicons induced by the nonlinear refractive index in nematic liquid crystals. We invoke Hirota's bilinearization method for two coupled partial differential equations governing the dynamics of self-focusing of a laser light in a nematic liquid crystal system. We believe that this type of collision of optical solitons and nematicons reveals the many possibilities of all-optical switching schemes for spatial demultiplexing, network reconfiguration and logic gates. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Nematic liquid crystals (NLCs) are the simplest of liquid crystals. They possess only orientational order. Depending upon the shape of the molecules and the interaction between them, the medium as a whole can be either optically uniaxial like calcite crystals or biaxial like aragonite crystals. The liquid crystal molecules can be viewed as rigid rods and their collective behavior may be described in terms of the vector field n(r) which indicates the average direction of orientation of the molecules but has neither head nor tail and hence the states corresponding to − n and + n are indistinguishable. Liquid crystals are soft materials and are extremely sensitive to external electric and magnetic fields. It was noticed long ago in 1918 by Moll and Ornstein that the optical transmission by nematic liquid crystals increased when it was kept in a magnetic field [1]. That this is due to the suppression of director fluctuations by the magnetic field was pointed out by de Gennes [2], who also worked out the enhancement in the dielectric anisotropy due to the external magnetic field. The same effect can be expected, when a laser beam is passing through the liquid crystal. When a linearly polarized beam is passing through a nematic liquid crystal, with its electric vector parallel to the director, then the electric field of the laser beam suppresses the thermal fluctuations in the director, leading to an increase in the dielectric constant along the director.

1

E-mail address: [email protected] (L. Kavitha). Tel.: +91 427 2345766; fax: +91 427 2345124.

http://dx.doi.org/10.1016/j.molliq.2014.04.040 0167-7322/© 2014 Elsevier B.V. All rights reserved.

Nematic liquid crystals are particularly interesting materials due to their infiltration capabilities and huge optical nonlinearities associated with molecular ordering [3]. Indeed, the strong coupling between light and NLCs leads to a nonlinear response that is usually several orders of magnitude larger than Kerr nonlinearity in conventional dielectrics. For all-optical devices based on NLC orientation, optical nonlinearities have already been achieved to route light by light using solitons [3]. Nematic liquid crystals are unique materials found in most consumer electronic applications. Several reduced mathematical models for the optical self-focusing process in bulk NLCs have been derived beginning from the most fundamental coupled field models for light and nematics — the vector forms of the Maxwell and Frank free energy equations [4]. Nematicons [5] are spatial optical solitons [6] in NLCs. They have been generated in these materials by either thermal nonlinearities [7] or reorientational nonlinearities [8–10]. Due to the molecular reorientation under the influence of a linearly polarized optical electric field, the refractive index is higher where the optical intensity is higher. This leads to a focusing nonlinear effect that can compensate for the spreading of the beam occurring during propagation because of natural diffraction [11]. In this way, it becomes possible to propagate beams with a practically invariant intensity profile; these entities are called spatial solitons and nematicons if we are dealing with nematic liquid crystals [12]. In nematic media, the change in refractive index of the media induced by the optical beam depends not only on the intensity of the optical beam where the localization is created but also on its vicinity. Spatial optical solitons — self-trapped

