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

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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

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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

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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

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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

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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

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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

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

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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

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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)

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Beam Waist Beam Waist = mm for ROC = m

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g-factor

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

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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

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RF Transmission, T = 0.5%

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

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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)

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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

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

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

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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

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Final OMC Design

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

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