Design of an Output Mode Cleaner to Enable

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

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

Gaussian Beams q Laser beams in and q q 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

Filtering Junk Light q RF sidebands are used for PDH and Schnupp locking q RF Sidebands also have “junk light” q Sidebands at the 40 m are at ± 33 and ± 166 Mhz and q q 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

Fabry-Perot Optical Cavity q Extreme Sensitivity to q q q resonant frequency Rejection of all nonresonant frequencies Light promptly reflects Some light circulates then transmits out Cavity length must be ½integer wavelength of the laser beam for resonance of the TEM 00 At resonance R 0, T 1

Design Criteria for the Output Mode Cleaner q Filter TEM 01 and all higher q q q 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 q Well defined beam waist q Well defined location of q q 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 counterpropagating light

Mode Cleaner q Fabry-Perot Cavity with folded geometry q 4 -mirror geometry so that reflected light does not return to IFO q Resonant frequency determined by cavity length q 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 q Guoy phase is an additional q q q 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 TEM 00

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

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

RF Transmission, T = 0. 5%

Cavity Material Coeff. Expan Therm sion. Materia (μm) l Expan for. (10 1 K 6/K) Alumin 25. 5 um Stainle ss 11 Steel Glass 4. 78 5. 35 2. 31 1. 0038

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

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

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

ROC 1 = 618. 4 mm ROC 2 = 150. 0 mm w. OMC = 0. 37965 mm w. ETM = 5. 2422 mm w. ITM = 3. 0266 mm w. BS = 3. 034 mm w. SRM = 3. 0355 mm w. OMMT = 3. 0355 mm

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

Final OMC Design

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