In the slowly varying envelope theory,

the pulse propagation along the transmission system is governed by the NLSE.

The NLSE which takes into account both dispersion and nonlinearity can be

written as 2

…………… (1)

Where A (z,

t) are the time retarded slowly varying complex amplitude of the field, t is

the retarded time, z is the propagation direction,

is the imaginary vector,

is the attenuation coefficient,

is the second order GVD,

is a

nonlinear parameter,

is the nonlinear

refractive index,

is the carrier frequency, C is

the velocity of light and

is

the effective cross section area of fiber.

Methodology:

NLSE can’t be solved analytically. Split-step Fourier method is

an efficient technique to solve Eq.1 numerically 15 to find the combined

effect of chirping, SPM and GVD. By Split Step Fourier method Eq.1 can be

represented in the following form

Where

)

Where, the operator

is used for loss and GVD, whereas the operator

includes the nonlinear effect. As a method, divide the optical fiber into small pieces, each of length h meters. The optical pulse is propagated through each segment from z to z + h, where z is a running variable for distance along the fiber. In first step, the fiber loss and GVD effects

is included using

operator over distance h. In the next step,

the output obtained in the first step is propagated using

operator by the same segment of fiber of length h meters. The general

process for solving Spilt Step Fourier Method can be represented as below 2:

Where

the factor

is performed in the Fourier domain using the following mathematical formula,

Where

denotes

the Fourier-transformation, and Eq.1 is replaced with (

) in accordance of the basic rules of

Fourier transformation.

Following this procedure, the optical pulse is

propagated from one end to the other

end. The output obtained at

the receiving end can be used to observe various effects such as the behavior

of pulses and peak power etc. In this paper, we have used the following

parameters to find our desired

result.