proper use of rotation transformation for light polarizations

2 files changed, 42 insertions, 38 deletions

diff --git a/compass.m b/compass.m
index d7617ea..1eeda9f 100644
--- a/compass.m
+++ b/compass.m
@@ -12,10 +12,10 @@ useful_constants;
 basis_transformation; % load subroutines
 
 % load atom energy levels and decay description
-%rb87_D1_line;
+rb87_D1_line;
 %four_levels_with_polarization;
 %four_levels;
-three_levels;
+%three_levels;
 %two_levels;
 
 % load EM field description
@@ -55,19 +55,20 @@ atom_properties.dipole_elements=dipole_elements;
 Ed=.1;     Edc=conj(Ed);
 Ep=0.8*Ed;  Epc=conj(Ep);
 
-%modulation_freq=[0,  wp, wd, -wp, -wd,  wp-wd, wd-wp];
-E_field_drive   =[0,  0 , Ed,  0  , Edc, 0,     0    ];
-E_field_probe   =[0,  Ep, 0 ,  Epc, 0  , 0,     0    ];
-E_field_zero    =[0,  0 , 0 ,  0  , 0  , 0,     0    ];
-E_field_lab.linear = E_field_zero + (1.00000+0.00000i)*E_field_probe  + (1.00000+0.00000i)*E_field_drive; 
-E_field_lab.right  = E_field_zero + (0.00000+0.00000i)*E_field_probe  + (0.00000+0.00000i)*E_field_drive;
-E_field_lab.left   = E_field_zero + (0.00000+0.00000i)*E_field_probe  + (0.00000+0.00000i)*E_field_drive;
+%light_positive_freq  = [wp, wd,  wp-wd];
+E_field_drive         = [0 , Ed,  0    ];
+E_field_probe         = [Ep, 0 ,  0    ];
+E_field_zero          = [0 , 0 ,  0    ];
+E_field_lab_pos_freq.linear = E_field_zero + (1.00000+0.00000i)*E_field_probe  + (1.00000+0.00000i)*E_field_drive; 
+%E_field_lab_pos_freq.right  = E_field_zero + (0.00000+0.00000i)*E_field_probe  + (0.00000+0.00000i)*E_field_drive;
+%E_field_lab_pos_freq.left   = E_field_zero + (0.00000+0.00000i)*E_field_probe  + (0.00000+0.00000i)*E_field_drive;
+
 
 % phi is angle between linear polarization and axis x
 phi=pi*2/8;
 % theta is angle between lab z axis (light propagation direction) and magnetic field axis (z')
+theta=0/4;
 theta=pi/2;
-theta=pi/4;
 
 
 
@@ -89,17 +90,21 @@ for phi=phis;
 			detuning_p=detuning_freq(detuning_p_cntr);
 			wp=wp0+detuning_p;
 			wm=wd-(wp-wd);
-			%modulation_freq=[0,  wp, wd, wm,   -wp, -wd, -wm,  wp-wd, wd-wp];
-			modulation_freq=[0,  wp, wd, -wp,   -wd,  wp-wd, wd-wp];
+
+		light_positive_freq=[ wp, wd, wp-wd];
 		% we define light as linearly polarized 
 		% where phi is angle between light polarization and axis x
-		[E_field_lab.x, E_field_lab.y] = rotXpolarization(phi, E_field_lab.linear, modulation_freq);
-		E_field_lab.z=E_field_zero;
+		[E_field_lab_pos_freq.x, E_field_lab_pos_freq.y] = rotXpolarization(phi, E_field_lab_pos_freq.linear);
+		E_field_lab_pos_freq.z=E_field_zero;
+
 		% now we transfor x,y,z, to x',y', and z' with respect to magnetic field az z' axis
-		coord_transf_m =  lin2circ * oldlin2newlin(theta);
-		E_field.right  = coord_transf_m(1,1)*E_field_lab.x + coord_transf_m(1,2)*E_field_lab.y + coord_transf_m(1,3)*E_field_lab.z;
-		E_field.left   = coord_transf_m(2,1)*E_field_lab.x + coord_transf_m(2,2)*E_field_lab.y + coord_transf_m(2,3)*E_field_lab.z;
-		E_field.linear = coord_transf_m(3,1)*E_field_lab.x + coord_transf_m(3,2)*E_field_lab.y + coord_transf_m(3,3)*E_field_lab.z;
+		E_field_pos_freq=xyz_lin2atomic_axis_polarization(theta, E_field_lab_pos_freq);
+
+		% we calculate dc and negative frequiencies as well as amplitudes
+		[modulation_freq, E_field] = ...
+			light_positive_frequencies_and_amplitudes2full_set_of_modulation_frequencies_and_amlitudes(...
+				light_positive_freq, E_field_pos_freq);
+
 			freq_index=freq2index(wp,modulation_freq);
 
 			atom_field_problem.E_field          = E_field;
diff --git a/liouville.m b/liouville.m
index 10ccc95..53a84ef 100644
--- a/liouville.m
+++ b/liouville.m
@@ -12,10 +12,10 @@ useful_constants;
 basis_transformation; % load subroutines
 
