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.