A look at interferometer topologies that use reflection gratings
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A look at interferometer topologies that use reflection gratings
Peter BeyersdorfStanford University
Spring 2005 LSC meetingG050171-00-Z
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Outline
Motivation for considering reflection gratings
Configurations that use gratings– Reflective RSE– Reflective power recycled Fabry-Perot
Michelson interferometer
Issues with seismic noise that are unique to gratings
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Motivation for considering reflection gratings
• Reflection gratings can be used as beamspliters or cavity couplers without the thermal deformation issues associated with absorption in the transmissive substrates of conventional beamsplitters or cavity couplers
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Revisiting RSE
RSE interferometer
Bandwidth enhancement is limited by loss in the signal extraction cavity
101 102 10310-25
10-24
10-23
10-22
10-21
f / Hz
h(f
) /
Hz1/
2
1- aBW=BW=
rETMtITM2
1-rITMrSEM 1-rITMrSEM
rITMrSEM
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Revisiting RSE
RSE interferoemter
Bandwidth enhancement is limited by loss in the signal extraction cavity
101 102 10310-25
10-24
10-23
10-22
10-21
f / Hz
h(f
) /
Hz1/
2
Loss in the signal extraction cavity is dominated by
absorbtion in the optical substrates
1- aBW=BW=
rETMtITM2
1-rITMrSEM 1-rITMrSEM
rITMrSEM
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Revisiting RSE
Rather than modify design to increase the bandwidth of the arm cavities (power recycled RSE), modify it to reduce the loss in the signal extraction cavity
•Take advantage of low-loss reflection gratings to eliminate ITM substrate absorption
•Reconfigure geometry to separate signal extraction cavity from the beamsplitter
101 102 103 10410-25
10-24
10-23
10-22
10-21
f / Hz
h(f
) /
Hz1/
2
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RSE with reflection gratings
Lossy beamsplitter is not inside a cavity
r≈0.99999…≈10-6
• Input power is split and critically coupled into arm cavities
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koL=(n+1/2)
RSE with reflection gratings
• Input power is split and critically coupled into arm cavities
• Carrier exiting arm at output coupler is cancelled by carrier from other arm
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kL=(n+1/2)
RSE with reflection gratings
• Input power is split and critically coupled into arm cavities
• Carrier exiting arm at output coupler is cancelled by carrier from other arm
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RSE with reflection gratings
• Input power is split and critically coupled into arm cavities
• Carrier exiting arm at output coupler is cancelled by carrier from other arm
• Signal exiting arm at output coupler is enhanced by signal from other arm
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RSE with reflection gratings
• Input power is split and critically coupled into arm cavities
• Carrier exiting arm at output coupler is cancelled by carrier from other arm
• Signal exiting arm at output coupler is enhanced by signal from other arm
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Partially transmissive mirror couples light out of the signal extraction
cavity
RSE with reflection gratings
• Input power is split and critically coupled into arm cavities
• Carrier exiting arm at output coupler is cancelled by carrier from other arm
• Signal exiting arm at output coupler is enhanced by signal from other arm
• Signal extraction cavity has no lossy elements inside of it
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RSE with reflection gratings
• Input power is split and critically coupled into arm cavities
• Carrier exiting arm at output coupler is cancelled by carrier from other arm
• Signal exiting arm at output coupler is enhanced by signal from other arm
• Signal extraction cavity has no lossy elements inside of it
• Laser noise is filtered by arm cavities
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RSE with reflection gratings
• Input power is split and critically coupled into arm cavities
• Carrier exiting arm at output coupler is cancelled by carrier from other arm
• Signal exiting arm at output coupler is enhanced by signal from other arm
• Signal extraction cavity has no lossy elements inside of it
• Laser noise is filtered by arm cavities
101 102 103 10410-25
10-24
10-23
10-22
10-21
f / Hz
h(f
) /
Hz1/
2
AdLIGO Q.N.Low-Loss RSE Q.N.
