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add nonlinearity page to documentation
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:orphan: | ||
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Nonlinear coefficient | ||
===================== | ||
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The time derivative term inside GNLSE models the dispersion of | ||
the nonlinearity. This is usually assiociated with effects such | ||
as self-steepening and optical shock formation, characterized by | ||
a timescale :math:`\tau_0 = 1/\omega_0`. In the context of fibre | ||
propagation, additional disperison of the nonlinearity arises | ||
from the frequency dependence of the effective area, | ||
and :math:`\tau_0 = 1/\omega_0` can be generalized for this in | ||
an approximate manner. | ||
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A better aproach is to include the dispersion of the nonlinear response is to | ||
describe it directly in the frequency domain [J07]_. | ||
In this case we can derive a GNLSE for the pulse evolution using | ||
:math:`\gamma(\omega)` defined as | ||
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.. math:: | ||
\gamma(\omega) = \frac{n_2 n_0 \omega}{c n_{eff}( \omega ) A_{eff}^{1/4}(\omega )}, | ||
with the substitution for the envelope of amplitude as scaled variable | ||
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.. math:: | ||
C(z, \omega) = \frac{A_{eff}^{1/4}(\omega_0 )}{A_{eff}^{1/4}(\omega )} A(z, \omega). | ||
.. autoclass:: gnlse.NonlinearityFromEffectiveArea |