A look at interferometer topologies that use reflection gratings

Peter BeyersdorfStanford University

Spring 2005 LSC meetingG050171-00-Z

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

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

Revisiting RSE

RSE interferometer

Bandwidth enhancement is limited by loss in the signal extraction cavity

101 102 10310-25

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f / Hz

h(f

) /

Hz1/

2

1- aBW=BW=

rETMtITM2

1-rITMrSEM 1-rITMrSEM

rITMrSEM

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

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

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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

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

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

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

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

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

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

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

reflective RSE reflective power recycled RSE(Drever 1995)

Other configurations with reflection gratings

Power recycled RSE with reflection gratings

• Input power is diffractively coupled into the middle of the power recycling cavity

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

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

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

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

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

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

Laser noise coupling Signal transfer function

Laser noise coupling to output

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

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

Geometry of various grating arrangements

Four basic geometries that use reflection gratings

ring cavity 1st order Littrowbeamsplitter2nd order Littrow

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

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

Effect of seismic noise with gratings

ring cavity 1st order Littrowbeamsplitter2nd order Littrow

Primary isolation direction

Principle axis of inertia tensor

Effect of seismic noise with gratings

ring cavity 1st order Littrowbeamsplitter2nd order Littrow

Primary isolation direction

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

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

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

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

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

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

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

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?

in

m

1a

1 2a a

2a

x

Consider phase shift on diffracted beam due to input beam displacement

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

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

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

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

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