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LISA
Introduction
• General ideas
• Cavities
• Reflection locking (Pound-Drever technique)
• Transmission locking (Schnupp asymmetry)
• Paraxial approximation
• Gaussian beams
• Higher-order modes
• Input-mode cleaner
• Mode matching
• Anderson technique for alignment
LISA
General ideas
Measure distance between 2 free falling masses using light
– h=2L/L (~10-22)
– L= 3 km L ~10-22 x 106 ~10-16 (=10-3 fm)
– light ~ 1 m
– Challenge: use light and measure L/~10-12
How long can we make the arms?
– GW with f~100 Hz GW ~c/f=3x108 km/s / 100 Hz = 3000 km
– Optimal would be GW/4 ~ 1000 km
– Need to bounce light 1000 km / 3 km ~ 300 times
How to increase length of arms?– Use Fabri-Perot cavity (now F=50), then L/~10-10
– Measure phase shift xy LBhe ~ 10.(3 km).200.10-22/10-6=10-9 rad
L + L
L + L
L - L
LISA
General ideas
Power needed
– PD measures light intensity
– Amount of power determines precision of phase measurement et of incoming wave train (phase ft)
– Measure the phase by averaging the PD intensity over a long period of time Tperiod GW/2 = 1/(2f)
– Total energy in light beam E=I0.1/(2f)=hbar.Ne
– Due to Poisson distributed arrival times of the photons we have N= Sqrt[N]
– Thus, E= N .hbar. e and t E= (e).Sqrt[N]. hbar. e >hbar
– We find Sqrt[N] N= 1018 photons
– Power needed I0 = Nhbar. e .2f ~ 100 W
Power is obtained through power-recycling mirror
– Operate PD on dark fringe
– Position PR in phase with incoming light
– GW signal goes into PD!
– Laser 5 W, recycling factor ~40L + L
L - L
LISA
Cavities
Fabri-Perot cavity (optical resonator)
Reflectivity of input mirror: -0.96908
Finesse = 50
FSR = 50 kHz
Power
Storage time
Cavity pole
-6 -4 -2 2 4 6
10
20
30
40
50
60
70
LISA
Cavity pole
LISA
Overcoupled cavities (r1 - r2 < 0)
On resonance 2kL=n Sensitivity to length changes
Note amplification factor
Note that amplitude of reflected light is phase shifted by 90o
Reflected light is mostly unchanged |Eref|2
Imagine that L is varying with frequency fGW
Loose sensitivity for fGW>fpole
Lik
rrrr
E
E
E
E
resonanceinc
ref
inc
ref 21
121
21
Amplification factor(bounce number)
fcLie Lffci 41)(4
LISA
Reflection locking – Pound Drever locking
Dark port intensity goes quadratic with GW phase shift.
How do we get a linear response?
Note, that the carrier light gets p phase shift due to over-coupled cavity.
RFPD sees beats between carrier and sidebands.
Beats contain information about carrier light in the cavity
Phase of carrier is sensitive to L of cavity
Laser EOM
3 x 1014 Hz
20 MHzFaraday isolator
carrier
L
sideband
RFFD
LISA
Reflection locking
Demodulation
Modulation
LISA
Transmission locking
Schnupp locking is used to control Michelson d.o.f.
– Make dark port dark and bright port bright
– Not intended to keep cavities in resonance
– Requires that sideband (reference) light comes out the dark port
LISA
Gaussian beams
P – complex phaseq – complex beam parameter
LISA
Higher-order modes
LISA
Input-mode cleaner
LISA
Applications – Anderson technique
LISA
Summary
Some of the optical aspects
– Simulate with Finesse
Frequency stabilization
– Presentation
Control issues
– Presentation