L. Kavitha et al. / Journal of Molecular Liquids 197 (2014) 142–151

light beams, have been proposed as building blocks in future ultra-fast all-optical devices. Spatial solitons can be used to create reconfigurable optical circuits that guide other light signals. Also, circuits with complex functionality and all-optical switching or processing can then be achieved through the evolution and interaction of one or more solitons [13–16]. Such soliton-like optical beam propagation was reported in nematic liquid crystals, with a few milliwatts of light power [17]. However the major possible application concerns the dynamics of the soliton formation [18]. For applications in computing, optical interconnects may be useful to reduce the network latency due to a higher bandwidth of optical connections [19]. Indeed, adding reconfigurability to the optical interconnects can open new possibilities by enhancing the speed of a multiprocessor system, but an adequate switching speed of the order of microseconds is required to outdo the electrical interconnects [20]. Also, for building an optical network the speed and the ease of switching light between fibers is of importance. Displays made with NLCs typically have a refresh rate of a few tens of milliseconds [21] and we can expect that the soliton formation will be of the same order of magnitude. Nonlinear evolution equations are often used as models to describe complex phenomena in various fields of sciences, especially in physics and engineering. One of the basic physical problems for those models is to find their traveling wave solutions. During the past decades, quite a few methods for dealing with traveling wave solutions of those nonlinear equations have been proposed [22–31]. Examples are the wave phenomena observed in fluid dynamics, plasma, elastic media, optical fibers, etc. In the past several decades, both mathematicians and physicists have made significant progress in this direction. Hirota developed a systematic method for obtaining exact solutions of nonlinear PDEs and this method [32] has profound impact on the soliton theory. Over the last three decades this method has been shown to be applicable to a large class of nonlinear evolution equations including differencedifferential and integro-differential equations. The essence of this method is to construct the N-soliton solutions for a given nonlinear evolution equation and be able to identify the collision property of the nonlinear equation associated with the solitons. One can indeed believe that all the completely integrable nonlinear evolution equations can be put into bilinear form and will admit N-soliton solutions for any value of integer N. However, the mere fact that an equation admits a bilinear representation, does not guarantee the existence of two soliton solutions and is nontrivial for a completely general bilinear equation. Hirota's bilinear method has been studied and used extensively [33–36,14]. The fundamental idea is to use a dependent variable transformation to convert nonlinear PDE into a new evolution equation where the new dependent variable appears bilinearly [33]. The paper is organized as follows: In Section 2, we introduce the mathematical model under consideration. Section 3 deals with the application of Hirota's bilinearization method to the coupled paraxial model governing the dynamics of optical and nematic fields. In Section 4, we discuss the observed collision dynamics of optical solitons and nematicons induced by the nonlinear refractive index. Finally we conclude our results.

143

2. Model and nematicon dynamics We consider the paraxial partial differential equations which model the interaction between the optical refraction and nematic deformation as [37] 2

2

2ikF z þ F xx þ k α sin θF ¼ 0;

2

θxx þ θzz þ j F j sin2θ ¼ 0:

ð1Þ

ð2Þ

This paraxial model (Eqs. 1 & 2) contains all of the essential physics required to observe the phenomena of self-focusing, undulation and filamentation. The scalar quantities F(x,z) and θ(x,z) representing the optical and nematic fields are governed by the coupling between a parabolic wave Eq. (1) and a nonlinear elliptic Eq. (2) respectively. The x and z co-ordinates identify the transverse and longitudinal directions and the parameters k and α denote the non-dimensionalized wave number and nonlinear refractive index. Also, Eq. (1) includes the effects of diffraction Fxx and the nematic anisotropy α sin2θ but by its scalar nature, neglects any polarization effects. The optical influence appears as the nonlinear term |F|2 which acts as a source of intensity induced nematic deformation. The basic configuration is shown in Fig. 1. For this, we assume that our liquid crystal system is contained in an extremely narrow container with a homeotropic alignment of molecules and with a strong surface anchoring at the boundaries. The nematicon is then taken to propagate in the z-direction and the axes are oriented such that the z-axis is the direction of propagation of light. At the transverse boundaries (x = ±1), Dirichlet conditions are applied to both electric and nematic fields F(x = ± 1,z) = 0, θ(x = ± 1,z) = 0. The incident light field is introduced through an initial value of F(x,z = 0) for the parabolic wave evolution. Also, because of the elliptic nature of the nematic partial differential equation, boundary conditions at both longitudinal boundaries (z = 0,L) and the Dirichlet condition at (z = 0), imply the perpendicular anchoring of the nematic at the boundaries. Thus on the boundary wall, all the nematic molecules are arranged to point normal to the boundaries and are expected to remain invariant during the propagation of light due to a strong surface anchoring. The nonlinear refractive index in NLCs can be easily influenced by temperature and external electric/magnetic fields. It can also be induced by a long-range molecular interaction in NLCs which exhibit orientational nonlocal nonlinearity [4]. Further, an increase in the refractive index varies as the square root of the laser intensity and is unlike the familiar nonlinear optical phenomenon where the change in refractive index is proportional to the laser intensity. It must be noted that the laser θ induced increase in the refractive index along the director is equivalent to an increase in the orientational order parameter of the nematic liquid crystal. If a nematic liquid crystal is at a temperature close to the nematic–isotropic phase transition, then even a slight increase in temperature will lead to a very large change

Fig. 1. Schematic of a nematic liquid crystal system with the propagation of laser light.

