Nlevels_with_doppler_with_z_4wm

%% field propagation
z_1=z_1*100; % z in cm
t_1=t_1*1e6; % time now measured in uS
figure(1)
subplot(2,2,1); imagesc(z_1, t_1, I1_out_1); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('I_1')
title('I_1')
subplot(2,2,2); imagesc(z_1, t_1, I2_out_1); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('I_2')
title('I_2')
subplot(2,2,3); imagesc(z_1, t_1, I3_out_1); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('I_3')
title('I_3')
subplot(2,2,4); imagesc(z_1, t_1, I4_out_1); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('I_4')
title('I_4')


print('-color','fields_propagation.eps')



%% fields before and after the cell
figure(2)
subplot(2,2,1);
plot( ...
	t_1,I1_out_1(:,1),'-;before;', "linewidth", 4,  ...
	t_1,I1_out_1(:,end), '-;after;', "linewidth", 4 ...
	)
xlabel('t (uS)')
ylabel('I_1 (1/s)^2')
title('I_1 before and after cell')
subplot(2,2,2);
plot( ...
	t_1,I2_out_1(:,1),'-;before;', "linewidth", 4,  ...
	t_1,I2_out_1(:,end), '-;after;', "linewidth", 4 ...
	)
xlabel('t (uS)')
ylabel('I_2 (1/s)^2')
title('I_2 before and after cell')
subplot(2,2,3);
plot( ...
	t_1,I3_out_1(:,1),'-;before;', "linewidth", 4,  ...
	t_1,I3_out_1(:,end), '-;after;', "linewidth", 4 ...
	)
xlabel('t (uS)')
ylabel('I_3 (1/s)^2')
title('I_3 before and after cell')

[b, a]=butter(3, 0.05);
I2_out_after=I2_out_1(:,end);
I2_out_after_filtered=filtfilt(b,a,I2_out_after);
settling_time=0.8; %uS
t_good_indx=t_1> min(t_1 + settling_time);
[m,max_pos_before]=max(I2_out_1(t_good_indx,1) ); [m,max_pos_after]=max(I2_out_after_filtered(t_good_indx));
delay_time=t_1(max_pos_after)-t_1(max_pos_before);
printf('Second field delay time  = %f uS\n',delay_time);

print('-color','fields_before_after_cell.eps')

subplot(2,2,4);
plot( ...
	t_1,I4_out_1(:,1),'-;before;', "linewidth", 4,  ...
	t_1,I4_out_1(:,end), '-;after;', "linewidth", 4 ...
	)
xlabel('t (uS)')
ylabel('I_3 (1/s)^2')
title('I_3 before and after cell')

figure(4)
I2_max_in=max(I2_out_1(t_good_indx,1));
I2_max_out=max(I2_out_1(t_good_indx,end));
I2_in_norm=(I2_out_1(:,1))/I2_max_in;
I2_out_norm=(I2_out_1(:,end))/I2_max_out;
tmin=-0.05;
tmax=0.05;
indx=(t_1>=tmin & t_1<=tmax);  % soom in in time to this region
plot( ...
	t_1(indx),I2_in_norm(indx),'-;before;', "linewidth", 4,  ...
	t_1(indx),I2_out_norm(indx), '-;after;', "linewidth", 4 ...
	)
xlim([tmin,tmax],'manual');	
xlabel('t (uS)')
ylabel('I_2')
title('I_2 before and after cell normalized')
print('-color','probe_before_after_cell.eps')

return;

%% all density matrix elements in one plot
% diagonal populations, 
% upper triangle real part of coherences, 
% lower diagonal imaginary part of coherences
z_2=z_2*100; % z in cm
t_2=t_2*1e6; % time now measured in uS
figure(3)
subplot(4,4,1); imagesc (z_2, t_2, r11_out_2);  caxis([0,1]); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('rho_{11}')
title('rho_{11}')
subplot(4,4,6); imagesc (z_2, t_2, r22_out_2);  caxis([0,1]); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('rho_{22}')
title('rho_{22}')
subplot(4,4,11); imagesc (z_2, t_2, r33_out_2);  caxis([0,1]); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('rho_{33}')
title('rho_{33}')
subplot(4,4,16); imagesc (z_2, t_2, r44_out_2); caxis([0,1]);  colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('rho_{44}')
title('rho_{44}')
% real parts of coherences
subplot(4,4,2); imagesc(z_2, t_2, r12_re_out_2); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('Real(rho_{12})')
title('Real(rho_{12})')
subplot(4,4,3); imagesc(z_2, t_2, r13_re_out_2); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('Real(rho_{13})')
title('Real(rho_{13})')
subplot(4,4,4); imagesc(z_2, t_2, r14_re_out_2); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('Real(rho_{14})')
title('Real(rho_{14})')
subplot(4,4,7); imagesc(z_2, t_2, r23_re_out_2); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('Real(rho_{23})')
title('Real(rho_{23})')
subplot(4,4,8); imagesc(z_2, t_2, r24_re_out_2); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('Real(rho_{24})')
title('Real(rho_{24})')
subplot(4,4,12); imagesc(z_2, t_2, r34_re_out_2); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('Real(rho_{34})')
title('Real(rho_{34})')
% imaginary parts of coherences
subplot(4,4,5); imagesc(z_2, t_2, r12_im_out_2); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('Imag(rho_{12})')
title('Imag(rho_{12})')
subplot(4,4,9); imagesc(z_2, t_2, r13_im_out_2); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('Imag(rho_{13})')
title('Imag(rho_{13})')
subplot(4,4,10); imagesc(z_2, t_2, r23_im_out_2); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('Imag(rho_{23})')
title('Imag(rho_{23})')
subplot(4,4,13); imagesc(z_2, t_2, r14_im_out_2); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('Imag(rho_{14})')
title('Imag(rho_{14})')
subplot(4,4,14); imagesc(z_2, t_2, r24_im_out_2); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('Imag(rho_{24})')
title('Imag(rho_{24})')
subplot(4,4,15); imagesc(z_2, t_2, r34_im_out_2); colorbar
xlabel('z (cm)')
ylabel('t (uS)')
zlabel('Imag(rho_{34})')
title('Imag(rho_{34})')