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exercise 1.3

ZIP with MATLAB scripts and note:

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 example 1.1 notes:

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syms A B a b E0

% Left Hand Circular Polarization
E_LHCP=A*[1 -1j 0]          % phasors for [nx ny nz]
                                         % nx ny nz normal base

% Right Hand Circular Polarization

E0_RHCP=B*[1 1j 0] 

[a b 0]  % phasor amplitude of arbitrary plane wave

eq1=a==1/E0*(A+B)
eq2=b==1/E0*(-1j*A+1j*B)

%%


clear A B a b E0
syms A B a b E0
eqns = [1/E0*(A+B)==a,1/E0*(-1j*A+1j*B)==b];
S = solve(eqns,A,B);
sol = [S.A; S.B ]



[S2,y] = equationsToMatrix(eqns,a,b)





z = S2\y
 
E_LHCP =[A, -A*1i, 0]




E0_RHCP =[B, B*1i, 0]

=[a, b, 0]

eq1 =a == (A + B)/E0
eq2 =b == -(A*1i - B*1i)/E0








sol =
(E0*(a + b*1i))/2
-(E0*(b + a*1i)*1i)/2

S2 =
[-1,  0]
[ 0, -1]
y =
     -(A + B)/E0
(A*1i - B*1i)/E0
z =
      (A + B)/E0
-((A - B)*1i)/E0
So any [x y] plane wave travelling along z axis can be decomposed into the sum of one LHCP wave and one RHCP wave.
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