1. Parametric Effects in a Macroscopic Optical Cavity
AIGO
Parametric Effects in a Macroscopic Optical Cavity
Sascha Schediwy
AIGO Workshop Thursday 6th October

2. Optical Spring
Circulating Power
Frequency
Q reduction Q 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 = 0.10 m
Proxy Mirrors
R = 0.98
F = 155
roc = 10.0 m
Super Mirrors
R ~ (rated: )
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
90°C
80°C
70°C
60°C

6. Yacca Gum Bonding

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

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

9. Quality Factor
Q = ± 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) )

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 Maximum Input Power
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

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