function [xi_linear, xi_left, xi_right]=propagation_problem(detuning_freq, Ep, psi_el, B_field, theta, phi) 
% calculates transmission  if light polarizations  vs B field in the cell
% for given laser probe and B fields array
% Probe field defined by field strength (Ep) and ellipticity angle (pse_el)
% Magnetic field defined by magnitude (B_field) and angles theta and phi. 
%
% Note: it is expensive to recalculate atom property for each given B_field strength
% so run as many calculation for constant magnetic field as possible

t0 = clock (); % we will use this latter to calculate elapsed time


% load useful functions;
useful_functions;

% some physical constants
useful_constants;

basis_transformation; % load subroutines


% load atom energy levels and decay description
rb87_D1_line;

% calculate E_field independent properties of the atom
% to be used as sub matrix templates for Liouville operator matrix
[L0m, polarizability_m]=L0_and_polarization_submatrices( ...
Nlevels, ...
H0, g_decay, g_dephasing, dipole_elements ...
);

global atom_properties;
atom_properties.L0m=L0m;
atom_properties.polarizability_m=polarizability_m;
atom_properties.dipole_elements=dipole_elements;

%light_positive_freq  = [wp];
E_field_drive         = [0    ];
E_field_probe         = [Ep   ];
E_field_zero          = [0    ];
E_field_lab_pos_freq.linear = E_field_zero + (1.00000+0.00000i)*E_field_probe  + (1.00000+0.00000i)*E_field_drive; 

% 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
[E_field_lab_pos_freq.x, E_field_lab_pos_freq.y] = rotXpolarization(phi, E_field_lab_pos_freq.linear);
% we add required ellipticity
E_field_lab_pos_freq.x*=exp(I*psi_el);
E_field_lab_pos_freq.y*=exp(-I*psi_el);
E_field_lab_pos_freq.z=E_field_zero;

E_field_pos_freq=xyz_lin2atomic_axis_polarization(theta, E_field_lab_pos_freq);


wp0=w_pf1-w_sf2;  %Fg=2 -> Fe=1
wp=wp0+detuning_freq;
light_positive_freq=[ wp];
% we calculate dc and negative frequencies 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;
atom_field_problem.modulation_freq  = modulation_freq;
atom_field_problem.freq_index       = freq_index;

problems_cell_array=atom_field_problem;

[xi_linear, xi_left, xi_right]=susceptibility_steady_state_at_freq( problems_cell_array);


elapsed_time = etime (clock (), t0)
return

endfunction

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