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Arm Length Stabilization by injecting green laser beams from the arm ends

Plan

time line

• time line describes where we are now and where we go.

Conceptual design

• Description of the optical / servo configuration [https://dcc.ligo.org/cgi-bin/private/DocDB/ShowDocument?docid=6888 LIGO DCC]

• Servo modeling (SimLink) [https://nodus.ligo.caltech.edu:30889/svn/trunk/docs/upgrade08/Green_Locking/Servo_modeling/ 40mSVN]

Detailed design

• Design and Purchasing Lists

  • Optical design / item list

  • Electronics / control design / item list

  • Purchase list

• Detailed considerations

  • Optical Layout ([attachment:green_optics.png Table]/ In-vac)

    • ETM / end table

    • ITM wedge effect

    • Periscopes for beam steering from PR3/SR3 transmissions to the PSL viewport

    • PSL viewport modification (viewport cover / tube / PSL box / periscope on the PSL table)
    • PSL table

    • Laser & SHG specs --- power, polarization, Xtals

      • - references

      • [1] G.D.Boyd and D.A. Kleinman, [http://jap.aip.org/japiau/v39/i8/p3597_s1 "Parametric interaction of Focused Gaussian Light Beams", J.A. Phys. 39, 3597 (1968)]

      • [2] C. Zhang, Y.Qin and Y.Zhu, [http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-33-7-720 "Perfect quasi-phase matching for the third-harmonic generation using focused Gaussian beams",Opt. Lett. 33, 720 (2008)]

  • Main optics specs (review)
  • Mode matching ([attachment:modematch_END.png mode matching at end table])
  • Green generation
    • [attachment:manual_oven.pdf manual for the covesion oven]
  • Expected performance / noise / control system range
  • Digital servo / operation
  • Alignment (initial / fine / automatic)

Green Preliminary Design: ETM region

attachment:green_ETM_preliminary_design.png

Green Preliminary Design: Vertex region

attachment:green_vertex_preliminary_design.png

Development roadmap

• End table arrangement

  • NPRO placement / optical assembly at the end
  • SHG at the end table
  • Control system placement
  • Coarse alignment to the cavity
  • Fine alignment
  • Lock of the green beam to the cavity

• At the PSL table

  • SHG at the PSL table

• Digital control

  • Virtual Green lock by RCG
  • GPIB interfaces

• Vertex tank optical arrangement

  • In-vac steering (PO transmission / Periscope / Mirrors)
  • Vertex phase noise measurement
    • Electronics placement
    • Control system implementation

• Performance evaluation

  • f_noise of green beam / PDH performance
  • Relative f_noise between the PSL green and the Arm transmitted green
  • ALS performance

• Sophistication of the scheme

  • Automatic handing off scripts
  • Ready-to-go panels for AdvLIGO
  • Automatic alignment of the green beam
  • ---
  • Green Michelson for precise ETM calibration

  • Absolute length / mode spacing measurement by green

Control information

Laser Frequency vs Crystal Temperature

Plots of the laser frequency vs temperature (measured by beating against a second laser) are shown below. [http://nodus.ligo.caltech.edu:8080/40m/2794 Also, see the elog here].

Lightwave laser

attachment:lightwave_temperature_sweep.png

Innolight laser

attachment:innolight_temperature_sweep.png

• attachment:greenskeleton.jpg

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 attachment:PhaseNoise.pdf] for derivation).

attachment:Cavity-Common-Diff.png

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

I first took a spectrum of ETMX OSEM pos signal to see the motion of the mirror with damping.BR The blue curve in the figure shows the calibrated OSEM spectrum using the well known 2V/mm OSEM BR calibration and the whitening filter shape (3Hz zero, 30Hz and 100Hz pole).BR However, OSEM signal is not a good measure of the seismic noise below the pendulum resonant frequencyBR because the suspension cage and the mirror move together at low frequencies.BR As a tentative solution, I put a filter to make the spectrum look like 1/f^2 below 0.8Hz.BR This is diffinitely a hacky solution, and should be replaced with a correctly measured BR seismic spectrum.

The estimated seismic motion was converted to the phase noise using the above formula.BR The RMS displacement noise above 0.1Hz is about 3e-12 m, which satisfies the requirement for BR the green lock stability (1e-11m).