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

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

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

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

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

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

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

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

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

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

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)

Beam Waist Beam Waist = 0.3797 mm for ROC = 1.000 m

g-factor

Selecting a ROC = 1.000 m g-factor = 0.775  Cavity Length 45 cm

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

RF Transmission, T = 0.5%

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

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)

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

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

ROC1 = 618.4 mm ROC2 = 150.0 mm wOMC = 0.37965 mm wETM = 5.2422 mm wITM = 3.0266 mm wBS = 3.034 mm wSRM = 3.0355 mm wOMMT = 3.0355 mm

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

Final OMC Design

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