1. A look at interferometer topologies that use reflection gratings
Peter Beyersdorf Stanford University
Spring 2005 LSC meeting G Z

2. 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

3. 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

4. Revisiting RSE
Bandwidth enhancement is limited by loss in the signal extraction cavity a
DBW=
rETMtITM 2
1-rITMrSEM
rITMrSEM
RSE interferometer

5. Revisiting RSE
Bandwidth enhancement is limited by loss in the signal extraction cavity a
DBW=
rETMtITM 2
1-rITMrSEM
rITMrSEM
RSE interferoemter
Loss in the signal extraction cavity is dominated by absorbtion in the optical substrates

6. 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

7. RSE with reflection gratings
Input power is split and critically coupled into arm cavities
r≈ …
h≈10-6
Lossy beamsplitter is not inside a cavity

8. 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
koL=(n+1/2)l

9. 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
koL=(n+1/2)l

10. 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

11. 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

12. 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
Partially transmissive mirror couples light out of the signal extraction cavity

13. 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

14. 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
NS-NS inspiral range
187->236 MPc

15. Other configurations with reflection gratings
reflective RSE
reflective power recycled RSE
(Drever 1995)

16. Power recycled RSE with reflection gratings
Input power is diffractively coupled into the middle of the power recycling cavity

17. 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

18. 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

19. 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

20. 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

21. 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

22. Power gain dependence on diffraction efficiency
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

23. Laser noise coupling to output
Signal transfer function

24. Reflection grating interferometer comparison
reflective RSE
Grating efficiency 10ppm
Laser power 50W
Good separation of signal and laser noise
reflective power recycled RSE
Grating efficiency 0.001
Laser power 25W
Poor separation of signal and laser noise

25. Geometry of various grating arrangements
Four basic geometries that use reflection gratings
ring cavity
2nd order Littrow
beamsplitter
1st order Littrow

26. 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

27. 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 diffracted beam
Reference surface for reflected beam

28. Effect of seismic noise with gratings
Primary isolation direction
ring cavity
2nd order Littrow
beamsplitter
1st order Littrow

29. Effect of seismic noise with gratings
Primary isolation direction
Principle axis of inertia tensor
ring cavity
2nd order Littrow
beamsplitter
1st order Littrow

30. 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
1% efficiency

31. Cancellation of phase noise from transverse motion
Input noise
Displacement noise
frequency
total noise =
Displacement noise
frequency

32. Cancellation of phase noise from transverse motion
Input noise
Cavity “transmission” x -
Displacement noise
Cavity transmission
frequency
frequency
total noise =
Displacement noise
frequency

33. Cancellation of phase noise from transverse motion
Input noise
Cavity “transmission”
Output noise x -
Displacement noise
Cavity transmission
Displacement noise
frequency
frequency
frequency
total noise =
Displacement noise
frequency

34. Upcoming experiments
Quantify effect of lateral displacement noise on phase shift in various configurations
phase of diffracted order in Littrow-mount grating
phase of
specular order
phase of specular order relative to diffracted order in grating beamsplitter
phase of
diffracted order
phase of
twice-diffracted order
phase of twice-diffracted order with time delay

35. 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

36. Summary With 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

37. Empirical observation: grating loss increases with increasing efficiency
Lower diffraction efficiency gratings seem to be capable of having very low loss
loss
mirror
grating efficiency
99%
grating
How will future detectors be optimized for use with diffractive optics?

38. Consider phase shift on diffracted beam due to input beam displacement
qin
f2a qm
f1a Dx

39. Consider phase shift on diffracted beam due to input beam displacement
qin
f2a qm
qin
f1a
f2b Dx

40. Consider phase shift on diffracted beam due to input beam displacement
f1b
qin qm qm
f1a Dx

41. Consider phase shift on diffracted beam due to input beam displacement
f1b
qin
f2a qm
qin qm
f1a
f2b Dx

42. Consider phase shift on diffracted beam due to input beam displacement
f1b
qin
f2a qm
qin qm
f1a
f2b Dx
grating equation:

43. If you just consider lateral translation of grating
qin qm
f1a
f2b Dx
grating equation: