tidy3d.NonlinearSusceptibility

class NonlinearSusceptibility

Bases: NonlinearModel

Model for an instantaneous nonlinear chi3 susceptibility. The expression for the instantaneous nonlinear polarization is given below.

Parameters:

• attrs (dict = {}) – Dictionary storing arbitrary metadata for a Tidy3D object. This dictionary can be freely used by the user for storing data without affecting the operation of Tidy3D as it is not used internally. Note that, unlike regular Tidy3D fields, attrs are mutable. For example, the following is allowed for setting an attr obj.attrs['foo'] = bar. Also note that Tidy3D` will raise a TypeError if attrs contain objects that can not be serialized. One can check if attrs are serializable by calling obj.json().

• chi3 (float = 0) – [units = um^2 / V^2]. Chi3 nonlinear susceptibility.

• numiters (Optional[PositiveInt] = None) – Deprecated. The old usage ‘nonlinear_spec=model’ with ‘model.numiters’ is deprecated and will be removed in a future release. The new usage is ‘nonlinear_spec=NonlinearSpec(models=[model], num_iters=num_iters)’. Under the new usage, this parameter is ignored, and ‘NonlinearSpec.num_iters’ is used instead.

Notes

This model uses real time-domain fields, so \(\chi_3\) must be real.

\[P_{NL} = \varepsilon_0 \chi_3 |E|^2 E\]

The nonlinear constitutive relation is solved iteratively; it may not converge for strong nonlinearities. Increasing tidy3d.NonlinearSpec.num_iters can help with convergence.

For complex fields (e.g. when using Bloch boundary conditions), the nonlinearity is applied separately to the real and imaginary parts, so that the above equation holds when both \(E\) and \(P_{NL}\) are replaced by their real or imaginary parts. The nonlinearity is only applied to the real-valued fields since they are the physical fields.

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

>>> nonlinear_susceptibility = NonlinearSusceptibility(chi3=1)

Attributes

complex_fields	Whether the model uses complex fields.
attrs

Methods

Inherited Common Usage

chi3

numiters

property complex_fields

Whether the model uses complex fields.

__hash__()

Hash method.