Suspended diffractive cavity investigations

Suspended diffractive cavity investigationsBryan BarrInstitute for Gravitational ResearchOverview

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?

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

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…

Option 1:1st order Littrow mountInput light enters via the 1st diffracted order pathGrating = 2 port deviceRequires high efficiency, low loss grating Option 2:2nd order Littrow mountInput light enters via the 2nd diffracted order path1st order is normal to the grating surfaceGrating = 3 port deviceRequires low 1st order efficiency, low loss gratingDiffractive Cavity OptionsConventional2nd Order LittrowConventional vs. Diffractive Couplersrt=,reflection,transmissiondiffractionConventionalDiffractiveConventional vs. Diffractive CavitiesAdditional 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

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

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

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

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.

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?

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

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

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

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

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…

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

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

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…

Success!!! …or is it?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

Rotational Twisting Only - Success!!!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

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?

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