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in refractive index. In this context, we attempt to explicitly construct two soliton solutions to the paraxial model equations in the framework of Hirota's bilinearization method. 3. Application of Hirota's bilinearization method to the paraxial model In the present section, we perform a systematic analysis on the collision behavior of optical solitons/nematicons and examine the shape-changing collisions through Hirota's bilinearization procedure [33]. We define the following bilinear transformation for both optic and nematic fields as follows

n



m

Dx Dz ða  bÞ ¼

∂ ∂ − ∂x ∂x0

n 

∂ ∂ − ∂z ∂z0

m

 0 0 aðx; zÞb x ; z jx¼x0 ;z¼z0 :

ð3Þ

h ; f

ð4Þ

2

4

f ¼ 1 þ ϵ f 2 þ ϵ f 4;

ð8Þ

3

5

ð9Þ

3

5

ð10Þ

g ¼ ϵg 1 þ ϵ g 3 þ ϵ g 5 ;

where ϵ is the formal expansion parameter. The resulting set of equations, after collecting the terms with the same power in ϵ recasts as follows
 1 2 ϵ : 2ikDz þ Dx g 1 ¼ 0; 2

where g is a complex function while f and h are real valued functions of x and z. Upon substituting the above transformation in Eqs. (1) & (2) we arrive at 2

2ikDz ðg  f Þ þ Dx ðg  f Þ ¼ 0; 2 2 −Dx ð f  f Þ þ k α ðh  hÞ ¼ 0;

ð5Þ

and
 2 2 Dx þ Dz ðh  f Þ ¼ 0; h i 2 2  −Dx −Dz ð f  f Þ þ 2gg ¼ 0; 4 3  − h gg ¼ 0; 3

ð7Þ

The above set of equations can be solved by introducing the following power series expansions for g, h and f

h ¼ ϵh1 þ ϵ h3 þ ϵ h5 ;

g F¼ ; f

θ¼

where the Hirota's bilinear operators Dx and Dz are defined by

2

2

2

−2Dx f 2 þ kαh1 ¼ 0; ϵ :
3 2 ϵ : 2ikDz þ Dx ðg 3 þ g 1 f 2 Þ ¼ 0;
 4 2 2 2 ϵ : −Dx 2f 4 þ f 2 þ k αh1 h3 ¼ 0;

ð11Þ

and
 1 2 2 ϵ : Dx þ Dz h1 ¼ 0;
 2 2 2  ϵ : −Dx −Dz 2f 2 þ 2g 1 g1 ¼ 0;
 3 2 2 ϵ : Dx þ Dz ðh3 þ h1 f 2 Þ ¼ 0;

 4 2 2 2 ϵ : −Dx −Dz 2f 4 þ f 2 þ g 1 g 3 ¼ 0:

ð12Þ

ð6Þ The above set of equations can be solved recursively to obtain the forms of g, f and h in the following section.

4. Multisoliton solutions In this section, on the basis of bilinear equations, we describe an algorithm to construct the multisoliton solutions of paraxial partial differential equations. Constructing soliton solutions for the coupled optic and nematic paraxial equations is a challenging task without decoupling the associated parameters. 4.1. One soliton solution In order to obtain the one soliton solutions, we assume that f and g are polynomial functions eη when ϵ = 1. Expanding f, g and h as follows g ¼ ϵg1 ;

ð13Þ

h ¼ ϵh1 ;

ð14Þ

2

f ¼ 1 þ ϵ f 2:

ð15Þ

Then by solving the resulting linear set of equations recursively, one can write down the explicit form of one soliton solution using Eqs. (13)–(15) as η

