Module chirality 

Chirality-density forms of plane-wave modes, averaged over an interval.

Two kernels compute these forms from different inputs, and each differentiates its own. chirality_density takes the full and normal wavenumbers of modes with real transverse wavevectors in the xy plane and returns the forms without the helicity sign. oriented_chirality takes the real transverse components and the normal wavenumber along any Cartesian axis and includes the helicity sign of each mode.

Both kernels exist because their gradients answer different questions: the first differentiates with respect to the medium (k, kz), the second with respect to the direction of incidence (q, kz). On modes with q.q = k^2 - kz^2 their forms agree up to the helicity sign.

Upstream: treams.chirality_density. Its interval average decays with Re(kz) instead of Im(kz) and drops the phase of the cross form; these kernels keep both.

Modules

saved 🔒

Fixed numeric layouts of the per-mode chirality derivative state. treams-rs extension.

Structs

ChiralityDensityGradient

Complex full/normal wavenumber and real interval-endpoint cotangents.

ChiralityDensityResidual

What chirality_density saves for its pullback: the full and normal wavenumbers and the interval.

OrientedChiralityGradient

Real transverse, complex normal and real interval-endpoint cotangents.

OrientedChiralityResidual

What oriented_chirality saves for its pullback: the real transverse components, the normal wavenumbers, the polarizations, the axis and the interval.

Constants

INTERVAL 🔒

See KS.

KS 🔒

Jet seed offsets of the six real local parameters of one mode: the full wavenumber k (real, imaginary) of chirality_density or the transverse components q of oriented_chirality at KS or Q, the normal wavenumber (real, imaginary) at KZS and the interval endpoints at INTERVAL.

KZS 🔒

See KS.

Q 🔒

See KS.

Functions

chirality_density

Up, down and coherent cross coefficients, shape (3, modes), before polarization.

chirality_forms 🔒

The same scaled formulas for value, coordinate derivatives and directional jets.

chirality_mode 🔒

The up, down and cross forms of one mode of chirality_density.

mean_exp 🔒

The mean of exp(slope z) over z in interval, from a six-term series when the exponent changes by less than 0.1 across the interval.

mode_cotangents 🔒

Pair the six local real derivatives of every mode’s forms with its column of the (3, modes) cotangent, in parallel from 1024 modes.

mode_forms 🔒

The three forms of every mode as a (3, modes) matrix, in parallel from 1024 modes.

oriented_chirality

Signed helicity up/down/cross forms, shape (3, modes), for any Cartesian normal.

oriented_chirality_forms 🔒

Jets of the real coordinates retain the non-holomorphic polarization inner products.

oriented_chirality_mode 🔒

The helicity-signed up, down and cross forms of one mode of oriented_chirality.

real_direction 🔒

Real and imaginary coordinates of one complex directional input.