solprop.polarisation#

Construct Jones optics and describe transverse polarisation in the optics convention.

Jones vectors are [E_x, E_y]. Stokes vectors are [I, Q, U, V] with V = -2 Im(E_x conj(E_y)), so (x + i y)/sqrt(2) has positive V. A waveplate’s fast axis is x: its retardance delays the vertical component relative to the horizontal one, and in the optics convention a delay is a positive phase (conventions.md §2), so a quarter-wave plate turns light linear at +45° into (x + i y)/sqrt(2). Convert internal FFT-convention fields at the existing Fourier boundary before using these helpers.

The ellipse orientation is atan2(U, Q)/2, which keeps the sign of U. Circular and zero fields use zero orientation by convention; normalised Stokes coordinates require nonzero intensity.

Functions

`cartesian`(parameters)	Return normalised Stokes coordinates on or inside the Poincare sphere.
`ellipse`(parameters)	Return ellipse semiaxes, orientation and handedness from Stokes parameters.
`ellipticity`(parameters)	Return the unsigned minor-to-major semiaxis ratio.
`horizontal`()	Return the unit Jones vector along x.
`linear_polariser`()	Return an ideal linear polariser transmitting x.
`rotate`(matrix, angle)	Rotate a Jones optical element from x towards y.
`rotation`(angle)	Return a passive rotation of the transverse coordinate axes.
`stokes`(field, *[, normalise])	Return Stokes parameters for one optics-convention Jones vector.
`waveplate`(retardance)	Return a waveplate with its fast axis along x in the optics convention.

Classes

PolarisationEllipse(major, minor, angle, ...)

Describe the ellipse associated with a Stokes vector.

class solprop.polarisation.PolarisationEllipse(major, minor, angle, handedness)[source]#

Bases: object

Describe the ellipse associated with a Stokes vector.

Attributes:

majorfloat: Major semiaxis, in the field’s amplitude units, non-negative.
minorfloat: Minor semiaxis in the same units, between zero and major.
anglefloat: Major-axis orientation from x towards y, rad, in [-pi/2, pi/2]. Zero for circular or zero fields, whose orientation is undefined.
handednessint: Sign of Stokes V: -1, 0 or +1. This names the algebraic sign without assuming an observer’s viewing direction.

angle: float#

handedness: int#

major: float#

minor: float#

solprop.polarisation.cartesian(parameters)[source]#

Return normalised Stokes coordinates on or inside the Poincare sphere.

Parameters:

parametersarray_like: Physical Stokes vector, shape (4,), with positive I.

Returns:

numpy.ndarray: Dimensionless [Q, U, V]/I, shape (3,).

Raises:

PolarisationError: If the vector is invalid or I is zero.

solprop.polarisation.ellipse(parameters)[source]#

Return ellipse semiaxes, orientation and handedness from Stokes parameters.

Parameters:

parametersarray_like: Physical Stokes vector [I, Q, U, V], shape (4,).

Returns:

PolarisationEllipse: Semiaxes in field units, orientation in rad, and the sign of V. For a partially polarised Stokes vector this describes its equivalent ellipse.

Raises:

PolarisationError: If the Stokes vector is nonphysical or not finite.

solprop.polarisation.ellipticity(parameters)[source]#

Return the unsigned minor-to-major semiaxis ratio.

Parameters:

parametersarray_like: Physical Stokes vector, shape (4,), with positive intensity.

Returns:

float: Ratio in [0, 1]: zero for linear polarisation, one for circular.

Raises:

PolarisationError: If the vector is invalid or the field has zero intensity.

solprop.polarisation.horizontal()[source]#

Return the unit Jones vector along x.

Returns:

numpy.ndarray: Dimensionless [1, 0], shape (2,), complex128.

solprop.polarisation.linear_polariser()[source]#

Return an ideal linear polariser transmitting x.

Returns:

numpy.ndarray: Dimensionless Jones matrix diag(1, 0), shape (2, 2).

solprop.polarisation.rotate(matrix, angle)[source]#

Rotate a Jones optical element from x towards y.

Parameters:

matrixarray_like: Finite dimensionless Jones matrix, shape (2, 2).
anglefloat: Finite physical rotation angle, rad.

Returns:

numpy.ndarray: rotation(-angle) @ matrix @ rotation(angle).

Raises:

PolarisationError: If the matrix or angle is invalid.

solprop.polarisation.rotation(angle)[source]#

Return a passive rotation of the transverse coordinate axes.

Parameters:

anglefloat: Finite angle from x towards y, rad.

Returns:

numpy.ndarray: Dimensionless matrix [[cos, sin], [-sin, cos]].

Raises:

PolarisationError: If the angle is not finite.

solprop.polarisation.stokes(field, *, normalise=False)[source]#

Return Stokes parameters for one optics-convention Jones vector.

Parameters:

fieldarray_like: Finite Jones vector [E_x, E_y], shape (2,).
normalisebool, optional: Divide by the total intensity; requires a nonzero field.

Returns:

numpy.ndarray: [I, Q, U, V], shape (4,), in squared field units or dimensionless when normalised. Positive V corresponds to (x + i y)/sqrt(2).

Raises:

PolarisationError: If the vector is invalid, squared amplitudes overflow, or normalisation is requested for zero intensity.

Examples

>>> from solprop.polarisation import stokes
>>> stokes([1, 1j], normalise=True).tolist()
[1.0, 0.0, 0.0, 1.0]

solprop.polarisation.waveplate(retardance)[source]#

Return a waveplate with its fast axis along x in the optics convention.

Parameters:

retardancefloat: Finite retardance of the slow y component behind the fast x one, rad. A delay is a positive optics-convention phase, so y gains +retardance relative to x.

Returns:

numpy.ndarray: Unitary Jones matrix diag(exp(-i phase/2), exp(+i phase/2)).

Raises:

PolarisationError: If the retardance is not finite.