F¼

g γ1 e 1 ; ¼ f 1 þ De2η1

θ¼

h γ3 e 1 ¼  ; f 1 þ Eeη1 þη1

η

ð16Þ

ð17Þ

L. Kavitha et al. / Journal of Molecular Liquids 197 (2014) 142–151

145

where η

g1 ¼ γ1 e 1 ; η h1 ¼ γ 3 e 1 ; η1 ¼ k1 x þ ω1 z þ η1 ð0Þ; −k21 ; ω ¼ −k1 ; ω1 ¼ B 2 Aγ D ¼ 23 ; 2k1 2 jγ 1 j ; E¼ 4k1 k1 2 A ¼ k α:





ω1 ¼ k1 ;

A typical plot of nonsingular bright one solitons (Eqs. 16 & 17) of Eqs. (1) & (2) are shown in Fig. 2. Fig. 2 shows the snapshot of the evolution of a single soliton profile for the physical quantities F and θ for the parametric choices k1 = 0.2 + i, γ1 = 0.1 + 0.1i, γ2 = 0.1 + 0.1i, γ3 = 0.3, k = 2, ω = 2.7 and η1 = 1. It is observed from Fig. 2a that the optical beam while it is passing through the nematic liquid crystal medium evolves in the form of a robust and coherent bell shaped solitonic profile. On the contrary, the evolution of nematicon is breaking up into a train of switching soliton pulses as could be observed from Fig. 2b. In the corresponding contour plots, the bright orange represents the maximum amplitude and the bluish area characterizes the minimum or zero amplitude. 4.2. Two-soliton solution The two soliton solution can be obtained by terminating the power series expansion up to the order of ϵ given by 3

ð18Þ

3

ð19Þ

g ¼ ϵg1 þ ϵ g 3 ; h ¼ ϵh1 þ ϵ h3 ; 2

4

f ¼ 1 þ ϵ f 2 þ ϵ f 4:

ð20Þ

(a)

α=2

(b)

Fig. 2. Snapshots of one soliton/nematicon evolution for the nematic liquid crystal system with the parametric choices of k1 = 0.2 + i, γ1 = 0.1 + 0.1i, γ3 = 0.3, k = 2, ω = 2.7 and η1 = 1.

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By substituting the above expansions into the bilinear Eqs. (1) & (2) and solving the set of equations, we get g3, h3 and f4 respectively. Therefore, we write down the explicit form of the two soliton solution for the paraxial system as F¼

g ϵg 1 þ ϵ3 g3 ; ¼ f 1 þ ϵ2 f 2 þ ϵ4 f 4

ð21Þ

θ¼

h ϵh1 þ ϵ3 h3 ; ¼ f 1 þ ϵ2 f 02 þ ϵ4 f 04

ð22Þ

where ϵ ¼ 1; η η g1 ¼ γ1 e 1 þ γ2 e 2 ; 3η1 þa1 3η2 þb1 2η þη þc 2η þη þd g3 ¼ e þe þ e 2 1 1 þ e 1 2 1; η η h1 ¼ γ 3 e 1 þ γ4 e 2 ; h3 ¼ 0; 2η þR 2η þR η þη þR f 2 ¼ e 1 1 þ e 2 2 þ e 1 2 3; f 4 ¼ 0; 0 η þη þa η þη þa η þη þa η þη þa f 2 ¼ e 1 1 11 þ e 1 2 12 þ e 1 2 13 þ e 2 2 14 ; 0 3η1 þη2 þb11 3η2 þη1 þb12 2η1 þ2η2 þb15 f4 ¼ e þe þe ; η1 ¼ k1 x þ ω1 z þ η10 ; η2 ¼ k2 x þ ω2 z þ η20 ; −k21 −k22 ; ω2 ¼ ; ω1 ¼ −k1 ; ω2 ¼ −k2 ; ω1 ¼ 2ik 2ik 2 k α R e 1 ¼ 2; 4k1 k2 α R2 e ¼ 2; 4k2 k2 α R3 ; e ¼ ðγ3 k1 þ γ 4 k2 Þ2 2 2 γ k α a e 1 ¼− 3 2 ; 12k1 2 2 k αγ4 b1 ; e ¼− 2 h 12k2





