Module channels 

Plane-wave channels of periodic arrays: how the multipoles of a 2D array of spheres or a 1D array of cylinders couple to the diffracted plane waves on either side.

Upstream: treams.sw.periodic_to_pw, treams.cw.periodic_to_pw, and the plane-wave expansions inside treams.SMatrices.from_array.

Item	Contents	Upstream
sw_periodic_to_pw	one plane-wave amplitude radiated by a spherical multipole of a 2D array	sw.periodic_to_pw
cw_periodic_to_pw	one plane-wave amplitude radiated by a cylindrical mode of a 1D array	cw.periodic_to_pw
spherical_channels	the incident and radiated coefficients of a whole spherical basis, with a pullback	SMatrices.from_array on a TMatrix
cylindrical_channels	the same for a cylindrical basis	SMatrices.from_array on a TMatrixC

Each channel matrix has one column per plane mode and 4 d rows for d multipoles: row side * d + i holds the regular expansion of the incident plane wave (the pw.to_sw or pw.to_cw coefficient, with the phase of the multipole position), and row (2 + side) * d + i the amplitude of the plane wave that multipole i radiates. On side 0 the plane wave travels up, toward +z for spheres and +y for cylinders; on side 1 it travels down.

Both families share ChannelGradient, input checks and matrix assembly. Each evaluates its own channel type and jet size; pullbacks share an ordered traversal while keeping the family-specific transverse-wavevector rules explicit.

The inline tests module checks the error paths; the reciprocity, scaling and adjoint identities of the channels are in properties/plane.rs.

Structs

ChannelGradient

Cotangents of positions, medium wavenumbers, transverse plane vectors and the unit-cell measure.

CylindricalChannel 🔒

One diffraction channel of a 1D array of cylinders along x in one direction: the plane wave (kx, ±ky, kz), as jets in the slots above. The axial kz is a fixed label.

CylindricalChannelsResidual

What cylindrical_channels saves for its pullback: its inputs alone.

SphericalChannel 🔒

One diffraction channel of a 2D array of spheres in one direction: the plane wave (qx, qy, ±kz) and the angles at which the multipole coefficients are evaluated, as jets in the slots above.

SphericalChannelsResidual

What spherical_channels saves for its pullback: its inputs alone.

Constants

CYLINDRICAL_MEASURE 🔒

Slot of the period of a 1D array.

CYLINDRICAL_SLOTS 🔒

Jet size of a cylindrical channel.

K 🔒

Slot of the medium wavenumber k.

POSITION 🔒

First of the three slots of the multipole position.

Q 🔒

First transverse-wavevector slot: (qx, qy) for spheres, kx alone for cylinders.

SPHERICAL_MEASURE 🔒

Slot of the unit-cell area of a 2D array.

SPHERICAL_SLOTS 🔒

Jet size of a spherical channel.

Functions

channel_direction 🔒

Both families use the same input shapes and slot layout, except that cylinders have only the kx transverse slot. Contract each small local jet directly; no global Jacobian or output-sized cotangent seeds are needed.

channel_matrix 🔒

Assemble incident/radiated pairs, constructing each channel once per side. Each worker owns complete plane-mode columns without buffering intermediate values.

channel_pullback 🔒

Reverse the shared matrix assembly in fixed column, side and multipole order. Each column writes its own transverse gradient; only the shared gradients enter the ordered reduction. Construct channels before skipping zero-weight entries, preserving validation and avoiding evaluation of unused, possibly overflowing jets.

channel_state_size 🔒

The shared numerical channel inputs, with one byte for the family’s flags.

cw_periodic_to_pw

Amplitude of the plane wave vector = (kx, ky, kz) that the cylindrical mode mode of a 1D array along x with lattice period radiates.

cylindrical_channels

Incident and radiated channels of a cylindrical basis in a 1D array along x with lattice period.

read_channel_state 🔒

spherical_channels

Incident and radiated channels of a spherical basis in a 2D array with unit-cell area.

sw_periodic_to_pw

Amplitude of the plane wave vector that the spherical multipole mode of a 2D array with unit-cell area radiates. The sign of kz (of its imaginary part for a complex kz) picks the side.

validate_channel_tangent 🔒

validate_channels 🔒

Check the inputs both channel families share; measure is the area or the period.

write_channel_state 🔒

Type Aliases

ChannelState 🔒