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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.

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Presentation on theme: "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."— Presentation transcript:

1 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 TEM 00  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 TEM 00 mode  It will filter out carrier HOM and RF TEM 00 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 TEM 00  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 TEM mn, this phase is equal to (m+n)* Ψ tan(Ψ) = L OMC /Z R Z R 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 TEM 00

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  g 1 = 1 – L OMC /ROC 1, g 2 = 1 – L OMC /ROC 2  Stable Cavity for 0 ≤ g 1 g 2 ≤ 1  Treat cavity as half symmetric resonator  gfac = 1 – L OMC /(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-δ loss )/δ loss )  δ loss = 4*Loss mirr + 2*T mirr

16 RF Transmission, T = 0.5%

17 Cavity Material Material Coeff. Therm. Expan. (10 -6 /K) Expansion (μm) for 1K Aluminum Stainless Steel Glass Invar Super Invar

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 ((λ d) / (2 π ω 0 )) 2 (ω 0 ' / ω 0 - 1) 2 coupling coefficients for each type of mismatch MM 2 = ((λ d) / (2 π ω 0 )) 2 + (ω 0 ' / ω 0 - 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 wOMC = mm wETM = mm wITM = mm wBS = mm wSRM = mm wOMMT = mm ROC1 = mm ROC2 = 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


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