ω 1 ¼ k1 ;





ω 2 ¼ k2 ;

h
 ii 2 2 2 2 2 2 γ1 γ 4 ð−3k2 þ 2k1 Þðγ3 k1 þ γ 4 k2 Þ k α þ 2k2 Aγ2 γ 3 γ4 −2 γ 3 k1 þ γ4 k2 þ 4k2 ðγ 3 k1 þ γ 4 k2 Þ−2ðγ 3 k1 þ γ4 k2 Þ    2  e ¼ ; 2 2 2 2k2 ðγ 3 k1 þ γ 4 k2 Þ − 2k2 γ 2 þ k1 γ 1 þ ð2γ 2 k2 h
i þ γ 1 k1 Þ h i 2 2 2 2 2 2 2 2k1 γ1 γ 3 γ4 k α −2 γ 3 k1 þ γ 4 k2 þ 4k1 ðγ3 k1 þ γ 4 k2 Þ−2ðγ 3 k1 þ γ 4 k2 Þ þ γ 3 γ2 ðγ 3 k1 þ γ 4 k2 Þ k α ð−3k1 þ 2k2 Þ d1     e ¼ ; 2k1 ðγ 3 k1 þ γ4 k2 Þ2 − 2γ 1 k21 þ γ2 k22 þ ð2γ 1 k1 þ γ 2 k2 Þ2 2 jγ j a e 11 ¼ 1  ; 2k1 k1 γ γ a e 12 ¼ 1 2 ; 2k1 k2 γ γ a13 e ¼ 1 2 ; 2k1 k2 2 jγ j a14 e ¼ 2 ; 2k2 k2 γ2 ea1 þ ed1 γ1 b11 ; e ¼ ð3k1 þ k2 Þ2 −ð3ω1 þ ω2 Þ2 b1 c1 γ1 e þ e γ2 b ; e 12 ¼  ð3k2 þ k1 Þ2 þ ð3ω2 þ ω1 Þ2 c1 d1 γ1 e þ e γ2 b ; e 15 ¼  ð2k1 þ 2k2 Þ2 þ ð2ω1 þ 2ω2 Þ2 c1

2

A ¼ k α:

4.3. Collision/switching dynamics of optical solitons/nematicons In this section, we demonstrate the collision between two optical solitons and nematicons in the framework of Hirota's bilinearization method. One of the most exciting phenomena associated with optical solitons and nematicons is their collisions. In linear media, a localized wave packet propagates through another wave packet completely unaffected by its presence. In contrast, optical solitons can exchange energy, bounce off each other, spiral around each other and display many other exciting interaction associated phenomena [38]. Figs. 3 & 4, portray the snapshots of collision

L. Kavitha et al. / Journal of Molecular Liquids 197 (2014) 142–151

147

(a) α = 0.5

(b) α = 1

(c) α = 2

Fig. 3. Snapshots of two spatial soliton collision for the incident light beam profile with the choices of parameter as γ1 = 5.4 + 2i, γ2 = 1.5, γ3 = −0.1, γ4 = 1, η1 = 0.5 + 3i, η2 = 0.5 − 3i, k1 = 1.0 + 0.8i, k2 = 1.0 − 0.8i, ω1 = 1.0 − 1, Ω2 = 1.0 + 1i, k = 1, η10 = 1.5 + 2.5i and η20 = 1.5 − 2.5i.

scenarios of optical solitons and nematicons as a function of nonlinear refractive index. Fig. 3a–c demonstrates the collision scenario of optical solitons and Fig. 4a–c represents the collision and switching scenario of the nematicons along with their respective contour plots. From Fig. 3a–c, we could observe that the incoming optical solitons S1 and S2 co-propagate with a particular angle and at a particular z, these two optical solitons collide inelastically with each other for the parametric choices γ1 = 5.4 + 2i, γ2 = 1.5, γ3 = − 0.1, γ4 = 1, η1 = 0.5 + 3i, η2 = 0.5 − 3i, k1 = 1.0 + 0.8i, k2 = 1.0 − 0.8i, ω1 = 1.0 − 1, Ω2 = 1.0 + 1i, k = 1, η10 = 1.5 + 2.5i and η20 = 1.5 − 2.5i. In Figs. 3a & 4a, when the nonlinear refractive index α = 0.5, the collision gives distinct pictures for both F and θ. In Fig. 3a, the optical solitons S1 with amplitude 0.53 and S2 with amplitude 0.88, collides inelastically at z = 0.1 and after collision there is an abrupt exchange of energy among the solitons and S1 and S2 emerge with an increase and

