proper polarization rotation transformation for positive frequencies

2 files changed, 45 insertions, 14 deletions

diff --git a/basis_transformation.m b/basis_transformation.m
index 179e333..82945fe 100644
--- a/basis_transformation.m
+++ b/basis_transformation.m
@@ -2,20 +2,26 @@
 
 % matrix of circular to linear transformation
 % [x, y, z]' = lin2circ * [r, l, z]'
-circ2lin= [ ...
-		[  1/sqrt(2),  1/sqrt(2), 0]; ...
-  	[-1i/sqrt(2), 1i/sqrt(2), 0]; ...
-		[          0,          0, 1] ...
-	];
+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]'
-lin2circ= [
-		[  1/sqrt(2),  1i/sqrt(2), 0]; ...
-  	[  1/sqrt(2), -1i/sqrt(2), 0]; ...
-		[          0,          0,  1] ...
-	];
-
+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
@@ -30,10 +36,22 @@ 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, modulation_freq) 
+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*sign(modulation_freq)).*E_field_linear;
-	E_field_y=sin(phi*sign(modulation_freq)).*E_field_linear;
+	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
diff --git a/useful_functions.m b/useful_functions.m
index 2eef299..e675ba1 100644
--- a/useful_functions.m
+++ b/useful_functions.m
@@ -307,5 +307,18 @@ function total_absorption=total_field_absorption(atom_field_problem)
 	total_absorption=sum(total_absorption_v);
 endfunction
 
+% create full list of atom modulation frequencies from positive light frequency amplitudes
+function [modulation_freq, E_field_amplitudes] = ...
+light_positive_frequencies_and_amplitudes2full_set_of_modulation_frequencies_and_amlitudes(...
+	positive_light_frequencies, positive_light_field_amplitudes )
+	% we should add 0 frequency as first element of our frequencies list
+	modulation_freq    = cat(2, 0, positive_light_frequencies, -positive_light_frequencies);
+	% negative frequencies have complex conjugated light fields amplitudes
+	E_field_amplitudes.left = cat(2, 0, positive_light_field_amplitudes.left, conj(positive_light_field_amplitudes.left) );
+	E_field_amplitudes.right = cat(2, 0, positive_light_field_amplitudes.right, conj(positive_light_field_amplitudes.right) );
+	E_field_amplitudes.linear = cat(2, 0, positive_light_field_amplitudes.linear, conj(positive_light_field_amplitudes.linear) );
+endfunction	
+
+
 
 % vim: ts=2:sw=2:fdm=indent