Detailed analysis of MSE spectra

where M m is the Müeller matrix for a mirror, M P EM1 and M P EM2 are the Müeller matrices for
the first and second photoelastic modulators, M p is the Müeller matrix for a static polarizer
at 22.5 o , and S v is the Stokes vector for the partially polarized light incident on the mse
diagnostic:
⎡
⎤
I b + I 0
I
S v = 0 cos(2γ)
⎢
⎥
(17)
⎣ I 0 sin(2γ) ⎦
0
where I 0 is the intensity of the polarized light (polarized at an angle γ to the horizontal) and
I b is the intensity of the background, unpolarized light. The Müeller matrix for the mirror
is
⎡ r m+1 r m−1
⎤
0 0
2 2 r m−1 r m+1
0 0
M m = ⎢ 2 2 √ √ ⎥
(18)
⎣ 0 0 rm cos(δ) rm sin(δ)
0 0 − √ ⎦
√
r m sin(δ) rm cos(δ)
The Müeller matrices for the PEMs at 0 o and 45 o are:
⎡
M P EM1 = ⎢
⎣
⎡
M P EM2 = ⎢
⎣
1 0 0 0
0 cos(A) 0 − sin(A)
0 0 1 0
0 sin(A) 0 cos(A)
1 0 0 0
0 1 0 0
0 0 cos(B) sin(B)
0 0 − sin(B) cos(B)
⎤
⎥
⎦
⎤
⎥
⎦
(19)
(20)
and the PEM for a fixed polarizer at 22.5 o is
⎡
M p = 1 ⎢
4 ⎣
√ √
√
2 2 2 0
√ 2 1 1 0
2 1 1 0
0 0 0 0
⎤
⎥
⎦
(21)
Relationship of Measured Intensities to Polarization Angle
I used Maple to carry out the matrix multiplication. The output intensity, taken from
the first component of the output Stokes vector, is
[
4I net = (I b + I 0 ) 1 + r m + r ]
m − 1
√ (cos(A) + sin(A) sin(B))
2
[
+I 0 cos(2γ) r m − 1 + r ]
m + 1
√ (cos(A) + sin(A) sin(B))
2
+I 0 sin(2γ) √ 2r m [cos(δ) cos(B) + sin(δ)(sin(A) − sin(B) cos(A))] (22)
39