anafibre.fibre¶

StepIndexFibre¶

Parameters:

Name	Type	Description	Default
`core_radius`	`float or Quantity[m]`		required
`core`	`RefractiveIndexMaterial`	Core material object (highest precedence for the core side).	`None`
`clad`	`RefractiveIndexMaterial`	Cladding material object (highest precedence for the cladding side).	`None`
`eps_core`	`float or callable`	Core relative permittivity `eps(lambda)` if `core` is not provided.	`None`
`eps_clad`	`float or callable`	Cladding relative permittivity `eps(lambda)` if `clad` is not provided.	`None`
`n_core`	`float or callable`	Core refractive index `n(lambda)` used if neither `core` nor `eps_core` is provided.	`None`
`n_clad`	`float or callable`	Cladding refractive index `n(lambda)` used if neither `clad` nor `eps_clad` is provided.	`None`
`mu_core`	`float or callable`	Core relative permeability `mu(lambda)`.	`1.0`
`mu_clad`	`float or callable`	Cladding relative permeability `mu(lambda)`.	`1.0`
`exp_type`	`str`	Passed to `RefractiveIndexMaterial.get_eps` when `core`/`clad` are provided.	`"exp_minus_i_omega_t"`
`real_eps_from_material`	`if True, use n^2 (real). If False and k is available in`	`the database, use (n ± i k)^2 depending on exp_type.`	`True`

Mode Constructors¶

Cylindrical step-index fibre model with analytical mode utilities.

The class stores core/cladding constitutive parameters and provides methods to compute dispersion roots, propagation constants, and mode objects.

`HE` ¶

Construct an HE_{ell,n} mode.

Parameters:

Name	Type	Description	Default
`ell`	`int`	Azimuthal mode index (`ell > 0`).	required
`n`	`int`	Radial index in HE/EH notation (mapped to internal odd `m`).	required
`wl`	`float`	Wavelength in meters.	required
`**kwargs`		Forwarded to :class:`anafibre.fields.GuidedMode`.	`{}`

Returns:

Type	Description
`GuidedMode`	Guided HE mode object.

`EH` ¶

Construct an EH_{ell,n} mode.

Parameters:

Name	Type	Description	Default
`ell`	`int`	Azimuthal mode index (`ell > 0`).	required
`n`	`int`	Radial index in HE/EH notation (mapped to internal even `m`).	required
`wl`	`float`	Wavelength in meters.	required
`**kwargs`		Forwarded to :class:`anafibre.fields.GuidedMode`.	`{}`

Returns:

Type	Description
`GuidedMode`	Guided EH mode object.

`TE` ¶

Construct a TE_{0,n} mode.

Parameters:

Name	Type	Description	Default
`n`	`int`	Radial mode index.	required
`wl`	`float`	Wavelength in meters.	required
`**kwargs`		Forwarded to :class:`anafibre.fields.GuidedMode`.	`{}`

Returns:

Type	Description
`GuidedMode`	Guided TE mode object.

`TM` ¶

Construct a TM_{0,n} mode.

Parameters:

Name	Type	Description	Default
`n`	`int`	Radial mode index.	required
`wl`	`float`	Wavelength in meters.	required
`**kwargs`		Forwarded to :class:`anafibre.fields.GuidedMode`.	`{}`

Returns:

Type	Description
`GuidedMode`	Guided TM mode object.

Material And Profile¶

Cylindrical step-index fibre model with analytical mode utilities.

The class stores core/cladding constitutive parameters and provides methods to compute dispersion roots, propagation constants, and mode objects.

`n_core` ¶

Return core refractive index at a wavelength.

Parameters:

Name	Type	Description	Default
`wl`	`float \| array - like`	Wavelength in meters.	required

Returns:

Type	Description
`float \| complex \| ndarray`	Core refractive index.

`n_clad` ¶

Return cladding refractive index at a wavelength.

Parameters:

Name	Type	Description	Default
`wl`	`float \| array - like`	Wavelength in meters.	required

Returns:

Type	Description
`float \| complex \| ndarray`	Cladding refractive index.

`eps` ¶

Return radial relative permittivity profile.

