Balanced Homodyne Detection

Requirements

1. Displacement noise of OMC/LMC mirrors
   • Are we using a single cavity or two?
2. Scatter loss in mirrors
   • This will affect the backscatter into the IFO
   • This will limit the transmissivity of the cavity for a given finesse.
3. Cavity design: triangle, quad ring, quad zig-zag (reference the new OMC paper from Koji)
   • What does this mean?
4. Laser amplitude / frequency noise including DC offsets in various other lock points and motions to simulate bilinear noise
5. Oscillator noise: AM / FM
   • This will set the requirement on the filtering necessary.
6. Aux length noise: MICH/PRC/ SRC
7. Req. on offsets/asymmetries: arm finesse, arm reflectivity, mass imbalance of ETMs
8. Phase noise of LO
   • This will set the requirement on whatever we use to control the homodyne angle.
9. Polarization stability requirement for polarization BHD
   • i.e. let's say we have some finite Ip/Is ratio. What does this mean for the readout in signal-referred units?
10. Backscatter
    • RIN on the LO
    • Phase noise due to motion of the mirrors
11. Pointing
    • If we opt to not use a mode-cleaner for the LO field, what is the pointing requirement on whatever option we choose?
12. Suspension
    • What kind of suspension(s) are we planning to use?

    • VOPO and OMCS seem too big to fit on any of our existing tables.

13. Control scheme
    • How will we control the LO phase?

Some preliminary calculations can be found in this elog

Modeling/Noise Budget

Modeling to determine the BHD noise requirements is being done in the 40m BHD repo. The models use Finesse 2.2 and are called from Python 3 using PyKat.

In order of priority, here is the list of couplings to be modeled. Items denoted with (HOM) require a multi-mode analysis.

1. Classical noise on LO
   • RIN
   • Phase noise
     • Laser phase noise
     • LO path length/control noise
     • OMC length noise
2. Asymmetries
   • Reflectance/transmittance imbalance of homodyne BS
   • Finesse imbalance of OMCs
3. Readout electronics noise
4. Angular pointing noise (HOM)
   • Mode-overlap variation at homodyne BS
   • Mode coupling into OMCs
5. Backscatter noise (HOM)

Layout options

Schematic BHD layout options. In the linked document, some options for placement of the BHD optics are schematically sketched (but I don't consider the option of adding a new table). Some more discussion may be found in this elog.

7/8: A more detailed layout sketch, that accounts for LO and AS beam routing, may be found here.

Action items

• Design SRC so that
  1. Suppress 02/20 modes
  2. Partially transmit 01/10 modes for AS WFS
  3. Suppress thermally generated modes
  4. After the above have been satisfied, choose transmission to maximize ponderomotive squeezing
• Budget above noises, but especially investigate polarization stability.
• How is homodyne angle controlled?
• Beam routing
  • Where to pick off LO?
  • Can we use ETMX transmission for LO? (Koji is crazy)
• A+ BHD noise budget for both baseline double OMC and polarization BHD.
• Can we add a heater back to OMC mirror to control ROC? How should the temperature be sensed and controlled?
  • Heater below breadboard for cavity length control

  • Heater on back of mirror for RoC Control

  • Offload PZT DC voltage to slow servo (breadboard heater) to always keep PZT in the middle of the range

Polarization BHD

• Some thoughts on polarization BHD (LIGO-G1802013)

• Polarization BHD notes

Other Links

• A+ BHD wiki

• MIT A+ BHD workshop wiki

• Evan Hall's note on the algebra for using 4 PDs for BHD, allowing a null-stream readout in addition to the GW signal stream.