Suspended diffractive cavity investigations

1. Suspended diffractive cavity investigations Bryan Barr Institute for Gravitational Research

2. Overview • Diffractive Optics • Overview of diffractive cavity basics • Experimental options • The Glasgow JIF laboratory • Commissioning the diffractive cavity • Length sensing and control • Getting the most from the system • Results and discussion • Expected and unexpected – but all interesting • Plans • What’s next?

3. All Reflective Optics • Why use diffraction gratings? • Conventional interferometers use partially transmitting optics (mirrors + beam-splitters) to split laser light along different paths with known phase shifts • Diffraction gratings can also split light beams with known phase shifts • Using reflection gratings the light need not pass through the mirror substrate • Advantages over conventional systems • Non-transmissive materials can be used – improved thermal noise • Thermal lensing of substrates not an issue. • What’s the catch? • More complex geometry • Complicated phase + length sensing relations

4. Traditional Optical Cavities • Optical cavities are the simple building-blocks of gravitational wave interferometers • Conventional instruments use highly reflective mirrors to achieve high finesse arm cavities • This allows high power build up in the arms • To use diffractive optics we must be able to produce a cavity with high finesse using an all-reflective input coupler…

5. Option 1: 1st order Littrow mount Input light enters via the 1st diffracted order path Grating = 2 port device Requires high efficiency, low loss grating Option 2: 2nd order Littrow mount Input light enters via the 2nd diffracted order path 1st order is normal to the grating surface Grating = 3 port device Requires low 1st order efficiency, low loss grating Diffractive Cavity Options

6. Conventional 2nd Order Littrow Conventional vs. Diffractive Couplers r t = , reflection , transmissi on diffractio n

7. Conventional Diffractive Conventional vs. Diffractive Cavities

8. Additional Diffractive Properties • Translational effects • The phase of a diffracted field shifts if the beam translates across the grating : 360 degrees shift per grating period d • Well known effect • e.g. acousto-optic modulators • Angular effects • In a conventional cavity misaligning the input coupler simply misaligns the cavity • In a diffractive cavity misaligning the input coupler also misaligns the effective input pointing

9. JIF Laboratory – Simple Layout • Basic layout of the Glasgow laboratory • The aim: build and operate a fully suspended diffractive cavity on a prototype scale • Want finesse comparable to a conventional cavity • Investigate length sensing and control signals • Investigate translational effects • Investigate alignment effects on a suspended instrument

10. Reconfiguring The Optical Layout • Tasks (mechanical/optical): • Add beam-splitter (dual suspension) • Move corner steering mirror (dual) • Add final steering mirror (dual) • Replace silica optic with diffractive coupler (triple suspension) • Swap power recycling mirror (not shown) for blank lens to preserve mode-matching • Adjust mode-matching for diffractive cavity • We run a multi-purpose lab. Should be able to swap between experiments with minimum effort

11. Reconfiguring The Electronics • Local controls • The JIF suspension alignment system is based on the GEO600 local control set-up • 7 new rack-mounted modules were commissioned to control the new cavity • An additional module was added to the M1D controller to provide roll alignment control

12. Inside The Diffractive Tank • The diffractive optic is a 1 inch optic with a 1x1cm over-coated grating. It is mounted in a jig attached to a standard ‘dummy’ mass.

13. Length Sensing and Control • Once the diffractive cavity is in place and aligned… • …we need to implement a global control scheme • Traditional cavities use the PDH approach • Can we implement the same thing for diffractive cavities?

14. Extracting More Information • Conventional non-resonant sideband approach • Ports c1 and c3 give good information • Sidebands do not reach the photodetector at port c2t • We can only probe 2 of the 3 ports • Partially resonant sideband approach • Choose a sideband frequency close to the cavity FSR • Some sideband power leaks through to c2t

15. Interesting Diffractive Cavity Feature • Unbalanced signals • Created diffractive cavity model from the earlier equations – ideal grating • Chose reasonable value for eta_1 • Chose mid-range value for eta_2 to emphasise unbalanced effect • Conventional cavity reflected signal • Diffractive cavity port c1 + c3 signals

16. Measured and Modelled – Forward Port • Comparison of the demodulated signals at port c3 • Note: differences between the plots are due to the additional partially resonant sidebands in the measured signal – only one set of sidebands used in the model

17. Measured and Modelled – Reflected Port • Comparison of the demodulated signals at port c1 • Note: the signals at the back reflected port behave very much like amplitude modulation signals – with a bit of phase modulation apparent near the minimum

18. Measured and Modelled - Throughput • Comparison of the demodulated signals at port c2t • Symmetrical -> zero crossing corresponds to centre of resonance • So we have good qualitative agreement between measured and modelled, but what about the relative signal sizes…

19. RF Demodulated Signal Responses • Model adjusted for losses in steering optics, pick-offs etc • DC power measurements for the resonant condition were made at each port • Model grating parameters were carefully adjusted within specification errors • Once the measured and modelled DC levels match the slopes of the demodulated signals can be compared • The relative gradients of the slopes – normalised to Through signal

20. Translational Effects • With these signals we can lock the cavity… • Next step is to investigate the performance of the locked cavity • In particular, what happens if we scan the grating from side to side? • We bonded a magnet to the side of the aluminium holder and set up a coil… • As mentioned before, the theory states that moving a grating from side to side will modulate the phase of the diffracted beam • For a small modulation (i.e. motion << one grating period) the forward signal should have an f response to side displacement – Birmingham/ Hannover • Larger displacements can be more complicated due to cavity resonance • Won’t go into mathematical detail here

21. Side to Side Displacement • The side coil provided side movement, and the global control coils were used to cancel longitudinal twisting… • Lock cavity, inject peak into side, minimise longitudinal signal using rear coils • An independent measurement of the side to side motion indicates a clear 1/f^2 slope – exactly what one would expect from a freely suspended mass • The demodulated forward response of the signal will thus be expected to produce a 1/f response to side-coil driving voltage…

22. Success!!! …or is it?

23. What’s Happening? • Given the measured displacement we can predict how large the demodulated forward signal should be… our measurement was approx 700 times too large! • The problem lies with the alignment of the input coupler and the variation of the input pointing • If the input coupler rotates, then the mode resonating inside the cavity translates across the coupler • Thus the phase of the field coupling out of the cavity will be shifted by a different amount than the side-motion induced input coupling shift • There is also no suppression of this effect by the cavity resonance

24. Rotational Twisting Only - Success!!!

25. Conclusion • Demonstrated that the coupling relations for diffractive cavities are well understood • Shown that a suspended diffractive cavity can be locked quite simply using existing length sensing and control techniques • Experimental evidence that translational motion of the beam across the input coupler can be detected on the length sensing and control signals for a grating cavity • Also, we have indications that alignment and cavity geometry may be even more important that we thought for diffractive systems

26. Future Plans • Finalise the translational work • Need more understanding of the Through and Reflected responses • Alignment control • Currently have a project student implementing an auto-alignment sensing system for the diffractive cavity • Wavefront sensing • Polarisation • Gratings have different properties for different polarisations • How are the control signals affected?

27. Thanks! • Glasgow: • B. Barr, M. Edgar, M. Plissi, J. Nelson, K. Strain • Hannover • O. Burmeister, M. Britzger, K. Danzmann, R. Schnabel • Jena • T. Clausnitzer, F. Brückner, E. Kley, A. Tünnermann