Nonlinear coefficient

The time derivative term inside GNLSE models the dispersion of

the nonlinearity. This is usually associated with effects such as self-steepening and optical shock formation, characterized by a timescale \(\tau_0 = 1/\omega_0\). In the context of fibre propagation, an additional dispersion of the nonlinearity arises due to the frequency dependence of the effective mode area. The last effect can be accounted in \(\tau_0\) coefficient in an approximate manner.

A better - still approximate - approach to include the dispersion of the effective mode area is to describe it directly in the frequency domain [J07]. In this case, we can derive a GNLSE for the pulse evolution using \(\gamma(\omega)\) defined as

\[\overline{\gamma}(\omega) = \frac{n_2n_{\mathrm{eff}}(\omega_0)\omega_0} {\mathrm{c}n_\mathrm{eff}(\omega)\sqrt{A_{\mathrm{eff}}(\omega)A_{\mathrm{eff}}(\omega_0)}}.\]

This approach is more rigorous than the approximation of (\(\gamma = \gamma(\omega_0)\)) and requires the definition of a pseudo-envelope \(C(z, \omega)\) as

\[C(z, \omega) = \frac{A_{eff}^{1/4}(\omega_0 )}{A_{eff}^{1/4}(\omega )} A(z, \omega).\]

class gnlse.NonlinearityFromEffectiveArea(neff, Aeff, lambdas, central_wavelength, n2=2.7e-20, neff_max=None)

Calculate the nonlinearity coefficient in frequency domain based on modified gnlse example form J. Lægsgaard, “Mode profile dispersion in the generalized nonlinear Schrödinger equation,” Opt. Express 15, 16110-16123 (2007).

Attributes

neffndarray (N)

Effective refractive index

Aeffndarray (N)

Effective mode area

lambdasndarray (N)

Wavelength corresponding to refractive index

central_wavelengthfloat

Wavelength corresponding to pump wavelength in nm

n2float

Nonlinear index of refraction in m^2/W