% illustrating the concept of polarization of plane wave

% parameters of x,y components of plane wave's amplitude
a1=1; d1=0; 
a2=1; d2=-pi/4; 

%calculating the amplitudes and frequency
ax=a1*exp(1i*d1); 
ay=a2*exp(1i*d2); 
omg=1; 

%setting up time array
tPts=100; 
tArr=linspace(0,2*pi/omg,tPts+1);

%setting up coordinate grid to plot the vector field 
xArr=(-6:2:6); 
[x,y]=meshgrid(xArr,xArr); 

% assembling the movie
fig=figure(1);
F(tPts)=struct('cdata',[],'colormap',[]); 
for it=1:tPts
    t=tArr(it); 
    phs=exp(-1i*omg*t+0i*x+0i*y); %phase of the wave
    quiver(x,y, real(ax*phs),real(ay*phs),0, 'linewidth',2)

    xlim(7.5*[-1 1])
    ylim(7.5*[-1 1])
    daspect([1 1 1])
    title(['S_0=',num2str(a1^2+a2^2,3),...
        '; S_1=', num2str(a1^2-a2^2,3),...
        '; S_3=', num2str(2*a1*a2*cos(d2-d1),3),...
        '; S_4=', num2str(2*a1*a2*sin(d2-d1),3)]) 

    set(gca,'FontSize',16)
    set(gca,'xtick',[],'ytick',[]) 
    xlabel('x'); ylabel('y')
    box on 
    drawnow
    F(it)=getframe(gcf); 
end 

%playing the movie
% movie(fig,F,2)