P010010-00-R - LIGO - California Institute of Technology

Coupled cavity transmission
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
φ dt =0
φ dt =π/4
φ dt =π/2
φ dt =3π/4
φ dt =π
No signal mirror
31
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2
x 10 4
0
Frequency (Hz)
Figure 2.7: Transmissivity of a three mirror coupled cavity as a function of frequency
and detuning. The signal cavity is over-coupled. The arm length is 4000 m, the signal
cavity is 6 m. The optics are the same as in Figure 2.6.
2.1.2 RSE Transfer Functions
The effect of the gravitational wave on the end mirrors can be interpreted as a tidal
force causing the mirrors to move relative to the beamsplitter. The motion of the
mirrors phase modulates the fields incident on the mirror, as seen in Figure 2.8. It’s
assumed for this analysis that the mirror motion is sinusoidal at frequency ω = 2πf.
If the incident field at the dashed line is given by Ei, then the field returning from
Ei
l
i2k(l+δl/2 cos (ωt))
rEie
δl/2 cos (ωt)
Figure 2.8: The effect of a field incident on a moving mirror.
r