psfsim.polarisation_decomposition

Functions to handle decomposition of (un)polarised E fields into TE and TM modes and rotation of E field components from local coordinates to focal plane coordinates.

Functions

`local_to_fpa_rotation`(ux, uy, sgn)	Local --> FPA rotation for electric field.
`polarisation_mode_decomposition`(ux, uy, E, sgn)	Decomposes incident electric field (specified by components along FPA axes) into TE and TM modes.
`unpolarised_mode_decomposition`(ux, uy[, E0])	Decomposition for unpolarized light.

Module Contents

local_to_fpa_rotation(ux, uy, sgn)[source]

Local –> FPA rotation for electric field.

This constructs an array of 3x3 rotation matrices from {incident ray in yz-plane} –> {focal plane coordinates}. The z-axis is perpendicular to the detector surface in both cases.

By construction, this function has a discontinuity at u=0. It defaults to 0 for unphysical rays (ux, uy outside the unit circule).

Parameters:

ux (np.ndarray of float) – Orthographic projection of ray directions (each component). Should be the same shape.
uy (np.ndarray of float) – Orthographic projection of ray directions (each component). Should be the same shape.
sgn (float) – Whether to flip z-direction for diagonal rays; should be +1 or -1.

Returns:

RT – Shape is shape of ux + (3, 3). Each entry ends in a rotation matrix.

Return type:

np.ndarray of float

polarisation_mode_decomposition(ux, uy, E, sgn)[source]

Decomposes incident electric field (specified by components along FPA axes) into TE and TM modes.

The convention is that the “TE” (S) direction is given by {propagation of ray} cross {original z axis} and the “TM” (P) direction is in the plane of incidence, pointed toward sgn * {original z axis}.

Parameters:

ux (np.ndarray of float) – The orthographic projection of directions of propagation, each is an array.
uy (np.ndarray of float) – The orthographic projection of directions of propagation, each is an array.
E (np.ndarray of complex) – The incident electric field. Same shape as ux.shape + (3,).
sgn (float) – Whether the z-direction of the initial coordinate system should be the same (+1) or opposite (-1) the AR coating coordinate system.

Returns:

The keys are “TE” and “TM”, and each have the same shape as ux and uy.

Return type:

dict of np.ndarray of complex