tidy3d.plugins.microwave.Custom2DPathIntegral

class Custom2DPathIntegral

Bases: Custom2DPathIntegralSpec

Class for defining a custom path integral defined as a curve on an axis-aligned plane.

Parameters:

• axis (Literal[0, 1, 2]) – Specifies dimension of the planar axis (0,1,2) -> (x,y,z).

• position (float) – Position of the plane along the axis.

• vertices (ArrayLike[dtype=float, ndim=2]) – [units = um]. List of (d1, d2) defining the 2 dimensional positions of the path. The index of dimension should be in the ascending order, which means if the axis corresponds with y, the coordinates of the vertices should be (x, z). If you wish to indicate a closed contour, the final vertex should be made equal to the first vertex, i.e., vertices[-1] == vertices[0]

Notes

Given a set of vertices \(\vec{r}_i\), this class approximates path integrals over vector fields of the form \(\int{\vec{F} \cdot \vec{dl}}\) as \(\sum_i{\vec{F}(\vec{r}_i) \cdot \vec{dl}_i}\), where the differential length \(\vec{dl}\) is approximated using central differences \(\vec{dl}_i = \frac{\vec{r}_{i+1} - \vec{r}_{i-1}}{2}\). If the path is not closed, forward and backward differences are used at the endpoints.

Example

>>> import numpy as np
>>> vertices = np.array([[0, 0], [1, 0], [1, 1], [0, 1]])
>>> path = Custom2DPathIntegral(
...     axis=2,
...     position=0.5,
...     vertices=vertices,
... )

Attributes

axis
position
vertices

Methods

compute_integral(field, em_field)

Computes the path integral defined by vertices given the input em_field.

Inherited Common Usage

compute_integral(field, em_field)

Computes the path integral defined by vertices given the input em_field.

Parameters:

• field (Literal['E', 'H']) – Can take the value of "E" or "H". Determines whether to perform the integral over electric or magnetic field.

• em_field (IntegrableMonitorDataType) – The electromagnetic field data that will be used for integrating.

Returns:

Result of integral over remaining dimensions (frequency, time, mode indices).

Return type:

IntegralResultType