Examples

Each example in the first table repeats a calculation from the treams documentation with treams-rs. Its page shows the treams-rs script, the same calculation in treams 0.4.5 and the printed results.

Example	What it computes	treams counterpart
Single sphere	Averaged extinction and scattering spectra up to l = 4 and for dipoles only; the intensity around the sphere	sphere.py
Cluster of spheres	Cross sections and near fields of four coupled spheres, with local, global and rotated T-matrices	cluster.py
Chain of spheres	The near field of a chain periodic along z	chain.py
Grid of spheres	The near field of a square array in the xy plane	grid.py
Photonic crystal	The smallest singular value of the lattice interaction matrix of a cubic crystal	crystal.py
Chiral slab	Transmission and reflection of a chiral slab for both helicities	slab.py
Array of spheres on a slab	Transmission and reflection of a square array of chiral spheres on a slab at oblique incidence	array_spheres.py
Band structure	Bloch wavenumbers of a periodic stack of sphere arrays and slabs	band_structure.py
Single cylinder	Averaged extinction and scattering cross widths up to m = 4 and for m = 0 only; the intensity around the cylinder	cylinder_tmatrixc.py
Chain of spheres in cylindrical waves	The near field of a chain periodic along z, from its cylindrical T-matrix and from spherical waves	chain_tmatrixc.py
Chain and cylinder	The near field of a chain of spheres coupled to an infinite cylinder	cluster_tmatrixc.py
Cylinder crystal	The smallest singular value of the lattice interaction matrix of a square lattice of cylinders	crystal_tmatrixc.py
Grating	The near field of chains of spheres and cylinders repeated along x	grating_tmatrixc.py
Array of spheres from cylindrical waves	Transmission and reflection of the sphere array on a slab, built from chains in cylindrical waves	array_spheres_tmatrixc.py

Beyond treams

These examples differentiate a result with respect to the geometry, which treams cannot do. They have no treams counterpart; each checks its gradient against central differences.

Example	What it computes	Framework
Sphere radius optimization	Five gradient-ascent steps on the radius of a sphere to maximize its scattering efficiency	Advect
Array transmission gradient	The derivatives of the transmission of a sphere array on a slab with respect to the sphere radius and the slab thickness	JAX
Changes across a field map	Forward-mode changes at every field point when the wavelength or common sphere radius changes	JAX
Cluster scattering gradient	Reverse-mode changes in one scattering cross section with respect to eight radii and all particle positions	JAX

Choosing a differentiation mode compares both modes on the same results, with a runnable timing script.

Running the examples

Run a script from the repository root with treams-rs installed:

python docs/examples/sphere.py

The scripts print tables and draw no figures. Constants at the top, such as FREQUENCIES and GRID_POINTS, set small sizes so that each script runs in under a second. Enlarge them for full sweeps; the treams versions use 200 frequencies and grids of up to 101 x 101 points. The two gradient examples need the treams-rs[advect] and treams-rs[jax] extras; the JAX example takes about five seconds.

The test suite runs every script and compares what it prints with the recorded output, to a relative tolerance of 1e-6. When treams is installed, it also runs the treams versions and compares the results, to a relative tolerance of 1e-10. Values near zero also get an absolute tolerance. The grating and the array of spheres from cylindrical waves get a relative tolerance of 3e-8 and 2e-8, because treams sums a lattice of cylinders less accurately. The test states the reason for each tolerance.