1. Marcus Ng Mentor: Alan Weinstein Co-mentor: Robert Ward
Design of an Output Mode Cleaner to Enable DC Readout in the LIGO 40-Meter Interferometer
Marcus Ng
Mentor: Alan Weinstein
Co-mentor: Robert Ward

2. Overview LIGO 40m Gaussian beams OMC design criteria OMC Parameters
Geometry
Guoy Phase
ROC
g-factor
Finesse
Mirror Transmission
Cavity Material
Mode Mismatch
Conclusion

3. LIGO 40 meter 40 meter interferometer Prototype for AdLIGO
Test bed for complex configuration and control systems
DC readout
This summer I worked on design of an OMC and on Mode Matching into the OMC

4. Gaussian Beams
Laser beams in and propagating between optical cavities have Hermite-Gaussian Transmverse profiles
Transverse Excited Modes (TEM)
LIGO uses TEM00
Higher Order TEM modes (HOMs) are also present
“Junk light” must be filtered out for effective DC readout
Kogelnik & Li 1966

5. Filtering Junk Light RF sidebands are used for PDH and Schnupp locking
RF Sidebands also have “junk light”
Sidebands at the 40m are at ±33 and ±166Mhz and HOM
Wavefront curvature differs for each TEM
The OMC is an optical resonator that transmits only the carrier TEM00 mode
It will filter out carrier HOM and RF TEM00 and RF HOM
Purpose of this SURF was to select parameters for the OMC so that it will effectively filter the junk light

6. Fabry-Perot Optical Cavity
Extreme Sensitivity to resonant frequency
Rejection of all non-resonant frequencies
Light promptly reflects
Some light circulates then transmits out
Cavity length must be ½-integer wavelength of the laser beam for resonance of the TEM00
At resonance R 0, T1

7. Design Criteria for the Output Mode Cleaner
Filter TEM01 and all higher order TEMs
Filter 33 and 166 MHz RF sidebands
Filter HOM of RF sidebands
Stable cavity
Reliable dither-locking
Low thermal expansion coeff s.t. PZT only need compensate for less than a few microns
Well defined beam waist
Well defined location of beam waist
Well defined (and suitably minimized) astigmatism
Mode matching telescope
Angle of incidence large to prevent back reflection to IFO
Internal angles large to avoid backreflection and counter-propagating light

8. Mode Cleaner Fabry-Perot Cavity with folded geometry
4-mirror geometry so that reflected light does not return to IFO
Resonant frequency determined by cavity length
Bandwidth determined by finesse

9. 4- v. 3- Mirror Cavity Geometry
4-mirror cavity has half the accidental resonances as a 3 mirror cavity

10. Guoy Phase
Guoy phase is an additional phase a hermite gaussian acquires beyond a plane wave
Different HOM have different guoy phases
For TEMmn, this phase is equal to (m+n)* Ψ tan(Ψ) = LOMC/ZR ZR is the Rayleigh range
An optical cavity will resonate for a beam with only one particular round trip phase
It will filter out HOM which have this additional guoy phase
Similarly RF sidebands also have a different phase than the carrier TEM00

11. Cavity Parameters Radius of Curvature (ROC): One curved mirror
Influences astigmatism
Determines guoy phase advance of HOM in the cavity
g-factor:
Measure of the stability of a cavity
g1 = 1 – LOMC/ROC1, g2 = 1 – LOMC/ROC2
Stable Cavity for 0 ≤ g1g2 ≤ 1
Treat cavity as half symmetric resonator
gfac = 1 – LOMC/(2*ROC)

12. Beam Waist
Beam Waist = mm
for ROC = m

13. g-factor

14. Selecting a ROC = m
g-factor =  Cavity Length 45 cm

15. Cavity Parameters Finesse:
Higher finesse corresponds to sharper, finer resonant peak therefore more suppression of HOM and RF sidebands
fin = FSR/FWHM
fin = π√((1-δloss)/δloss)
δloss = 4*Lossmirr + 2*Tmirr

16. RF Transmission, T = 0.5%

17. Cavity Material Material Coeff. Therm. Expan. (10-6/K)
Expansion (μm) for 1K
Aluminum
25.5
5.35
Stainless Steel 11
2.31
Glass
4.78
1.0038
Invar
1.3
0.273
Super Invar
0.63
0.1323

18. Mode Matching
After finalizing OMC parameters, we had to design a system to mode match the input beam into the OMC
We will construct a Mode Matching Telescope (MMT)

19. Mode Mismatch Mismatch in Waist Location Mismatch in Waist Size
coupling coefficients for each type of mismatch
MM2 = ((λ d) / (2 π ω0))2 + (ω0' / ω0 - 1)2

20. OMMT Two Curved Mirrors Variable Telescope Length
ROCs selected “off-the-shelf” from catalog
Selection Criteria: Minimize Mode Mismatch
Above Design by Mike Smith

21. ROC1 = mm
ROC2 = mm
wOMC = mm
wETM = mm
wITM = mm
wBS = mm
wSRM = mm
wOMMT = mm

22. Conclusion
We have designed parameters for an OMC to filter out junk light from the output beam of the 40m IFO
We have designed an optical system for mode matching into the OMC
The system will be constructed and commissioned in the coming months

23. Final OMC Design

24. Special thanks to: Alan Weinstein Rana Adhikari Osamu Miyakawa Caltech
Robert Ward
Keita Kawabe
Mike Smith
NSF