Abstract:

This paper
presents the optical solitons in the presence of perturbation terms by the aid
of collective variables. SUPER- Gaussian and SUPER SECH solitons are selected
retain the pulse to establish the soliton setting. The numerical Simulations
are attain to complete the article.

Introduction:

Optical Soliton form the basic thread in
the field of telecommunication industry. These solitons are the carriers for the
transfer of information and data through optical fibers. These information
transmission carriers serve the modern-day telecommunication system through
Internet activity. These include electronic mail transmission, Facebook,
twitter and other such social media activities. As it is established that
solitons are caused by the delicate balance between nonlinear and dispersive
effects. The soliton refers to special kind of wave packets that can travel
undistorted over a long distance.

Optical Metamaterials are the type of micro
structured material. These MMs are synthetic physical properties at terahertz
and optical frequencies. MMs are demonstrated in different optical regions with
different waveguide structures. Metamaterials intensify the nonlinearity by using
the electric field, so by using Metamaterials losses and nonlinearity can be balance.
This is property of MMs it allow propagation of solitary waves with efficient
phase-matching and instability.

Pulses propagating in MMs can be explained
by a (NLSE) in which linear and nonlinear coefficients can be attained. These
nonlinear MMs are spatiotemporal dynamics and promising applications. These MMs
allow the propagation of variety of soliton. The Soliton propagation through
these optical MMs is governed by the (NLSE) with perturbation terms.

Governing
Model:

 

The governing  NLSE with
perturbation terms that is studied in nonlinear optics is given in its dimensionless
form as

 

                                                                 
(1)

 

 In (1),  represents the
complex-valued wave profile with two independent variables  and   which represents
spatial and temporal components respectively. On the left side of equation (1),
the first term is the linear temporal evolution, while from the second term,   is the coefficient of
group velocity dispersion (GVD). The two nonlinear terms are with  and  that are quadratic and
cubic nonlinear terms respectively. On the right side of (1) are the
perturbation terms. The coefficient of  is inter-modal
dispersion, while the coefficients of   and   respectively are
self-steepening term and nonlinear dispersion.

 

Collective Variable Approach algorithm:

In the algorithm for collective
variable(CV) ,the solution of the NLSE is assumed to be split into two parts,
the first represents the soliton solution and the second one is residual
radiation which is named as small amplitude dispersive waves. Decomposition of
the original soliton field q(z,t) is made at position z in the fiber and the
time t, as follows:

The soliton field is q(z,t) is split into
the sum of two parts as

 

                          Equation                                                      
(2)

 

Where f represents the pulse configuration
while g represents the residual filed. Collection of variables represents
soliton amplitude, temporal position , pulse width, chirp frequency and phase
of pulse.

CV introduces the function f increases the
degrees of freedom resulting in the system for the expansion of available phase
space.

The residual free energy (RFE) is given by

                                         Eq(4)

From this definition, let Cj denote the
rate of change of RFE with respective to the jth CV xj so that

                                  Eq(5)

before(8)  

Then the rate of change with respect to the
normalized distance is defined as

 

 

Soliton Parameter Dynamics:

In this section the adiabatic parameter
dynamics in optical metamaterials will be attained by the CV approach. We assume
the desired form of function.

For optical soliton N=6 will be interpreted.
Gaussian soliton ansatz, chirped soliton pulse can take as

Gaussian
pulse********************************

Here x1 is the soliton amplitude, x2 is the
center position of the soliton, x3 is the inverse width of the pulse, x4 is the
soliton chirp,x5 is the frequency of the soliton and x6 is the phase of the
soliton. In this case, N=6,

  

Results and Conclusion:

CV approach was applied to obtain the
evolution equation that governs the dynamics of the soliton and its propagation
through optical metamaterials.

 

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