Gravitational Wave Astronomy

Dr. Giles HammondInstitute for Gravitational Research

SUPA, University of Glasgow

Universität Jena, August 2010

Interferometry• The EOM applies sidebands onto the carrier light (typically few MHz)

• The above assumes that the modulation depth is small or that m<1

...2cos)(2sin)(2)( 2100sin

0 tmJtmiJmJeEeEE titmtiin

carrier + sidebands

...

22)()(

0tititi

in em

em

eEE To 1st order:

Interferometry

• The output power in the presence of the EOM modulation and a GW signal is:

• and at the dark fringe (0=0) we can expand the trigonometric function to give

)sin(2cos12 0

20 tmE

I SIG

...

!4

sin22

!2

sin2211

2

4220 tmtmE

I SIGSIG

...

2

sin4sin44

2

22220

tmtmEI SIGSIG

...2cossin22

2222

20 tmtmmE

ISIGSIG

Interferometry

• The output power in the presence of the EOM modulation and a GW signal is:

• and at the dark fringe (0=0) we can expand the trigonometric function to give

• A small DC term and terms at and 2 appear. Can use lock-in techniques (mixer) to demodulate term at .

• In an interferometer a small length asymmetry is applied to the arms called the Schnupp asymmetry (to hold at dark fringe)

=> carrier light interferes destructively at the beamsplitter (-> laser)

=> sidebands interfere constructively and leave the output port

)sin(2cos12 0

20 tmE

I SIG

...2cossin22

2222

20 tmtmmE

ISIGSIG

Example Output

...2cossin22

2222

20 tmtmmE

ISIGSIG

0

00

SIG

Example Output

...2cossin22

2222

20 tmtmmE

ISIGSIG

CSIG

CSIG

00

Example Output

...2cossin22

2222

20 tmtmmE

ISIGSIG

tSIGCSIG sin

00

Signal provides AM modulation => at low frequency

Example Output

...2cossin22

2222

20 tmtmmE

ISIGSIG

Signal amplitude larger by modulation depth: but now sensitive to many other noise sources

tSIGCSIG sin

00

Cavity Control

• Optimum armlength for a GW at 150Hz is:

• Utilise arm cavities to increase storage time in km-scale detectors

• Cavity finesse is similar to an optical quality factor (typically few hundred)

kmLOPT 5001504

103 8

2/2 optL

Cavity Control• Utilise reflection locking scheme to keep cavity at resonance

• Sidebands promptly reflected off the front of cavity (not in resonance)

• At cavity resonance: the carrier builds up in the cavity (=1800)

• Away from cavity resonance: the carrier and sidebands form a beat note from the front surface (AM modulation) as carrier phase varies from 1800.

• This output can be demodulated to form an error signal to lock cavity

fcfs

Cavity Control• Utilise reflection locking scheme to keep cavity at resonance

• Pick-off ports used to demodulate sensing signals

• These signals control 4 DOF’s: CARM, DARM, MICH and PRC (4 sidebands)

LIGO I configuration

2/2/

2/

2/

21

21

21

21

llPRC

llMICH

LLDARM

LLCARM

Cavity Control

1) Choose a reference cavity and set on resonance

2) Adjust laser wavelength to maintain resonance

3) Adjust 2nd cavity to maintain resonance

4) Signal is control effort required at the 2nd cavity

Power Recycling

• All the carrier (assume losses small) goes back towards the laser as it interferes destructively (for the south port) at the beamsplitter

• Sidebands interfere constuctively and leave the instrument

•Thus the interferometer as viewed from the West or South looks like a very good mirror (West is bright, South is dark )

Power Recycling

• Most power goes back towards the laser

• Use a mirror to recycle this light back into the interferometer (for LIGO/GEO a 10W laser produces 10kW in the arms)

• Called the “Power Recyling” mirror

Signal Recycling

• GEO-600 uses an additional mirror at the output port

• A signal recycling mirror forms an additional cavity between the output port and the main interferometer

• Modulation sidebands have opposite sign in each arm (due to the quadrupolar GW) and interfere constructively to the South

• After /2 direction of phase shift changes sign => optimum length for interferometer arms

This is not an accurate estimation of the signal

Signal Recycling• Signal Recycling reflects the sidebands back into the detector with the correct phase so they can continue to be enhanced by interaction with a GW (i.e. flip the sign after /2)

• This resonant enhancement only works for the tuned wavelength => narrow band but more sensitive operation

• SR mirror and end mirrors form a coupled resonant system => can tune gain/phase with position and reflectivity of SR mirror

Signal Recycling

• These are several varieties of Signal Recycling which can be implemented (Dual Recyling and Resonant Sideband extraction are two common types)

We will not discuss it in detail but noise entering the output port gives rise to phase noise (builds up in SR cavity)

This is in addition to radiation pressure noise due to the circulating power

Advanced interferometers will inject certain states of light into the dark port to reduce noise!!!