Parameters:

Name	Type	Description	Default
`r`	`float \| array - like`	Radial coordinate in meters.	required
`wl`	`float \| array - like`	Wavelength in meters.	required

Returns:

Type	Description
`float \| complex \| ndarray`	Piecewise `eps_core` inside the core and `eps_clad` outside.

`mu` ¶

Return radial relative permeability profile.

Parameters:

Name	Type	Description	Default
`r`	`float \| array - like`	Radial coordinate in meters.	required
`wl`	`float \| array - like`	Wavelength in meters.	required

Returns:

Type	Description
`float \| complex \| ndarray`	Piecewise `mu_core` inside the core and `mu_clad` outside.

`n` ¶

Return radial refractive index profile.

Parameters:

Name	Type	Description	Default
`r`	`float \| array - like`	Radial coordinate in meters.	required
`wl`	`float \| array - like`	Wavelength in meters.	required

Returns:

Type	Description
`float \| complex \| ndarray`	Refractive index profile `sqrt(eps * mu)`.

Dispersion And Propagation¶

Cylindrical step-index fibre model with analytical mode utilities.

The class stores core/cladding constitutive parameters and provides methods to compute dispersion roots, propagation constants, and mode objects.

`V` ¶

Compute normalised frequency parameter V.

Parameters:

Name	Type	Description	Default
`wl`	`float \| array - like`	Wavelength in meters.	required

Returns:

Type	Description
`float \| ndarray`	normalised frequency `V = k0 a sqrt(n_core^2 - n_clad^2)`.

Notes

This corresponds to the paper definition \(V=k_0\rho_0\sqrt{n_1^2-n_2^2}\), where \(\rho_0\) is the core radius.

`wl_of_V` ¶

Invert V(lambda) to obtain wavelength. This function does not work well for V<~0.5 when the indices are wavelength-dependent, so use with caution in that regime.

Parameters:

Name	Type	Description	Default
`V`	`float \| array - like`	Target normalised frequency value(s).	required
`wl_bracket`	`tuple[float, float] \| None`	Search interval in meters used when material properties are wavelength-dependent. If `None`, attempts to use the overlap of `core`/`clad` material validity ranges and falls back to `(2e-7, 5e-6)`.	`None`
`rtol`	`float`	Relative tolerance for scalar root solving.	`1e-12`
`maxiter`	`int`	Maximum iterations for scalar root solving.	`100`
`_grid_pts`	`int`	Number of logarithmic sampling points used to bracket roots.	`64`

Returns:

Type	Description
`float \| ndarray`	Wavelength in meters. `V == 0` maps to `np.inf`.

Raises:

Type	Description
`ValueError`	If the bracket is invalid or no wavelength in the bracket reaches a target `V`.

Notes

Solves the implicit equation \(V(\lambda)=\frac{2\pi a}{\lambda}\sqrt{n_\mathrm{core}(\lambda)^2-n_\mathrm{clad}(\lambda)^2}\). For constant material parameters, the closed-form inverse is used.

`Phi` ¶

Return :math:\Phi_\ell^\alpha for the fibre dispersion model.

Parameters:

Name	Type	Description	Default
`ell`	`int`	Azimuthal mode index.	required
`b`	`float \| complex \| array - like`	normalised propagation constant candidate(s).	required
`V`	`float \| array - like`	normalised frequency. Provide either `V` or `wl`.	`None`
`wl`	`float \| array - like`	Wavelength in meters. Used when `V` is not provided.	`None`
`alpha`	`sequence`	Length-2 sequence `[alpha1, alpha2]` for core/cladding parameters. Each entry may be a scalar, array, or callable `f(wl)`.	`None`

Returns:

Type	Description
`float \| complex \| ndarray`	Value(s) of :math:`\Phi_\ell^\alpha`.

`F` ¶

Return the dispersion function F(b, V) or F(b, wavelength) for given mode.

