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Parametric Effects in a Macroscopic Optical Cavity

This presentation from the AIGO Workshop on October 6th delves into the parametric effects observed in macroscopic optical cavities. We highlight the properties of a niobium resonator, characterized by a quality factor (Q) of 1.562(8)*10^5 and mechanical specifications such as fmech and effective mass. We also examine the role of Yacca gum bonding in optical mirror alignment and reflectivity. The model proposed by Braginsky and Vyatchanin explores instability and spring constants, providing insights into radiation pressure effects and modifications of cavity parameters for enhanced performance.

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Parametric Effects in a Macroscopic Optical Cavity

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  1. AIGO Parametric Effects in aMacroscopic Optical Cavity Sascha Schediwyschediwy@physics.uwa.edu.au AIGO WorkshopThursday 6th October

  2. Optical Spring CirculatingPower Frequency Q reductionQ increase

  3. Q Increase - Parametric Gain

  4. Niobium Resonator • Cavity Properties • Niobium • Qm = 1.562 (8)*105 • fmech = 780 Hz • meff = 32.3 g • l = 0.10m • Proxy Mirrors • R = 0.98 • F = 155 • roc = 10.0 m • Super Mirrors • R ~ 0.99968 (rated: 0.9994+) • F ~ 9800 (rated: 5200+) • roc = 1.0 m

  5. Yacca Gum Properties • viscous at 80°C+ • reversible bonds • dissolves in alcohol • relatively low loss • Q ~ 100 60°C 70°C 80°C 90°C

  6. Yacca Gum Bonding

  7. temp mirror 2 key: 3525 object position (mm) beam power (%) optical loss (%) temp mirror 1 Experimental Design

  8. Optical Error Signal Ringdown Ringdown Linear Fit time (s) time (s) (experimental results)

  9. Quality Factor Q = 0.700 ± 0.002 x105

  10. Proxy Mirror Q Modification F[rad] (N) Quality Factor (-) Mechanical Q k[opt] (N/m) Modified Q

  11. Super Mirror Q Modification F[rad] (N) Quality Factor (-) Mechanical Q (Hz) Damage Threshold Limited k[opt] (N/m) (Hz) (Hz) Laser Maximum

  12. Parametric Instability Tranquilisation • Model proposed by:Braginsky & Vyatchanin (Phys. Lett. A 293 (2002) 228-234)

  13. Any Question?

  14. Q Modification / Optical Spring Const.

  15. Circulating Power • Cavity Properties • Rayleigh Range / Beam Waist • R1 = R2 = 1.0 m • L = 0.1 m • Spot Size at Mirror ( z = 0.05 m )

  16. Circulating Power • Newport Supermirrors • Damage Threshold: • Maximum Circulating Power: • Maximum Input Power • R1 = R2 > 99.94% • T1 > 0.06%

  17. Radiation Pressure Force • Radiation pressure force for FP Cavity ≈ unity • let:

  18. Optical Spring Constant • substitute ABC back in x space in f space

  19. Cavity Alignment

  20. “Low Q” / “High Q” • Low Q – when the bandwidth is larger than ωm • High Q – when the bandwidth is smaller than ωm FWHM –ωm ωm FWHM –ωm ωm

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