dtmm.jones

Jones calculus functions. You can use this module for simple normal incidence jones calculus.

2x2 matrices

• jonesvec() : jones vector

• mirror() : mirror matrix

• polarizer() : polarizer matrix

• retarder() : retarder matrix

• quarter_waveplate() : quarter-wave plate matrix

• half_waveplate() : half-wave plate matrix

• circular_polarizer() : circular polarizer matrix

• linear_polarizer() : linear polarizer matrix

Conversion functions

• as4x4() : convert to 4x4 matrix for (…,4) field vector.

• rotated_matrix() : to view the matrix in rotated frame.

Examples

>>> j_in = jonesvec((1,1)) #input light polarized at 45
>>> r = retarder(0.2,0.4)
>>> p = linear_polarizer((1,0)) # x polarization
>>> c = circular_polarizer(+1) # left handed
>>> m = multi_dot([r,p,c])
>>> j_out = dotmv(m,j_in) #output light E field
>>> i = jones_intensity(j_out) #intensity

Module Contents

dtmm.jones.jones_intensity(jones)

Computes intensity of the jones vector

Parameters

jones ((..,2) array) – Jones vector.

Returns

intensity – Computed intensity.

Return type

(..) float array

dtmm.jones.jonesvec(pol, phi=0.0, out=None)

Returns a normalized jones vector from an input length 2 vector., Additionaly, you can use this function to view the jones vector in rotated coordinate frame, defined with a rotation angle phi.

Numpy broadcasting rules apply.

Parameters

• pol ((..,2) array) – Input jones vector. Does not need to be normalized.

• phi (float or (..,1) array) – If jones vector must be view in the rotated frame, this parameter defines the rotation angle.

• out (ndarray) – Output array in which to put the result; if provided, it must have a shape that the inputs broadcast to.

Returns

vec – Normalized jones vector

Return type

ndarray

Example

>>> jonesvec((1,1j)) #left-handed circuar polarization
array([0.70710678+0.j        , 0.        +0.70710678j])

In rotated frame

>>> j1,j2 = jonesvec((1,1j), (np.pi/2,np.pi/4))
>>> np.allclose(j1, (0.70710678j,-0.70710678))
True
>>> np.allclose(j2, (0.5+0.5j,-0.5+0.5j))
True

dtmm.jones.mirror(out=None)

Returns jones mirror matrix.

Parameters

out (ndarray, optional) – Output array in which to put the result; if provided, it must have a shape that the inputs broadcast to.

Returns

mat – Output jones matrix.

Return type

ndarray

dtmm.jones.retarder(phase, phi=0.0, out=None)

Returns jones matrix of general phase retarder

Numpy broadcasting rules apply.

Parameters

• phase (float or array) – Phase difference between the fast and slow axis of the retarder.

• phi (float or array) – Fast axis orientation

• out (ndarray, optional) – Output array in which to put the result; if provided, it must have a shape that the inputs broadcast to.

Returns

mat – Output jones matrix.

Return type

ndarray

dtmm.jones.quarter_waveplate(phi=0.0, out=None)

Returns jones quarter-wave plate matrix.

Numpy broadcasting rules apply.

Parameters

• phi (float or array) – Fast axis orientation

• out (ndarray, optional) – Output array in which to put the result; if provided, it must have a shape that the inputs broadcast to.

Returns

mat – Output jones matrix.

Return type

ndarray

dtmm.jones.half_waveplate(phi=0.0, out=None)

Returns jones half-wave plate matrix.

Numpy broadcasting rules apply.

Parameters

• phi (float or array) – Fast axis orientation

• out (ndarray, optional) – Output array in which to put the result; if provided, it must have a shape that the inputs broadcast to.

Returns

mat – Output jones matrix.

Return type

ndarray

dtmm.jones.polarizer(jones, out=None)

Returns jones polarizer matrix.

Numpy broadcasting rules apply.

Parameters

• jones ((..,2) array) – Input normalized jones vector. Use jonesvec() to generate jones vector

• out (ndarray, optional) – Output array in which to put the result; if provided, it must have a shape that the inputs broadcast to.

Returns

mat – Output jones matrix.

Return type

ndarray

Examples

>>> pmat = polarizer(jonesvec((1,1))) #45 degree linear polarizer
>>> np.allclose(pmat, linear_polarizer(np.pi/4)+0j )
True
>>> pmat = polarizer(jonesvec((1,-1))) #-45 degree linear polarizer
>>> np.allclose(pmat, linear_polarizer(-np.pi/4)+0j )
True
>>> pmat = polarizer(jonesvec((1,1j))) #left handed circular polarizer
>>> np.allclose(pmat, circular_polarizer(1) )
True

dtmm.jones.linear_polarizer(angle, out=None)

Return jones matrix for a polarizer.

Numpy broadcasting rules apply.

Parameters

• angle (float or array) – Orientation of the polarizer.

• out (ndarray, optional) – Output array in which to put the result; if provided, it must have a shape that the inputs broadcast to.

Returns

mat – Output jones matrix.

Return type

ndarray

dtmm.jones.circular_polarizer(hand, out=None)

Returns circular polarizer matrix.

Numpy broadcasting rules apply.

Parameters

• hand (int or (..,1) array) – Handedness +1 (left-hand) or -1 (right-hand).

• out (ndarray, optional) – Output array in which to put the result; if provided, it must have a shape that the inputs broadcast to.

Returns

mat – Output jones matrix.

Return type

ndarray

dtmm.jones.rotated_matrix(jmat, phi)

jones matrix viewed in the rotated frame, where phi is the rotation angle

Performs (R.T).jmat.R where R is the rotation matrix.

Numpy broadcasting rules apply.

Parameters

• jmat ((..,2,2) array) – Jones matrix

• phi (float) – Rotation angle.

Returns

out – Rotated jones matrix.

Return type

(..,2,2) array

dtmm.jones.as4x4(jmat, out=None)

Converts jones 2x2 matrix to eigenfield 4x4 matrix.

Parameters

• jmat ((..,2,2) array) – Jones matrix

• out (ndarray, optional) – Output array in which to put the result; if provided, it must have a shape that the inputs broadcast to.

Returns

mat – Output jones matrix.

Return type

(..,4,4) ndarray