Parameters:

Name	Type	Description	Default
`ell`	`int`	Azimuthal mode number.	required
`b`	`float or array - like`	normalised propagation constant.	required
`V`	`float`	normalised frequency.	`None`
`wl`	`float`	Wavelength (used if V not given).	`None`
`mode_type`	`str`	For ell=0, specify 'TE' or 'TM'.	`None`

Returns:

Type	Description
`float or ndarray`	Value of the dispersion equation F(b, V).

Notes

This is the API-level wrapper of :func:anafibre.dispersion.F_dispersion, corresponding to the regularized scalar dispersion function used for robust root-finding in the paper.

`b` ¶

Return normalised propagation constant b for a guided mode.

Parameters:

Name	Type	Description	Default
`ell`	`int`	Azimuthal mode index.	required
`m`	`int`	Radial mode index (1-based).	required
`V`	`float \| array - like`	normalised frequency values.	`None`
`wl`	`float \| array - like`	Wavelength values in meters.	`None`
`mode_type`	`(TE, TM, None)`	Mode family selector for `ell == 0`.	`"TE"`
`N_b`	`int`	Number of samples used for root bracketing.	`2000`
`tol`	`float`	Real root-finder tolerance.	`1e-15`
`complex_tol`	`float`	Complex root acceptance tolerance.	`1e-8`
`maxiter`	`int`	Maximum iterations for complex root refinement.	`100`

Returns:

Type	Description
`float \| complex \| ndarray`	Guided root(s) `b`.

Notes

\(b\) is the normalised propagation constant used in the paper: \(b=\frac{n_\mathrm{eff}^2-n_2^2}{n_1^2-n_2^2}\), constrained to \([0,1]\) for guided modes in lossless conditions.

`neff` ¶

Return effective index for a selected guided mode.

Parameters:

Name	Type	Description	Default
`ell`	`int`	Azimuthal and radial mode indices.	required
`m`	`int`	Azimuthal and radial mode indices.	required
`V`	`float \| array - like`	normalised frequency values.	`None`
`wl`	`float \| array - like`	Wavelength values in meters.	`None`
`mode_type`	`(TE, TM, None)`	Mode family selector for `ell == 0`.	`"TE"`
`**kwargs`		Forwarded to :meth:`b` (for example `N_b`, `tol`).	`{}`

Returns:

Type	Description
`float \| complex \| ndarray`	Effective index `n_eff`.

Notes

Equivalent to composing :meth:b with \(n_\mathrm{eff}(b)=\sqrt{b\,n_1^2+(1-b)\,n_2^2}\).

`kz` ¶

Return longitudinal propagation constant for a guided mode.

Parameters:

Name	Type	Description	Default
`ell`	`int`	Azimuthal and radial mode indices.	required
`m`	`int`	Azimuthal and radial mode indices.	required
`V`	`float \| array - like`	normalised frequency values.	`None`
`wl`	`float \| array - like`	Wavelength values in meters.	`None`
`mode_type`	`(TE, TM, None)`	Mode family selector for `ell == 0`.	`"TE"`
`**kwargs`		Forwarded to :meth:`b` (for example `N_b`, `tol`).	`{}`

Returns:

Type	Description
`float \| complex \| ndarray`	Propagation constant `k_z` in rad/m.

Notes

Uses \(k_z=n_\mathrm{eff}k_0\) with \(k_0=2\pi/\lambda\).

Cylindrical step-index fibre model with analytical mode utilities.

The class stores core/cladding constitutive parameters and provides methods to compute dispersion roots, propagation constants, and mode objects.

`m_max` ¶

Find the highest guided radial index m for fixed ell and wavelength.

Parameters:

Name	Type	Description	Default
`ell`	`int`	Azimuthal mode index.	required
`wl`	`float`	Wavelength in meters.	required
`mode_type`	`(TE, TM, None)`	Mode family selector for `ell == 0`.	`"TE"`
`N_b`		Root-finding controls passed to :meth:`b`.	`2000`
`tol`		Root-finding controls passed to :meth:`b`.	`2000`
`complex_tol`		Root-finding controls passed to :meth:`b`.	`2000`
`maxiter`		Root-finding controls passed to :meth:`b`.	`2000`

Returns:

Type	Description
`int`	Largest guided radial index, or `0` if no guided solution exists.

