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Diffstat (limited to 'psr/basis_transformation.m')
| -rw-r--r-- | psr/basis_transformation.m | 57 |
1 files changed, 57 insertions, 0 deletions
diff --git a/psr/basis_transformation.m b/psr/basis_transformation.m new file mode 100644 index 0000000..82945fe --- /dev/null +++ b/psr/basis_transformation.m @@ -0,0 +1,57 @@ +1; + +% matrix of circular to linear transformation +% [x, y, z]' = lin2circ * [r, l, z]' +function transformation_matrix = circ2lin() + transformation_matrix = ... + [ ... + [ 1/sqrt(2), 1/sqrt(2), 0]; ... + [-1i/sqrt(2), 1i/sqrt(2), 0]; ... + [ 0, 0, 1] ... + ]; +endfunction + + +% matrix of linear to circular transformation +% [r, l, z]' = lin2circ * [x, y, z]' +function transformation_matrix = lin2circ() + transformation_matrix = ... + [ ... + [ 1/sqrt(2), 1i/sqrt(2), 0]; ... + [ 1/sqrt(2), -1i/sqrt(2), 0]; ... + [ 0, 0, 1] ... + ]; +endfunction +% linear basis rotation +% x axis untouched +% z and y rotated by angle theta around 'x' axis +% [x_new, y_new, z_new]' = oldlin2newlin * [x_old, y_old, z_old]' +function oldlin2newlin_m = oldlin2newlin(theta) + oldlin2newlin_m = [ ... + [ 1, 0, 0]; ... + [ 0, cos(theta), -sin(theta)]; ... + [ 0, sin(theta), cos(theta)]... + ]; +endfunction + +% rotate x polarized light by angle phi around +% light propagation axis (Z) +function [E_field_x, E_field_y] = rotXpolarization(phi, E_field_linear) + % important negative frequency behave as they rotate in opposite direction + E_field_x=cos(phi)*E_field_linear; + E_field_y=sin(phi)*E_field_linear; +endfunction + +% transform x,y,z linearly polarized light in the lab/light system coordinate +% to left, right, linear along z atom system of coordinate +% atom magnetic field is along new axis Z wich is at angle theta with respect to +% light propagation direction +function E_field_pos_freq=xyz_lin2atomic_axis_polarization(theta, E_field_lab_pos_freq) + coord_transf_m = lin2circ() * oldlin2newlin(theta); + E_field_pos_freq.right = coord_transf_m(1,1)*E_field_lab_pos_freq.x + coord_transf_m(1,2)*E_field_lab_pos_freq.y + coord_transf_m(1,3)*E_field_lab_pos_freq.z; + E_field_pos_freq.left = coord_transf_m(2,1)*E_field_lab_pos_freq.x + coord_transf_m(2,2)*E_field_lab_pos_freq.y + coord_transf_m(2,3)*E_field_lab_pos_freq.z; + E_field_pos_freq.linear = coord_transf_m(3,1)*E_field_lab_pos_freq.x + coord_transf_m(3,2)*E_field_lab_pos_freq.y + coord_transf_m(3,3)*E_field_lab_pos_freq.z; +endfunction + + +% vim: ts=2:sw=2:fdm=indent |