Nonlinear Fiber Optics - 4 ed. Agrawal

Appendix B
Numerical Code for the NLS
Equation
The split-step Fourier method of Section 2.4.1 can be implemented using a number
of programming languages such as C++ or Fortran. The use of software package
MATLAB (sold by MathWorks, Inc.) is also quite common for this purpose. This
Appendix lists a sample MATLAB m-file that may help some readers of this book.
It should be stressed that this code should be used as a guideline only because several
parameters that are fixed in the code may need to be changed, depending on the problem
under consideration.
It is a good idea in general to normalize the NLS equation before solving it. With
the normalization scheme given in Eq. (5.2.1), the NLS equation (5.1.1) takes the form
∂U
∂ξ = −is ∂ 2 U
2 ∂τ 2 + iN2 |U| 2 U,
(B.1)
where s = sgn(β 2 )=±1, depending on whether fiber dispersion is normal (s = 1) or
anomalous (s = −1) and N is related to the fiber and pulse parameters as
√
N = γP 0 T0 2/|β
2|. (B.2)
Any numerical solution of Eq. (B.1) requires that N and s be specified together with
the input amplitude U(0,τ), related to shape and chirp of the pulse as
U(0,τ)= f (τ)exp(−iCτ 2 /2),
(B.3)
where f (τ) represents the pulse shape and C is the chirp parameter. In the following
code, an integer m is used (coded as mshape) such that f (τ)=sech(τ) when m = 0but
U(0,τ)=exp[− 1 2 (1 + iC)τ2m ], for m > 0. (B.4)
This form represents a super-Guassian shape for the input pulse, and it reduces to a
Gaussian profile for m = 1. The following code requires that s, N, and m be specified
together with the total fiber length (in units of the dispersion length L D ).
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