solprop.modes.rectangular#

Model gas-filled rectangular waveguides with dielectric or metallic walls.

The two wall pairs use the TE-like and TM-like reflection corrections of Laakmann and Steier (1976), with the filled-core contrast eps_cl - eps_co and the TM-like permittivity ratio eps_cl / eps_co. Complex wall corrections contribute to both phase and attenuation. This is an asymptotic model, not exact boundary matching: squaring the first-order boundary factor keeps a real second-order term the expansion does not control, and the normalisation carries the vacuum admittance where the modal power strictly carries the filled core’s, a choice of the order of the gas susceptibility. The indices follow one convention: m runs along x and n along y.

One wall pair’s decrement (_transverse_term) and the material sampling and TE-like/TM-like reflection coefficients (_WallPairFill) are shared with the hollow planar guide of solprop.modes.slab, which is the one-wall-pair limit b -> infinity of this guide.

Classes

RectMode(half_width_x, half_width_y[, gas, ...])

Describe one polarisation of a hollow rectangular waveguide mode.

class solprop.modes.rectangular.RectMode(half_width_x, half_width_y, gas=None, pressure=0.0, *, n=1, m=1, polarisation='x', loss=True, cladding=None, temperature=None, susceptibility=None, mixture=None)[source]#

Bases: _WallPairFill

Describe one polarisation of a hollow rectangular waveguide mode.

Attributes:

half_width_x, half_width_yfloat or ZProfile: Positive half-widths a and b in m. A shared path object gives a uniform scale taper; independently varying paths are not scale invariant.
gasGas or str or None: Legacy gas declaration; None means vacuum unless a mixture is supplied.
pressurefloat or ZProfile: Legacy gas pressure in bar, non-negative.
n, mint: Positive mode indices along y and x respectively.
polarisation{‘x’, ‘y’}: Nonzero transverse electric-field component. Its partner is a distinct mode with a different index unless the geometry makes them degenerate.
lossbool or float or callable: Shared hollow-mode policy: model loss, no loss, a non-negative model scale, or an absolute power attenuation in 1/m.
claddingGlassIndex or complex or None: Wall index, positive imaginary part for absorption. None selects fused silica.
temperaturefloat, ZProfile or None: Positive legacy fill temperature in K, or a path of it along z in m, which the density follows. None (the default) is 293.15 K for a gas and the mixture’s own beside a mixture; a different one beside it is refused.
susceptibilityGasSusceptibility or None: Explicit legacy gas susceptibility; None takes the built-in gas’s.
mixtureMixture or None: Ordered material populations; excludes competing legacy fill arguments.
width_x, width_yZProfile: Resolved geometry paths in m.
densityZProfile: Total number-density path in m^-3.
cladding_indexGlassIndex or complex: Resolved wall material.
model{‘full’, ‘reduced’}: Fixed internally to full, selecting the shared evanescent floor.

References

K. D. Laakmann and W. H. Steier, Applied Optics 15, 1334-1340 (1976), doi:10.1364/AO.15.001334. The filled-core factor eps_cl / (eps_co s) of the TM-like coefficient follows from grazing-incidence Fresnel reflection; it reduces to the published eps_cl / s for an evacuated core.

Examples

>>> mode = RectMode(50e-6, 12.5e-6, "Ar", 1.0)
>>> mode.principal_component(), mode.orthogonal_polarisation.principal_component()
('x', 'y')
>>> f"{mode.aeff():.6e}"
'1.111111e-09'

aeff(z=0.0)[source]#

Return the closed-form effective area.

Parameters:

zfloat, optional: Position in m.

Returns:

float: 16 a b / 9 in m², independent of mode index and fill.

at_parameters(values)[source]#

Copy the mode with the supplied geometry and fill paths frozen.

Parameters:

valuescollections.abc.Mapping: A subset of the declared paths, in m, m^-3 or shared pressure in bar.

Returns:

RectMode: A copy retaining unspecified paths and the same wall model.

Raises:

ModeError: If a path is unknown or a half-width is invalid.

property azimuthal_order: int[source]#

Return the larger Cartesian order as a geometry-resolution hint.

Returns:

int: Maximum of n and m. Cartesian Gauss rules integrate trigonometric products, not polynomials; their required node count is measured, not derived (see solprop.modes.quadrature.cartesian_nodes()).

property channel_label: ChannelLabel[source]#

Return the rectangular family, its two indices and its polarisation.

