prysm.x.polarization

Jones and Mueller Calculus

prysm.x.polarization.jones_rotation_matrix(theta, shape=None)

A rotation matrix for rotating the coordinate system transverse to propagation. source: https://en.wikipedia.org/wiki/Rotation_matrix.

Parameters:

• theta (float) – angle in radians to rotate the jones matrix with respect to the x-axis.

• shape (list) – shape to prepend to the jones matrix array. shape = [32,32] returns an array of shape [32,32,2,2] where the matrix is assumed to be in the last indices. Defaults to None, which returns a 2x2 array.

Returns:

2D rotation matrix

Return type:

numpy.ndarray

prysm.x.polarization.linear_retarder(retardance, theta=0, shape=None)

Generates a homogenous linear retarder jones matrix.

Parameters:

• retardance (float) – phase delay experienced by the slow state in radians.

• theta (float) – angle in radians the linear retarder is rotated with respect to the x-axis. Defaults to 0.

• shape (list) – shape to prepend to the jones matrix array. shape = [32,32] returns an array of shape [32,32,2,2] where the matrix is assumed to be in the last indices. Defaults to None, which returns a 2x2 array.

Returns:

retarder – numpy array containing the retarder matrices

Return type:

numpy.ndarray

prysm.x.polarization.linear_diattenuator(alpha, theta=0, shape=None)

Generates a homogenous linear diattenuator jones matrix.

Parameters:

• alpha (float) – Fraction of the light that passes through the partially transmitted channel. If 1, this is an unpolarizing plate. If 0, this is a perfect polarizer

• theta (float) – angle in radians the linear retarder is rotated with respect to the x-axis. Defaults to 0.

• shape (list) – shape to prepend to the jones matrix array. shape = [32,32] returns an array of shape [32,32,2,2] where the matrix is assumed to be in the last indices. Defaults to None, which returns a 2x2 array.

Returns:

diattenuator – numpy array containing the diattenuator matrices

Return type:

numpy.ndarray

prysm.x.polarization.half_wave_plate(theta=0, shape=None)

Make a half wave plate jones matrix. Just a wrapper for linear_retarder.

Parameters:

• theta (float) – angle in radians the linear retarder is rotated with respect to the x-axis. Defaults to 0.

• shape (list) – shape to prepend to the jones matrix array. shape = [32,32] returns an array of shape [32,32,2,2] where the matrix is assumed to be in the last indices. Defaults to None, which returns a 2x2 array.

Returns:

a linear retarder with half-wave retardance

Return type:

linear_retarder

prysm.x.polarization.quarter_wave_plate(theta=0, shape=None)

Make a quarter wave plate jones matrix. Just a wrapper for linear_retarder.

Parameters:

• theta (float) – angle in radians the linear retarder is rotated with respect to the x-axis. Defaults to 0.

• shape (list, optional) – shape to prepend to the jones matrix array. shape = [32,32] returns an array of shape [32,32,2,2] where the matrix is assumed to be in the last indices. Defaults to None, which returns a 2x2 array.

Returns:

a linear retarder with quarter-wave retardance

Return type:

linear_retarder

prysm.x.polarization.linear_polarizer(theta=0, shape=None)

Make a linear polarizer jones matrix. Just a wrapper for linear_diattenuator.

Returns:

• theta (float) – angle in radians the linear retarder is rotated with respect to the x-axis. Defaults to 0.

• shape (list) – shape to prepend to the jones matrix array. shape = [32,32] returns an array of shape [32,32,2,2] where the matrix is assumed to be in the last indices. Defaults to None, which returns a 2x2 array.

Returns:

a linear diattenuator with unit diattenuation

Return type:

linear_diattenuator

prysm.x.polarization.jones_to_mueller(jones)

Construct a Mueller Matrix given a Jones Matrix. From Chipman, Lam, and Young Eq (6.99).

Parameters:

jones (ndarray with final dimensions 2x2) – The complex-valued jones matrices to convert into mueller matrices

Returns:

M – Mueller matrix

Return type:

np.ndarray

prysm.x.polarization.pauli_spin_matrix(index, shape=None)

Generates a pauli spin matrix used for Jones matrix data reduction. From CLY Eq 6.108.

Parameters:

• index (int) – 0 - the identity matrix 1 - a linear half-wave retarder oriented horizontally 2 - a linear half-wave retarder oriented 45 degrees 3 - a circular half-wave retarder

• shape (list, optional) – shape to prepend to the jones matrix array. shape = [32,32] returns an array of shape [32,32,2,2] where the matrix is assumed to be in the last indices. Default returns a 2x2 array

Returns:

pauli spin matrix of index specified

Return type:

jones

prysm.x.polarization.pauli_coefficients(jones)

Compute the pauli coefficients of a jones matrix.

Parameters:

jones (numpy.ndarray) – complex jones matrix to decompose

Returns:

complex coefficients of pauli matrices

Return type:

c0,c1,c2,c3