 % load atom energy levels and decay description
-%rb87_D1_line;
+rb87_D1_line;
 %four_levels_with_polarization;
 %four_levels;
-three_levels;
+%three_levels;
 %two_levels;
 
 % load EM field description
@@ -27,7 +27,7 @@ field_description;
 
 %tune probe frequency
 detuning_p=0;
-N_detun_steps=200;
+N_detun_steps=100;
 %detuning_p_min=-B_field*gmg*4; % span  +/-4 Zeeman splitting
 detuning_p_min=-0.1;
 detuning_p_max=-detuning_p_min;
@@ -53,32 +53,28 @@ atom_properties.L0m=L0m;
 atom_properties.polarizability_m=polarizability_m;
 atom_properties.dipole_elements=dipole_elements;
 
-%modulation_freq=[0,  wp, wd, -wp, -wd,  wp-wd, wd-wp];
-E_field_drive   =[0,  0 , Ed,  0  , Edc, 0,     0    ];
-E_field_probe   =[0,  Ep, 0 ,  Epc, 0  , 0,     0    ];
-E_field_zero    =[0,  0 , 0 ,  0  , 0  , 0,     0    ];
-E_field_lab.linear = E_field_zero + (1.00000+0.00000i)*E_field_probe  + (1.00000+0.00000i)*E_field_drive; 
-E_field_lab.right  = E_field_zero + (0.00000+0.00000i)*E_field_probe  + (0.00000+0.00000i)*E_field_drive;
-E_field_lab.left   = E_field_zero + (0.00000+0.00000i)*E_field_probe  + (0.00000+0.00000i)*E_field_drive;
+%light_positive_freq  = [wp, wd,  wp-wd];
+E_field_drive         = [0 , Ed,  0    ];
+E_field_probe         = [Ep, 0 ,  0    ];
+E_field_zero          = [0 , 0 ,  0    ];
+E_field_lab_pos_freq.linear = E_field_zero + (1.00000+0.00000i)*E_field_probe  + (1.00000+0.00000i)*E_field_drive; 
+%E_field_lab_pos_freq.right  = E_field_zero + (0.00000+0.00000i)*E_field_probe  + (0.00000+0.00000i)*E_field_drive;
+%E_field_lab_pos_freq.left   = E_field_zero + (0.00000+0.00000i)*E_field_probe  + (0.00000+0.00000i)*E_field_drive;
 
 % phi is angle between linear polarization and axis x
 phi=pi*2/8;
 % theta is angle between lab z axis (light propagation direction) and magnetic field axis (z')
-theta=0/2;
+theta=pi/2;
 phi=pi/4;
 
 % we define light as linearly polarized 
 % where phi is angle between light polarization and axis x
 	% only sign of modulation frequency is important now
 	% we define actual frequency later on
-	modulation_freq=[0,  1, 1, -1,   -1,  1, -1];
-		[E_field_lab.x, E_field_lab.y] = rotXpolarization(phi, E_field_lab.linear, modulation_freq);
-E_field_lab.z=E_field_zero;
+	[E_field_lab_pos_freq.x, E_field_lab_pos_freq.y] = rotXpolarization(phi, E_field_lab_pos_freq.linear);
+	E_field_lab_pos_freq.z=E_field_zero;
 
-coord_transf_m =  lin2circ * oldlin2newlin(theta);
-E_field.right  = coord_transf_m(1,1)*E_field_lab.x + coord_transf_m(1,2)*E_field_lab.y + coord_transf_m(1,3)*E_field_lab.z;
-E_field.left   = coord_transf_m(2,1)*E_field_lab.x + coord_transf_m(2,2)*E_field_lab.y + coord_transf_m(2,3)*E_field_lab.z;
-E_field.linear = coord_transf_m(3,1)*E_field_lab.x + coord_transf_m(3,2)*E_field_lab.y + coord_transf_m(3,3)*E_field_lab.z;
+	E_field_pos_freq=xyz_lin2atomic_axis_polarization(theta, E_field_lab_pos_freq);
 
 
 fprintf (stderr, "tuning laser in forloop to set conditions vs detuning\n");
@@ -89,8 +85,11 @@ for detuning_p_cntr=1:N_detun_steps+1;
 	detuning_p=detuning_p_min+detun_step*(detuning_p_cntr-1);
 	wp=wp0+detuning_p;
 	wm=wd-(wp-wd);
-	%modulation_freq=[0,  wp, wd, wm,   -wp, -wd, -wm,  wp-wd, wd-wp];
-	modulation_freq=[0,  wp, wd, -wp,   -wd,  wp-wd, wd-wp];
+	light_positive_freq=[ wp, wd, wp-wd];
+	% we calculate dc and negative frequiencies as well as amplitudes
+	[modulation_freq, E_field] = ...
+		light_positive_frequencies_and_amplitudes2full_set_of_modulation_frequencies_and_amlitudes(...
+			light_positive_freq, E_field_pos_freq);
 	freq_index=freq2index(wp,modulation_freq);
 
 	atom_field_problem.E_field          = E_field;