Module cw 

Cylindrical vector waves: mode labels, translation coefficients of mode pairs, expansion matrices between bases and over lattices, and the conversion to spherical waves.

Upstream: treams.cw, and treams.special.tl_vcw and tl_vcw_r.

File	Contents	Upstream
polar.rs	polar_translation and polar_translation_array of one order difference, tl_vcw and translate of one mode pair	special.tl_vcw, tl_vcw_r, cw.translate
cartesian.rs	cartesian_translation: one coefficient at a Cartesian displacement, with its derivatives	treams-rs extension
expansion.rs	expansion() and lattice_expansion	Expand, ExpandLattice, cw.translate_periodic
to_sw.rs	to_sw() and to_sw_matrix	cw.to_sw, Expand to a spherical basis

Conventions:

• A translation from a source position to a destination position takes the displacement destination - source. Lattice sums run over source - destination, the argument of crate::lattice::sum.
• Two modes couple only at equal axial wavenumbers kz and equal polarization indices pol. kz is an exact label: the coupling compares it bit for bit.
• pol is the polarization index, 0 or 1, with the meanings of crate::sw.
• Radial::Regular and Radial::Singular are the treams modetype values ‘regular’ and ‘singular’.
• In CartesianTranslation, every field other than value holds the derivative of value with respect to the input it is named after; position holds the derivatives with respect to the displacement components.

The inline tests modules check how each file computes its results; the physical and adjoint identities of translations and expansions are in properties/waves.rs.

Modules

cartesian 🔒

Cartesian cylindrical-wave translation and analytic derivatives.

expansion 🔒

Cylindrical expansion matrices between bases and over periodic arrays, with analytic pullbacks. Entries that share a CouplingKey share one coefficient, evaluated once.

polar 🔒

Cylindrical translation coefficients in polar coordinates, of one order difference and of one mode pair, with analytic pullbacks.

to_sw 🔒

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

Structs

CartesianTranslation

Translation coefficient and its continuous derivatives, with the axial wavenumbers of both modes moving together.

ExpansionResidual

What expansion saves for its pullback: the bases, the wavenumbers, the radial kind and the distinct couplings.

LatticeExpansionResidual

What lattice_expansion saves for its pullback: the bases, the wavenumbers, the lattice, the split and the distinct couplings.

Mode

One cylindrical-wave mode: axial wavenumber kz, order m and polarization index pol.

PolarTranslationResidual

What polar_translation_array saves for its pullback: the orders, the radial kind and the four arguments, each stored once when it is one value for all outputs.

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

cartesian_translation

Translation coefficient of the source mode from to the destination mode to, with its derivatives.

expansion

Construct a cylindrical expansion matrix in the supplied mode order.

lattice_expansion

Periodic cylindrical coupling with exact axial/polarization selection and cached orders.

polar_translation

Cylindrical translation in (k_rho*rho, phi, z, kz) with a fixed order difference, the kernel of tl_vcw. The two axial labels must move together; unequal labels are uncoupled.

polar_translation_array

Evaluate a broadcast array of cylindrical polar translation coefficients; orders holds order differences, as in polar_translation.

tl_vcw

Cylindrical translation coefficient of the mode pair (qz, m) to (kz, mu).

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.

translate

Cylindrical translation coefficient of one polarized mode pair.

transverse 🔒

Transverse wavenumber sqrt(k² - kz²) on the branch with nonnegative imaginary part.

transverse_wavenumber 🔒

transverse of a complex wavenumber and a real axial wavenumber.

Type Aliases

Basis

Cylindrical modes at Cartesian expansion positions.