finesse.utilities.homs module

Functions for manipulating Higher Order Modes.

finesse.utilities.homs.HG_to_LG(n, m)

Returns the coefficients and mode indices of the Laguerre-Gaussian modes required to create a particular Hermote-Gaussian mode.

Parameters

n, m: integer

Indices of the HG mode to re-create.

Returns

coeffcients: array_like

Complex coefficients for each order=n+m LG mode required to re-create HG_n,m.

ps, ls: array_like

LG mode indices corresponding to coefficients.

finesse.utilities.homs.HG_to_LG_matrix(hgs, lgs)

Returns a matrix that will convert a Hermite-Gaussian mode vector into Laguerre- Gaussian modes. The HG and LG modes provided to this function must contain all the required modes. A 2nd order HG mode will require 2nd order LG modes.

Parameters

hgsarray_like

Array of (n,m) indicies

lgsarray_like

Array of (p,l) indicies

Returns

Kmatrix

Matrix to multiply with a HG mode vector to get the equivalent LG modes.

finesse.utilities.homs.insert_modes(modes, new_modes)

Inserts the mode indices in new_modes into the modes array at the correct (sorted) position(s).

Parameters

modesnumpy.ndarray

An array of HOM indices.

new_modessequence, str

A single mode index pair or an iterable of mode indices. Each element must unpack to two integer convertible values.

Returns

outnumpy.ndarray

A sorted array of HOM indices consisting of the original contents of modes with the mode indices from new_modes included.

Raises

ValueError

If new_modes is not a mode index pair or iterable of mode indices.

See Also

make_modes

Examples

Make an array of even modes and insert new modes into this:

>>> modes = make_modes("even", 2)
>>> modes
array([[0, 0], [0, 2], [2, 0]], dtype=int32)
>>> insert_modes(modes, ["11", "32"])
array([[0, 0], [0, 2], [1, 1], [2, 0], [3, 2]], dtype=int32)

finesse.utilities.homs.jacobi_real_x(n, a, b, x)

Jacobi Polynomial P_n^{a,b}(x) for real x.

                n    / n+a \ / n+b \ / x-1 \^(s) / x+1 \^(n-s)
P_n^{a,b}(x)= Sum    |     | |     | | --- |     | --- |
                s=0  \ n-s / \   s / \  2  /     \  2  /

Parameters

n, a, bint

Polynomial coefficients

xfloat

Polynomial argument

Notes

Implementation of Jacobi function using binominal coefficients. This can handle values of alpha, beta < -1 which the special.eval_jacobi function does not.

finesse.utilities.homs.lens_diopt_to_f(f, d)

Convert a dioptre shift, at a lens, to a focal length.

Parameters

ffloat

The initial focal length of the lens.

dfloat, array-like

A value or array of values representing the dioptre shift.

Returns

outfloat, array-like

The new value(s) of the focal length.

finesse.utilities.homs.make_modes(select=None, maxtem=None)

Construct a 2D numpy.ndarray of HOM indices.

Parameters

selectsequence, str, optional; default: None

Identifier for the mode indices to generate. This can be:

• An iterable of mode indices, where each element in the iterable must unpack to two integer convertible values.

• A string identifying the type of modes to include, must be one of “even”, “odd”, “x” or “y”.

maxtemint, optional; default: None

Optional maximum mode order, applicable only for when select is a string. This is ignored if select is not a string.

Returns

modesnumpy.ndarray

An array of mode indices.

Raises

ValueError

If either of the arguments select, maxtem are invalid or non-unique.

See Also

insert_modes : Add modes to an existing mode indices array at the correct positions.

Examples

Modes up to a maximum order of 2:

>>> make_modes(maxtem=2)
array([[0, 0], [0, 1], [0, 2], [1, 0], [1, 1], [2, 0]], dtype=int32)

Even modes up to order 4:

>>> make_modes("even", maxtem=4)
array([[0, 0], [0, 2], [0, 4], [2, 0], [2, 2], [4, 0]], dtype=int32)

Sagittal modes up to order 3:

>>> make_modes("y", maxtem=3)
array([[0, 0], [0, 1], [0, 2], [0, 3]], dtype=int32)

Modes from a list of strings:

>>> make_modes(["00", "11", "22"])
array([[0, 0], [1, 1], [2, 2]], dtype=int32)

finesse.utilities.homs.make_modes_LG(maxtem)

Returns an array of LG modes ordered in increasing polynomial order, 2p+|l|.

Parameters

maxtemint

Maximum LG order to include, maxtem > 0.

Returns

plarray_like

array of (p,l) indicies

finesse.utilities.homs.remove_modes(modes, remove)

finesse.utilities.homs.surface_diopt_to_roc(roc, d)

Convert a dioptre shift, at a surface, to a radius of curvature.

Parameters

rocfloat

The initial radius of curvature of the surface.

dfloat, array-like

A value or array of values representing the dioptre shift.

Returns

outfloat, array-like

The new values of the radius of curvature.