Transcript Optical transducers for resonant detectors

Optical readout for a resonant gw bar
Old setup
New alignment mirrors system
New optical bench
l/4
plate
Auxiliary
cavity
Optical
fiber
l/2
plate
Mode-matching
lenses
Alignment prisms
DUAL sensitivity target
• Laser power = 7 W
• Finesse = 106
Sxx = 10-45 m2/Hz
… but
With a waist of w = 1 mm:
SBr = 5·10-44 m2/Hz
Srp = 8·10-41 m2/Hz
We need a waist of
w > 20 cm !!!!
Folded Fabry-Perot (FFP)
M3
M4
M1
D
F. Marin, L. Conti, M. De Rosa: “A
folded Fabry-Perot cavity for
optical sensing in gravitational wave
detectors”, Phys. Lett. A 309, 15
(2003)
M2
Signal:
N
Brownian noise:  N
Radiation pressure:  N·F (constant)
Displacement noise:  1/F  N
Linewidth ( bandwidth):  1/(N·F) (constant)
FFP for dual cylinder
Fixed total length: 2.3 m
10
-44
D = 10 cm
R = 100 m
20 W
15 W
10 W
-45
} shot-noise limited sensitivity
2
-1
Sxx (m /Hz )
10
10
} radiation pressure effect
-46
Brownian
10
-47
0
50
100
N
150
Prototype of FFP fabricated
- Two parallel rows of mirrors on independent oscillating masses,
with resonance frequencies of 1 kHz and 2 kHz
- Three possible configurations:
- 2 mirrors (simple FP)
- 9 mirrors
- 17 mirrors
Calculated response to modulated laser power
Simple cavity (2 mirrors)
10000
Laser freq. displacement (Hz/W)
Photothermal
1000
100
10
Mechanical masses
1
0.1
0.01
Mechanical mirrors
0.1
1
10
100
Frequency (Hz)
1000
10000
10000
Laser freq. displacement (Hz/W)
Laser freq. displacement (Hz/W)
10000
Photothermal
1000
100
10
Mechanical masses
Mechanical mirrors
1
0.1
0.01
0.1
1
FFP 17 mirrors
Photothermal
1000
100
FFP 9 mirrors
Mechanical masses
10
Mechanical mirrors
1
0.1
0.01
0.1
1
10
100
Frequency (Hz)
1000
10000
10
100
Frequency (Hz)
1000
10000
Photo-thermal effect: direct measurements
C1
PD1
Frequency
servo loop
Oscilloscope
+
PC
QW
PBS
AOM
Cavity
servo loop
13.3 MHz
Laser
O.I.
EOM1
PD2
EOM2
PBS
BS
QW
PD3
C2
PD4
Model for Photo-thermal + radiation
pressure displacements
High power:
- Bistability
- Kramers model for jump probability (wip)
Intermediate power:
- Hopf bifurcation
- ‘New’ dynamics (similar to FitzHugh-Nagumo)
- Self oscillations
F. Marino, M. De Rosa and F. Marin, to be published on Phys. Rev. E
Q=5
Q = 10
Q = 20
Q = 103
Q = 103
Q = 104
Q = 105
 The probability of a noise-induced state jump is non-zero
 In any case, a tight locking is probably necessary
 Several QND schemes are difficult to be implemented
 Comparing two cavities, the laser must be in tight resonance
with both cavities 
- two laser beams and heterodyne ??
(but the requirement on the phase noise of the reference tunable rf oscillator is
too stringent: -200dBc @ 2-5 kHz)
- locking the cavities (at least one) ??
(but high dynamic range and low noise are not easily obtained)