In the propagation direction, is the imaginary vector,

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)

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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.