solprop.translate.planar#

Translate the hybrid planar grid into the kernel schema 15 "slab" seam.

The hybrid planar transform expands the field in the slab modes of one gap in x and a raw DFT in y,

E(x, y, t) = sum_p V_p(x) A_p(y, t),

so the state’s columns are (p, k_y) with the mode index fastest. It is the Cartesian "free" kind with its x FFT replaced by the slab rule’s modal synthesis and projection, and k_x**2 replaced by each mode’s complex, frequency-dependent transverse square kappa_p(omega)**2: the longitudinal wave number of a column is

k_z = sqrt(k**2 eps_co - kappa_p**2 - k_y**2),

exact (non-paraxial) in y, with the free-space evanescent model and prefactor -i omega**2 / (2 eps0 c**2 Re k_z) per column. Constant media and a constant gap only: both are refused by name upstream, and the operator here is frozen along z.

The kernel formula, the kappa_sq leaf and the geometry are docs/dev/kernel-contract.md sections 3 and 4; the physics is docs/guide/waveguides/planar.md, “Resolving y”.

Functions

`planar_kappa`(space, dispersion)	Return each slab channel's transverse wave-number square `kappa_p**2`.
`planar_operators`(space, dispersion, *, ...)	Keep the planar operator in separable form, with each channel's wall term.
`planar_transform`(space, time, *, n_pol, z_max)	Freeze the slab synthesis and projection in x and the y FFT layout.
`square_residuals`(axis)	Return the exact residuals of an axis's rounded squares.

solprop.translate.planar.planar_kappa(space, dispersion)[source]#

Return each slab channel’s transverse wave-number square kappa_p**2.

kappa_p**2 = k**2 eps_co - beta_p**2 is formed from the mode’s own complex index as (omega/c)**2 (n_co - n_p)(n_co + n_p), whose difference factor is exact for indices this close.

Parameters:

spacesolprop.modes.slab.PlanarGrid: Slab channels and the y axis.
dispersionsolprop.spatial.SpatialDispersion: The fill as a bulk medium and the temporal grid.

Returns:

numpy.ndarray: Complex squares in m^-2, shape (n_p, n_omega), zero at inactive bins.

solprop.translate.planar.planar_operators(space, dispersion, *, n_pol, z_max, absorber=None, margin=0.05)[source]#

Keep the planar operator in separable form, with each channel’s wall term.

The material square k**2 eps_co and k_y**2 are split into a rounded value and an exact residual as in the Cartesian operator; each channel’s kappa_p**2 = k**2 eps_co - beta_p**2 is formed from the mode’s own complex index as (omega/c)**2 (n_co - n_p)(n_co + n_p), whose difference factor is exact for indices this close, so the column square at k_y = 0 reproduces beta_p**2 to a few rounding units of kappa_p**2. The frame is the first channel’s at k_y = 0, as the modal route’s, so a field uniform in y propagates exactly as the slab set does through prop_waveguide.

Parameters:

spacesolprop.modes.slab.PlanarGrid: Slab channels and the y axis.
dispersionsolprop.spatial.SpatialDispersion: The fill as a bulk medium, the temporal grid and the frame.
n_polint: State polarisation count; must be 1.
z_maxfloat: Positive propagation length in m.
absorbersolprop.boundaries.Absorber or None, optional: Shared spectral absorption rate in m^-1.
marginfloat, optional: Relative extension of the valid interval, nonnegative.

Returns:

tuple: Linear operator and the same separable record for the nonlinear prefactor.

Raises:

TranslationError: If the medium varies along z or is not the modes’ own fill, the state has two components or the interval is invalid.

Warns:

solprop.exceptions.GrazingIncidenceWarning: If an active column lies within the arithmetic uncertainty of its cutoff.

solprop.translate.planar.planar_transform(space, time, *, n_pol, z_max, absorber=None, node_budget=1073741824, margin=0.05)[source]#

Freeze the slab synthesis and projection in x and the y FFT layout.

Parameters:

spacesolprop.modes.slab.PlanarGrid: Slab modes and rule in x, periodic y axis and its collar.
timesolprop.grid.TimeGrid: Temporal grid: the pad scale folded into the synthesis, and the physical-node buffer size.
n_polint: State polarisation count; must be 1.
z_maxfloat: Positive run length in m.
absorbersolprop.boundaries.Absorber or None, optional: Spatial absorption reference length; None disables the in-stage y collar.
node_budgetint, optional: Shared node-buffer budget in bytes, positive.
marginfloat, optional: Relative extension of diagnostic tables beyond z_max, nonnegative.

Returns:

solprop.translate.modal.Transform: The slab matrices in x, with the pad scale folded into the synthesis, the "slab" geometry and a bounded physical-node chunk.

Raises:

TranslationError: If the state has two components, the span is invalid or one temporal column does not fit the budget.

Examples

>>> from solprop.grid import EnvelopeGrid
>>> from solprop.modes import PlanarGrid, SlabMode
>>> from solprop.translate.planar import planar_transform
>>> grid = EnvelopeGrid.from_limits(0.1, 800e-9, (650e-9, 1000e-9), 400e-15)
>>> space = PlanarGrid([SlabMode(63.5e-6, "Ar", 1.0)], 1e-3, 16)
>>> transform = planar_transform(space, grid, n_pol=1, z_max=0.1)
>>> transform.geometry.kind, transform.n_modes, transform.n_nodes
('slab', 16, 528)

solprop.translate.planar.square_residuals(axis)[source]#

Return the exact residuals of an axis’s rounded squares.

Parameters:

axisnumpy.ndarray: Stored binary wave numbers in rad/m.

Returns:

numpy.ndarray: value**2 in exact rational arithmetic minus its rounded float, in m^-2, one per entry, as the Cartesian kperp_sq_low is formed.