NS-NS inspiral range 187->236 MPc
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reflective RSE reflective power recycled RSE(Drever 1995)
Other configurations with reflection gratings
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Power recycled RSE with reflection gratings
• Input power is diffractively coupled into the middle of the power recycling cavity
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Power recycled RSE with reflection gratings
• Input power is diffractively coupled into the middle of the power recycling cavity
• Each grating arm cavity forms one end of the recycling cavity
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Power recycled RSE with reflection gratings
• Input power is diffractively coupled into the middle of the power recycling cavity
• Each grating arm cavity forms one end of the recycling cavity
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Power recycled RSE with reflection gratings
• Input power is diffractively coupled into the middle of the power recycling cavity
• Each grating arm cavity forms one end of the recycling cavity
• Signal sidebands from arm cavities exit the arms in two directions
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Power recycled RSE with reflection gratings
• Input power is diffractively coupled into the middle of the power recycling cavity
• Each grating arm cavity forms one end of the recycling cavity
• Signal sidebands from arm cavities exit the arms in two directions
• Signal extraction mirror closes the signal extraction cavity path
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Power recycled RSE with reflection gratings
• Input power is diffractively coupled into the middle of the power recycling cavity
• Each grating arm cavity forms one end of the recycling cavity
• Signal sidebands from arm cavities exit the arms in two directions
• Signal extraction mirror closes the signal extraction cavity path
• Laser technical noise follows the signal everywhere
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The total power gain in the arms of the grating ring RSE (loss of 1ppm per mirror and a signal tuning of 20 degrees)
The left-most axis is the diffraction efficiency of the arm cavity gratings, the right-most axis is that of the
recycling cavity grating
Power gain dependence on diffraction efficiency
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Laser noise coupling Signal transfer function
Laser noise coupling to output
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
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reflective RSE• Grating efficiency 10ppm• Laser power 50W• Good separation of signal and laser noise
Reflection grating interferometer comparison
reflective power recycled RSE• Grating efficiency 0.001• Laser power 25W• Poor separation of signal and laser noise
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Geometry of various grating arrangements
Four basic geometries that use reflection gratings
ring cavity 1st order Littrowbeamsplitter2nd order Littrow
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Effect of seismic noise with gratings
Effect of the grating’s displacement noise depends on the geometry; it is different for reflected and diffracted
beams
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Effect of seismic noise with gratings
Effect of the grating’s displacement noise depends on the geometry; it is different for reflected and diffracted
beams
Reference surface for
reflected beam
Reference surface for diffracted beam
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Effect of seismic noise with gratings
ring cavity 1st order Littrowbeamsplitter2nd order Littrow
Primary isolation direction
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Principle axis of inertia tensor
Effect of seismic noise with gratings
ring cavity 1st order Littrowbeamsplitter2nd order Littrow
Primary isolation direction
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1% efficiency
Effect of seismic noise with gratings
Ring cavity configuration seems best suited for use in a detector:
– Phase noise due to lateral displacement of grating can be cancelled to first order at low frequencies
– Direction of maximum isolation requirement is aligned to principle axis of inertia tensor of the mass
– Holds promise of low-loss
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Cancellation of phase noise from transverse
motion
frequency
Dis
pla
cem
ent
nois
e
frequency
Dis
pla
cem
ent
nois
e
=
Input noise
total noise
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Cancellation of phase noise from transverse
motion
frequency
Dis
pla
cem
ent
nois
e
frequency
Cavit
y t
ransm
issi
on
-x
frequency
Dis
pla
cem
ent
nois
e
=
Input noise Cavity “transmission”
total noise
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Cancellation of phase noise from transverse
motion
frequency
Dis
pla
cem
ent
nois
e
frequency
Cavit
y t
ransm
issi
on
frequency
Dis
pla
cem
ent
nois
e
-x
frequency
Dis
pla
cem
ent
nois
e
=
Input noise Cavity “transmission” Output noise
total noise
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Upcoming experiments• Quantify effect of lateral displacement noise
on phase shift in various configurations
phase of specular order
phase of diffracted order
phase of twice-diffracted order
phase of twice-diffracted order with time delay
phase of specular order relative to diffracted order in
grating beamsplitter
phase of diffracted order in Littrow-mount grating
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Upcoming experiments• Quantify effect of lateral displacement noise
on phase shift in various configurations• Determine constraints for grating suspension
– longitudinal noise performance– transverse noise performance– roll noise performance– roll positioning accuracy and range
• Compare suspension requirements to Advanced LIGO suspension performance
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SummaryWith reflection gratings on core optics
comes:– Promise of low loss– Capability of very high power storage– Possibility of lower loss in the signal
extraction cavity– Possibility of higher storage-time arm
cavities– New suspension design requirements
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Empirical observation: grating loss increases with increasing efficiency
Lower diffraction efficiency gratings seem to be capable of having very low loss
grating efficiency
loss
mirror 99%grating
How will future detectors be optimized for use with diffractive optics?
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in
m
1a
1 2a a
2a
x
Consider phase shift on diffracted beam due to input beam displacement
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in
in
m
1a
2a
2b
1 2a a
2b 2a mkgx k0x sin in
x
Consider phase shift on diffracted beam due to input beam displacement
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in
m
m1a
1b
1 2a a
2b 2a mkgx k0x sin in
1b 1a k0x sinm
x
Consider phase shift on diffracted beam due to input beam displacement
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in
in
m
m1a
2a
2b
1b
1 2a a
2b 2a mkgx k0x sin in
1b 2b mkgx k0x sin in sinm
1b 1a k0x sinm
x
Consider phase shift on diffracted beam due to input beam displacement
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in
in
m
m1a
2a
2b
1b
1 2a a
sinm sin in mkgk0
2b 2a mkgx k0x sin in
1b 2b mkgx k0x sin in sinm
1b 1a k0x sinm
0
x
grating equation:
Consider phase shift on diffracted beam due to input beam displacement
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in
m
1a
2b
1 2a a
sinm sin in mkgk0
2b 2a mkgx k0x sin in
1b 2b mkgx k0x sin in sinm
1b 1a k0x sinm
grating equation:
If you just consider lateral translation of grating
x
10 22 10 12
107
kg
103
L
mkgxmkgL