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.

Type: floating-point number

• Unit: μm²/W
• Default: 0

Linear Refractive Index

n0: Linear refractive index used by the Kerr model. If it is not set, Tidy3D computes it from the central frequency of the simulation sources (all sources must have the same central frequency). The editor does not show this field. To set it, use the Python interface.

Type: floating-point number

• Default: None

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.