Returns:

ChannelLabel: Family rect, with n and m in the azimuthal and radial fields – a rectangular guide has neither, but they are the two indices the record carries – and the polarisation in the display label. The other polarisation is a distinct mode with its own operator row, not a parity partner of this one, so parity stays None.

Examples

>>> from solprop.modes import RectMode
>>> RectMode(50e-6, 12.5e-6, "Ar", 1.0).channel_label.display_label
'rect1,1:x'

cladding: GlassIndex | complex | None = None#

cladding_index: GlassIndex | complex#

density: ZProfile#

dimlimits(z=0.0)[source]#

Return the Cartesian cross-section and its integration bounds.

Parameters:

zfloat, optional: Position in m.

Returns:

tuple: Cartesian rectangle from (-a, -b) to (a, b), in m.

dneff_domega(omega, z=0.0)[source]#

Return the analytic derivative including core and wall material slopes.

Parameters:

omeganumpy.ndarray: Positive frequencies in rad/s.
zfloat, optional: Position in m.

Returns:

numpy.ndarray: Complex index derivative in s/rad; only a slope-free loss callable uses the shared numerical loss derivative.

field(points, z=0.0)[source]#

Return the unnormalised real Cartesian electric-field components.

Parameters:

pointsnumpy.ndarray: Cartesian (x,y) coordinates in m, shape (n_points, 2).
zfloat, optional: Position in m.

Returns:

numpy.ndarray: (Ex,Ey), shape (n_points, 2); zero outside the hollow rectangle.

Raises:

ModeError: If points are non-finite or have an invalid shape.

gas: Gas | str | None = None#

half_width_x: float | ZProfile#

half_width_y: float | ZProfile#

loss: bool | float | Callable[[Float[ndarray, 'n_omega']], Float[ndarray, 'n_omega']] = True#

m: int = 1#

mixture: Mixture | None = None#

model: Literal['full', 'reduced'] = 'full'#

n: int = 1#

neff(omega, z=0.0)[source]#

Return the effective index with positive imaginary part for attenuation.

Parameters:

omeganumpy.ndarray: Positive frequencies in rad/s.
zfloat, optional: Position in m.

Returns:

numpy.ndarray: Complex effective index, shape (n_omega,).

neff_minus_one(omega, z=0.0)[source]#

Return refractivity directly from the small square-root argument.

Parameters:

omeganumpy.ndarray: Positive frequencies in rad/s.
zfloat, optional: Position in m.

Returns:

numpy.ndarray: Complex n_eff - 1, without subtracting unity from the returned index.

normalisation(z=0.0)[source]#

Return the power carried by the unnormalised transverse profile.

Parameters:

zfloat, optional: Position in m.

Returns:

float: Power eps0 c a b / 2 in W.

property orthogonal_polarisation: RectMode[source]#

Return the distinct mode with the other electric-field orientation.

Returns:

RectMode: Same indices, geometry and fill, with the other wall-pair assignment. It requires its own operator row; it is not a duplicated scalar index.

property parameter_paths: Mapping[str, ZProfile][source]#

Return the geometry and material paths carrying longitudinal variation.

Returns:

collections.abc.Mapping: Half-width paths plus the shared fill’s density or pressure paths.

polarisation: Literal['x', 'y'] = 'x'#

property polarisation_degenerate: bool[source]#

Return whether the two polarisations share one effective index.

Returns:

bool: False: the x- and y-polarised modes of one (n, m) take the TE-like and TM-like coefficients on opposite wall pairs, so they are distinct modes and need a row each.

pressure: float | ZProfile = 0.0#

principal_component(z=0.0)[source]#

Return the nonzero Cartesian electric-field component.

Parameters:

zfloat, optional: Longitudinal position in m; orientation is fixed.

Returns:

str: The component, x or y.

property radius_is_constant: bool[source]#

Return the transform’s geometry-constant trait for the rectangle.

Returns:

bool: True when both half-width paths are constant; the historical trait name also serves Cartesian modes.

property scale_invariant: bool[source]#

Return whether one scalar rescaling represents the geometry.

Returns:

bool: True for constant half-widths or the same path object on both axes.

susceptibility: GasSusceptibility | None = None#

temperature: float | ZProfile | None = None#

width_x: ZProfile#

width_y: ZProfile#

property z_constant: bool[source]#

Return whether every geometry and material path is constant.

Returns:

bool: True if all declared paths are constant.