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L. Kavitha et al. / Journal of Molecular Liquids 197 (2014) 142–151

(a) α = 0.5

(b) α = 1

(c) α = 2

Fig. 4. Snapshots of collision and switching of two nematicon profile for the nematic phase.

decrease in amplitudes respectively, and the same fact can be verified in the Fig. 5a. A further increase in the value of α = 1 makes both the optical solitons S1 and S2 which originally have the amplitudes 0.43 and 0.71 before collision to emerge with the increased amplitudes 0.69 and 0.74 for S1 and S2 respectively as can be seen from Figs. 3b to 5b. A similar trend is observed when α = 2, as could be verified from Figs. 3c to 5c. In the case of nematicons, the situation is associated with switching as well collision as evidenced from Figs. 4 to 6. From Fig. 4, we could observe that coherent and robust switching nematicon pulses ^S1 and ^S2 co-propagate at a particular angle and collide with each other at z = 0.1. From Fig. 4a, at the point of collision, both the switching train of pulses fuse with each other, leading to an abrupt exchange of energy as evidenced significantly from the contour plots of Fig. 4. As a result of this inelastic collision, the negative maxima of both the nematicon pulses ^S1 and ^S2 reduced and

L. Kavitha et al. / Journal of Molecular Liquids 197 (2014) 142–151

Before collision ( = −0.3)

149

After collision ( = 0.3)

(a)

α = 0.5

(d)

(b)

α=1

(e)

(c)

α=2

(f)

Fig. 5. Snapshots of inelastic collision between two spatial solitons at two typical moments (a–c) before collision at z = −0.3 and (d–f) after collision at z = 0.3.

surprisingly all the positive maxima of both the nematicon pulses ^S1 and ^S2 seem to be increased appreciably as evidenced from Figs. 4 to 6. Thus, it can be concluded that when the optical beam passes through the nematic liquid crystal it triggers the evolution of nematicons in the form of switching solitonic pulses. The director deformation in the liquid crystal is consistently solved through the collision dynamics observed in the present manuscript using the Hirota bilinearization. The first measurement of light scattering was made by Chatelian [39] who measured the intensity variation through the director deformation when it interacts with the optical field. The intensity variation in the present case is well observed through the scattering of two solitons in the space–time plane. The amplitude variations before and after collision show the variation of intensity. This predicts that the scattering of two solitons can exploit the nematic molecules that are consistently scattered in the evolution plane through the interaction of the optical field. Also we observed that for different values of nonlinear refractive indices for both the optical field and the nematic field there are intensity variations and the suppression of amplitude can be visualized as losses in the nematic–optic system.

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Before collision ( = −0.1)

After collision ( = 0.1)

(a)

α = 0.5

(d)

(b)

α=1

(e)

(c)

α=2

(f)

Fig. 6. Snapshots of inelastic collision and switching between two nematicons at two typical moments (a–c) before collision at z = −0.1 and (d–f) after collision at z = 0.1.

5. Conclusions As a medium for a nonlinear optical experiment, the dominant attributes of nematic liquid crystals are its extremely strong nonlinear response and its strict anchoring conditions at the boundaries. We have investigated a two dimensional time independent coupled paraxial model representing the propagation of the optical and nematic fields that are governed by the coupling between a parabolic wave

equation and a nonlinear elliptic equation. We have constructed one soliton and two soliton solutions in the framework of Hirota's bilinearization method and we demonstrate the collision scenario between the optical solitons and nematicons as a function of the nonlinear refractive index. The investigation on the collision dynamics of optical bright solitons shows that there exists an abrupt exchange of energy between co-propagating solitons as a result of an inelastic collision. Further, the collision scenario of the nematicons exhibits that there

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