function [psr_rad]=faraday_vs_B(detuning_freq, Ep, psi_el, B_fields, 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

%tune probe frequency
detuning_p=0;
N_steps=length(B_fields)
kappa_p      =zeros(1,N_steps+1);
kappa_m      =zeros(1,N_steps+1);
xi_linear=zeros(1,N_steps);
xi_left  =zeros(1,N_steps);
xi_right =zeros(1,N_steps);

% load useful functions;
useful_functions;

% some physical constants
useful_constants;

basis_transformation; % load subroutines

fprintf (stderr, "tuning laser in forloop to set conditions vs detuning\n");
fflush (stderr);
for B_field_cntr=1:N_steps;
	B_field=B_fields(B_field_cntr)

	% load atom energy levels and decay description
	rb87_D1_line;


	fprintf (stderr, "calculating atom properties\n");
	fflush (stderr);
	pfile='atomic_B_field.mat'; % the parent file where B_field is stored. This is the parameter for calculated L0_and_polarization_submatrices 
	cfile='L0m_and_polarizability_calculated.mat'; % the child  file to which calculated matrices are  written 
	need_update=false;
	[s, err_p, msg] = stat (pfile); 
	if(err_p)
		%file does not exist
		need_update=true;
	else
		B_field_cur=B_field;
		load (pfile); % loading old B_field value
		if (B_field ~= B_field_cur)
			% old and current B field are different
			B_field=B_field_cur;
			need_update=true;
		else
			need_update=false;
		endif
	endif

	[s, err, msg] = stat (cfile); 
	if(err) 
		%file does not exist
		need_update=true; 
	endif; 

	if ( !need_update)
		% matrices already calculated and up to date, all we need to load them
		load(cfile);
	else
		% 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 ...
		);
		save(pfile, 'B_field');
		save(cfile, 'L0m', 'polarizability_m');
	endif

	elapsed_time = etime (clock (), t0);
	fprintf (stderr, "elapsed time so far is %.3f sec\n",elapsed_time);
	fflush (stderr);

	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; 

	% 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;
	% psi_el is the ellipticity parameter (phase difference between left and right polarization)
	%psi_el=-30/180*pi;

	% 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;
	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;
	
save '/tmp/problem_definition.mat' problems_cell_array atom_properties  detuning_freq ;
fprintf (stderr, "now really hard calculations begin\n");
fflush (stderr);
	[xi_linear_i, xi_left_i, xi_right_i]=susceptibility_steady_state_at_freq( problems_cell_array);
	%[xi_linear, xi_left, xi_right]=cellfun( @susceptibility_steady_state_at_freq, problems_cell_array);
	xi_left(B_field_cntr)=xi_left_i;
	xi_right(B_field_cntr)=xi_right_i;
	xi_linear(B_field_cntr)=xi_linear_i;

endfor

save '/tmp/xi_vs_B.mat' detuning_freq xi_linear xi_left xi_right  E_field_pos_freq E_field_probe B_fields psi_el;

psr_rad=output_faraday_results_vs_B;

elapsed_time = etime (clock (), t0)
return

% vim: ts=2:sw=2:fdm=indent