Transcript l - Nikhef

Optics of GW detectors
Jo van den Brand
e-mail: [email protected]
Introduction
LISA
•
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
General ideas
 Measure distance between 2 free falling
masses using light
–
h=2DL/L (~10-22)
–
L= 3 km  DL
–
–
~10-22
x
106
~10-16
(=10-3
fm)
L + DL
llight ~ 1 mm
Challenge: use light and measure DL/l~10-12
 How long can we make the arms?
–
GW with f~100 Hz  lGW ~c/f=3x108 km/s / 100 Hz
= 3000 km
–
Optimal would be lGW/4 ~ 1000 km
–
Need to bounce light 1000 km / 3 km ~ 300 times
L - DL
 How to increase length of arms?
–
–
LISA
Use Fabri-Perot cavity (now F=50), then DL/l~10-10
Measure phase shift Df = dfx-dfy = 4pLBh/le ~
10.(3 km).200.10-22/10-6=10-9 rad
L + DL
General ideas
 Power needed
–
PD measures light intensity
–
Amount of power determines precision of phase measurement Df = weDt of
incoming wave train (phase f = 2pft)
–
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.Ngwe
–
Due to Poisson distributed arrival times of the photons we have DNg = Sqrt[Ng]
–
Thus, DE= DNg .hbar. we and Dt DE= (Df/we).Sqrt[Ng]. hbar. we >hbar
–
We find Df > 1/ Sqrt[Ng]  Ng > 1/(Df)2 = 1018 photons
–
Power needed I0 = Ng. hbar. we .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 ~40
L - DL
L + DL
LISA
Cavities
70
 Fabri-Perot cavity
60
(optical resonator)
50
 Reflectivity of input
40
30
mirror: -0.96908
20
 Finesse = 50
 FSR = 50 kHz
 Power
 Storage time
 Cavity pole
LISA
10
-6
-4
-2
2
4
6
Cavity pole
LISA
Overcoupled cavities (r1 - r2 < 0)
 On resonance 2kL=np
 Sensitivity to length changes
 Note amplification factor
 Note that amplitude of
Eref
reflected light is phase
shifted by 90o
Einc
 Reflected light is mostly
E 


rr
1 - 1 2 2ikdL 
=  ref 

 Einc  resonance 1 - r1r2
Amplification factor
(bounce number)
unchanged |Eref|2
 Imagine that dL is varying
with frequency fGW
 Loose sensitivity for fGW>fpole
LISA
ei 4pc ( f df ) L  1  i 4pcLdf
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 dL of cavity
RFFD
sideband
Laser
3x
1014
EOM
L
Hz
 20 MHz
LISA
carrier
Faraday
isolator
Reflection locking
Modulation
Demodulation
LISA
Transmission locking
 Schnupp locking is used to control Michelson d.o.f.
LISA
–
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
Gaussian beams
P – complex phase
q – complex beam parameter
LISA
Higher-order modes
LISA
Input-mode cleaner
LISA
Applications – Anderson technique
LISA
Summary

Some of the optical aspects
–

Frequency stabilization
–

Presentation
Control issues
–
LISA
Simulate with Finesse
Presentation