KerrNonlinearity

Model for Kerr nonlinearity which gives an intensity-dependent refractive index of the form $n = n_0 + n_2 I$. The expression for the nonlinear polarization is given below.

$P_{NL} = \varepsilon_0 c_0 n_0 Re(n_0) n_2 |E|^2 E$

Nonlinear Refractive Index

n2: Nonlinear refractive index in the Kerr nonlinearity. You can include complex values using the real and imaginary edit boxes.

Type: complex number

• Unit: μm²/W
• Default: 0

Notes

• The fields in Kerr equation are complex-valued, allowing a direct implementation of the Kerr nonlinearity. In contrast, the model NonlinearSusceptibility implements a chi3 nonlinear susceptibility using real-valued fields, giving rise to Kerr nonlinearity as well as third-harmonic generation. The relationship between the parameters is given by $n_2 = \frac{3}{4} \frac{1}{\varepsilon_0 c_0 n_0 Re(n_0)} \chi_3$. The additional factor of $3/4$ comes from the usage of complex-valued fields for the Kerr nonlinearity and real-valued fields for the nonlinear susceptibility.
• Different field components do not interact nonlinearly. For example, when calculating $P_{NL,x}$, we approximate $|E|^{2}\approx|E_x|^{2}$. This approximation is valid when the $E$ field is predominantly polarized along one of the x, y, or z axes.