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| When the cavity is locked to the green laser, the differential motion of the two mirrors will be suppressed by the servo. However, the common motion of the cavity mirrors will not be suppressed. This common motion will show up as phase noises of the lasers. The time derivative of phase noise is equivalent to frequency noise. The equivalent displacement noise seen by the cavity is dL=(w*x*L)/c, where w is the angular frequency, x is the displacement noise spectrum of the common motion, L is the length of the cavity and c is the speed of light (see [attachment:PhaseNoise.pdf|this]). |
When the cavity is locked to the green laser, the differential motion of the two mirrors will be suppressed by the servo.[[BR]] However, the common motion of the cavity mirrors will not be suppressed. This common motion will show up as phase noises [[BR]] of the lasers. The time derivative of phase noise is equivalent to frequency noise. The equivalent displacement noise seen [[BR]] by the cavity is dL=(w*x*L)/c, where w is the angular frequency, x is the displacement noise spectrum of the common motion, [[BR]] L is the length of the cavity and c is the speed of light (see [attachment:PhaseNoise.pdf] for derivation). The two lasers (PSL and green) see the same motion of the cavity but from the opposite sides. Hence, the effect of this phase [[BR]] noise to the two error signals of the green and the PSL lasers will be 180 deg. out of phase. The feedback from the green laser to [[BR]] the cavity length will, therefore, create a noise for the PSL laser. In order to estimate the contribution of this noise to the green lock, I plotted the estimated phase noise in the following figure.[[BR]] attachment:PhaseNoise.png |
Green Laser Injection for Arm Pre-Lock
We plan to install green lasers, which are phase locked to the PSL laser, at each end station to pre-lock the arm cavities before the lock acquisition.
Basic Concept
Noise Requirement
I'd say the arm cavity length should not change more than 1/100 of the resonance width in the time scale of 10sec.BR For this to be fulfilled, the RMS fluctuation of the cavity length must be suppressed below 1e-11m level.BR Does this make sense ?
Noise Sources
PLL phase noise
Phase noise from the cavity common mode motion
When the cavity is locked to the green laser, the differential motion of the two mirrors will be suppressed by the servo.BR However, the common motion of the cavity mirrors will not be suppressed. This common motion will show up as phase noises BR of the lasers. The time derivative of phase noise is equivalent to frequency noise. The equivalent displacement noise seen BR by the cavity is dL=(w*x*L)/c, where w is the angular frequency, x is the displacement noise spectrum of the common motion, BR L is the length of the cavity and c is the speed of light (see [attachment:PhaseNoise.pdf] for derivation).
The two lasers (PSL and green) see the same motion of the cavity but from the opposite sides. Hence, the effect of this phase BR noise to the two error signals of the green and the PSL lasers will be 180 deg. out of phase. The feedback from the green laser to BR the cavity length will, therefore, create a noise for the PSL laser.
In order to estimate the contribution of this noise to the green lock, I plotted the estimated phase noise in the following figure.BR attachment:PhaseNoise.png