Module expand 

Regular spherical and cylindrical expansions of plane waves, with analytic pullbacks.

Upstream: treams.pw.to_sw, treams.pw.to_cw, and the Expand operator from a plane-wave basis to a spherical or cylindrical basis.

Structs

AngularLabels 🔒

Angular plane-wave coefficients depend on a mode’s label, not on its position: modes that repeat at several positions share one evaluation.

ExpansionGradient

Plane-expansion cotangents.

ExpansionResidual

What expansion saves for its pullback: its inputs. The pullback recomputes the coefficients instead of keeping a Jacobian.

Functions

cylindrical_angular 🔒

The angular factor ((i kx + ky) / sqrt(kx^2 + ky^2))^m = (i exp(-i phi))^m of the cylindrical expansion of a plane wave, i^m on the z axis.

cylindrical_coefficient 🔒

The coefficient of mode in the regular expansion of a unit plane wave of polarization pol, without the position phase; zero unless the labels match.

cylindrical_mode_matches 🔒

Whether a plane wave of axial wavenumber kz and polarization pol couples to the cylindrical mode: equal pol, a real kz, and kz within 16 ulps of the mode’s.

expansion

Expand multiple plane waves in a regular multipole basis: column j holds the amplitudes of plane wave j at the basis positions.

spherical_coefficient 🔒

The coefficient of mode in the regular expansion of a unit plane wave of polarization pol, without the position phase: the prefactor times exp(-i m phi) times the polarized angular function of theta.

spherical_prefactor 🔒

Normalization and phase i^l of the spherical expansion of a plane wave, which depend on the degree and order alone.

to_cw

One plane-to-cylindrical coefficient with exact axial-label matching.

to_sw

Spherical expansion coefficient for a unit-amplitude plane wave.