Module to_sw 

Regular cylindrical-to-spherical conversion, including displaced positions.

Upstream: treams.cw.to_sw and the treams.Expand operator from a cylindrical to a spherical basis.

Structs

Column 🔒

The entries of one source column. Angular coefficients depend only on the destination mode label and translations only on the destination position and order, so each is evaluated once per column and shared by the modes of every destination position, degree and polarization.

ToSwResidual

What to_sw_matrix saves for its pullback: the bases, the wavenumbers and the polarization convention. The pullback recomputes the derivatives of every entry.

Functions

coefficient 🔒

The coefficient of the spherical mode mode in a regular cylindrical wave of polarization pol and axial wavenumber kz at one position, as a jet in kz and the wavenumber wave: i^(l - m) sqrt(4 pi (2l + 1) / (l (l + 1))) sqrt((l - m)! / (l + m)!) times the polarized angular function at cos theta = kz / k.

to_sw

Cylindrical-to-spherical coefficient of a sphere and an axis at one position, with fixed mode labels.

to_sw_matrix

Expand regular cylindrical waves around arbitrary spherical expansion positions: the matrix maps cylindrical input amplitudes to regular spherical amplitudes.