Optical readout for a resonant gw bar. Old setup.
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Optical readout for a resonant gw bar
Transcript of Optical readout for a resonant gw bar. Old setup.
Optical readout for a resonant gw bar
Old setup
New alignment mirrors system
New optical bench
Alignment prisms
Optical fiber
/2 plate
Mode-matching lenses
Auxiliary cavity
/4 plate
DUAL sensitivity target
• Laser power = 7 W• Finesse = 106
Sxx = 10-45 m2/Hz
… butWith 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)
M1
M2
M3
M4
D
Signal: N
Brownian noise: N
Radiation pressure: N·F (constant)
Displacement noise: 1/F N
Linewidth ( bandwidth): 1/(N·F) (constant)
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)
FFP for dual cylinder
0 50 100 15010-47
10-46
10-45
10-44
Brownian
20 W15 W10 W
D = 10 cmR = 100 m
Sxx
(m
2 /Hz-1
)
N
} shot-noise limited sensitivity
} radiation pressure effect
Fixed total length: 2.3 m
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
0.01 0.1 1 10 100 1000 100000.1
1
10
100
1000
10000
Mechanical mirrors
Mechanical masses
Photothermal
Simple cavity (2 mirrors)
La
ser
fre
q. d
isp
lace
me
nt (
Hz/
W)
Frequency (Hz)
0.01 0.1 1 10 100 1000 100000.1
1
10
100
1000
10000
Mechanical mirrors
Mechanical masses
Photothermal
FFP 9 mirrors
La
ser
fre
q. d
isp
lace
me
nt (
Hz/
W)
Frequency (Hz)
0.01 0.1 1 10 100 1000 100000.1
1
10
100
1000
10000
Mechanical mirrors
Mechanical masses
Photothermal
FFP 17 mirrors
La
ser
fre
q. d
isp
lace
me
nt (
Hz/
W)
Frequency (Hz)
Frequencyservo loop
Laser EOM1O.I.BS
PD1 QW
PBS
13.3 MHz
PD2
QWPBS
PD4
Cavity servo loopAOM
EOM2
C1
C2
PD3
Oscilloscope+
PC
Photo-thermal effect: direct measurements
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 = 20
Q = 10
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)
