resampling and evaluating fields

4. resampling and evaluating fields#

In cbeam, field values are saved only over the mesh nodes. If you have a field from one mesh and want to make it work with another mesh, you must resample the field on the new mesh’s points. This is done using the FEval submodule, as follows.

from cbeam import FEval

# resample takes: field, input mesh, output mesh
resampled_field = FEval.resample(field, mesh, newmesh)

If you want to propagate this resampled field, you then need to decompose the field into the modal basis of the propagator, which uses newmesh.

from cbeam.propator import Propagator

# initialize propagator however
# and characterize() or load()
prop = Propagator(...)

mode_vector = prop.make_mode_vector(resampled_field)

Take a look at multimode interference coupler for an example.

We can also evaluate a field computed on a mesh at an arbitrary point = (x,y). cbeam accelerates the repeated evaluation of fields on the same mesh by storing the mesh’s triangles in a bounding volume hierarchy (BVH) tree. For instance, to perform the field evaluation mentioned above, we can use

val = FEval.evaluate(point,field,tree)

where the arguments are:

  1. point: a length 2 numpy array containing the \((x,y)\) coordinates of the point to evaluate the field at.

  2. field: the field to be evaluated, discretized as a length \(M\) array where \(M\) is the number of mesh points.

  3. tree: the BVHtree representing the finite element mesh that field is discretized over (more on this next).

To construct a BVH tree, we use

tree = FEval.create_tree_from_mesh(mesh)

You can also resample onto \(N\) points at once (e.g. the points of another mesh, which is what resample() does under the hood) by passing an \(N\times 2\) point array, or resample onto a grid using FEval.evaluate_grid().