tidy3d.KerrNonlinearity#

class KerrNonlinearity[source]#

Bases: NonlinearModel

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.

Parameters:

• n2 (Union[tidycomplex, ComplexNumber] = 0) – [units = um^2 / W]. Nonlinear refractive index in the Kerr nonlinearity.

• n0 (Union[tidycomplex, ComplexNumber, NoneType] = None) – Complex linear refractive index of the medium, computed for instance using ‘medium.nk_model’. If not provided, it is calculated automatically using the central frequencies of the simulation sources (as long as these are all equal).

Note

$$P_{NL}={\epsilon }_0{c}_0{n}_0\mathrm{Re}(n_0)n_2|E{|}^{2}E$$

Note

The fields in this 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 $n_2=\frac{3}{4}\frac{1}{{\epsilon }_0{c}_0{n}_0\mathrm{Re}(n_0)}{\chi }_3$. The additional factor of $\frac{3}{4}$ comes from the usage of complex-valued fields for the Kerr nonlinearity and real-valued fields for the nonlinear susceptibility.

Note

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.

Example

>>> kerr_model = KerrNonlinearity(n2=1)

Attributes

complex_fields

Whether the model uses complex fields.

Methods

n2#

n0#

property complex_fields#

Whether the model uses complex fields.

__hash__()#

Hash method.