Detailed analysis of MSE spectra
Detailed analysis of MSE spectra
Detailed analysis of MSE spectra
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Ideal Nonideal<br />
0 ω 1<br />
2ω 1 3ω 1<br />
4ω 1 5ω 1<br />
6ω 1 7ω 1<br />
8ω 1 9ω 1<br />
2ω 2 ω 2<br />
4ω 2 3ω 2<br />
6ω 2 5ω 2<br />
8ω 2 7ω 2<br />
ω 1 ± ω 2 9ω 2<br />
3ω 1 ± ω 2 2ω 1 ± ω 2<br />
5ω 1 ± ω 2 4ω 1 ± ω 2<br />
7ω 1 ± ω 2 6ω 1 ± ω 2<br />
3ω 2 ± ω 1 8ω 1 ± ω 2<br />
5ω 2 ± ω 1 3ω 2 ± 2ω 1<br />
7ω 2 ± ω 1 4ω 1 ± 3ω 2<br />
3ω 1 ± 3ω 2 5ω 2 ± 2ω 1<br />
5ω 1 ± 3ω 2 6ω 1 ± 3ω 2<br />
5ω 2 ± 3ω 1 5ω 2 ± 4ω 1<br />
5ω 1 ± 5ω 2 7ω 2 ± 2ω 1<br />
7ω 1 ± 3ω 2<br />
7ω 2 ± 3ω 1<br />
9ω 1 ± 1ω 2<br />
9ω 2 ± 1ω 1<br />
Table 1: Frequencies at which we expect nonzero fft amplitudes for ideal and nonideal<br />
mirrors. Nonideal mirrors will have the frequency components listed in both columns.<br />
Expected Signals When only One PEM is Operating<br />
If we turn <strong>of</strong>f pem#2, then<br />
I net = M p · M P EM1 · M m · S v . (3)<br />
Doing the matrix multiplication with Maple yields an intensity<br />
4I net = (I 0 + I b )(1 + r m + r m − 1<br />
√ cos(A) 2<br />
+I 0 cos(2γ)(r m − 1 + r m + 1<br />
√ cos(A)) 2<br />
+I 0 sin(2γ) √ 2r m (cos(δ) + sin(δ) sin(A)). (4)<br />
Making the usual substitutions yields the intensities:<br />
I ω1 = I 0 sin(δ) √ r m J 1 (A 1 )<br />
√<br />
2<br />
sin(2γ)<br />
2
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