`ell_max` ¶

Find the highest guided azimuthal index ell for fixed radial order.

Parameters:

Name	Type	Description	Default
`wl`	`float`	Wavelength in meters.	required
`m`	`int`	Radial mode index to track while increasing `ell`.	`1`
`mode_type`	`(TE, TM, None)`	Mode family selector for `ell == 0`.	`"TE"`
`N_b`		Root-finding controls passed to :meth:`b`.	`2000`
`tol`		Root-finding controls passed to :meth:`b`.	`2000`
`complex_tol`		Root-finding controls passed to :meth:`b`.	`2000`
`maxiter`		Root-finding controls passed to :meth:`b`.	`2000`
`ell_max_search`	`int`	Maximum `ell` value checked before stopping.	`100`

Returns:

Type	Description
`int`	Largest guided azimuthal index found, or `-1` if none exists.

`list_modes_at` ¶

Enumerate all guided modes at a given wavelength.

Parameters:

Name	Type	Description	Default
`wl`	`float`	Wavelength in meters.	required

Returns:

Type	Description
`GuidedModeList`	Guided modes sorted by decreasing `n_eff`.

RefractiveIndexMaterial¶

Wrapper around the refractiveindex database material interface.

Parameters:

Name	Type	Description	Default
`shelf`	`str`	Refractiveindex.info shelf name.	required
`book`	`str`	Refractiveindex.info book name.	required
`page`	`str`	Refractiveindex.info page name.	required
`**ri_kwargs`		Additional keyword arguments forwarded to :class:`refractiveindex.refractiveindex.RefractiveIndex`.	`{}`

`from_upstream` `classmethod` ¶

Build wrapper from an upstream refractiveindex material instance.

`get_refractive_index` ¶

Return refractive index values from the database.

Parameters:

Name	Type	Description	Default
`wl`	`float \| array - like`	Wavelength in meters (or astropy quantity convertible to meters).	required

Returns:

Type	Description
`float \| ndarray`	Refractive index `n`.

`get_extinction_coefficient` ¶

Return extinction coefficient values from the database.

Parameters:

Name	Type	Description	Default
`wl`	`float \| array - like`	Wavelength in meters (or astropy quantity convertible to meters).	required

Returns:

Type	Description
`float \| ndarray`	Extinction coefficient `k`.

`get_eps` ¶

Evaluate permittivity from database material data.

Parameters:

Name	Type	Description	Default
`wl`	`float \| array - like`	Wavelength in meters (or astropy quantity convertible to meters).	required
`exp_type`	`(exp_minus_i_omega_t, exp_plus_i_omega_t)`	Time-harmonic convention used for complex permittivity sign.	`"exp_minus_i_omega_t"`
`real`	`bool`	If `True`, returns `n^2`. If `False`, returns `(n ± i k)^2`.	`True`

Returns:

Type	Description
`float \| complex \| ndarray`	Relative permittivity.

anafibre.fibre¶

StepIndexFibre¶

Mode Constructors¶

HE ¶

EH ¶

TE ¶

TM ¶

Material And Profile¶

n_core ¶

n_clad ¶

eps ¶

mu ¶

n ¶

Dispersion And Propagation¶

V ¶

wl_of_V ¶

Phi ¶

F ¶

b ¶

neff ¶

kz ¶

Modal Diagnostics¶

m_max ¶

ell_max ¶

list_modes_at ¶

RefractiveIndexMaterial¶

from_upstream classmethod ¶

get_refractive_index ¶

get_extinction_coefficient ¶

get_eps ¶

`HE` ¶

`EH` ¶

`TE` ¶

`TM` ¶

`n_core` ¶

`n_clad` ¶

`eps` ¶

`mu` ¶

`n` ¶

`V` ¶

`wl_of_V` ¶

`Phi` ¶

`F` ¶

`b` ¶

`neff` ¶

`kz` ¶

`m_max` ¶

`ell_max` ¶

`list_modes_at` ¶

`from_upstream` `classmethod` ¶

`get_refractive_index` ¶

`get_extinction_coefficient` ¶

`get_eps` ¶