New interferometer layout

In order to explain the functionality of the new interferometer it appears useful, to follow a stepwise description which recalls the design process. Each step provides a fully functional interferometer which may find its niche application.

In the first step the fixed part of the interferometer is reduced to only four polarizing beam splitters. Some additional retarder plates are necessary, but very thin and do not influence the optical path length. As illustrated in Figure 4.2(a), the layout is not fully Michelson- like. Beam splitting and recombination occur at different spots. It resembles much more a Mach-Zehnder interferometer. However, the measure device is still a displaced mirror which is hit under 90°, and the optical path to this mirror is travelled twice by the laser beam.

The big advantage of this layout is the extendibility to two sides without any new optics. As illustrated in Figure 4.2(b), a second laser is injected at a different spot. Then, the same optics is used to measure another axis on the opposite side.

The intention of the second step was to get rid of the Zeeman-stabilized helium-neon laser and its frequency mixing [KJM06]. The layout was modified such that a monochromatic laser is used to supply the interferometer (see Figure 4.3(a) and 4.3(b)). The light runs like in a homodyne interferometer, but before recombination each beam is frequency-shifted by an AOM. Both beams are shifted to provide a symmetric dependence on possible drifts of the AOM. Though, each beam has a slightly different frequency, typically 40.05 MHz and 39.95 MHz, resulting in a 100 kHz beating.

In the third step, see Figure 4.4(a) and 4.4(b), the AOMs were brought out of the inter- ferometer to avoid the heating of typically 50 mW. The laser beam is split outside the interferometer and both parts are shifted by different frequencies. These two beams enter the interferometer at different spots. To provide a working interferometer two additional optical elements are necessary to make the corresponding beams overlapping. In this layout the beams for the two axes cannot be separated spatially. All separation has to be done by polarization.

In the fourth step this spatial separation is re-established as illustrated in Figure 4.5. At the same time the practical realization of the layout is faced. So far all mirrors and polarizing beam splitters were assumed to be (infinitely) thin surfaces. However real beam splitters require a substrate. A common splitter is a cube that consists of two right angled prisms that are in contact on their hypotenuse-surfaces. The contact got a special coating which defines the reflection, transmission and polarization properties. These cubes match the theoretical thin surfaces quite well. However the perpendicularly passed entry and exit surfaces cause unavoidable reflections. This causes periodic non- linearities [Wu03]. Consequently, surfaces perpendicular to the beam should be avoided. Additionally those cubes deviate the transmitted beam due to imperfect manufacturing.

4.1. INTERFEROMETER

Naming conventions:

First letter – position on z-axis: L – lower side of the map and

close to the laser; M – middle part, used for

reference beams; U – upper side of the map; T – top, close to the detector

and serves for recombination of the beams.

Second letter – position on x-axis:

A – A-axis of spectrometer, the

γ-beam arrives here first. on

the left side of the layout-map.

B – B-axis of spectrometer,

Third letter – function: P – polarizing beam splitter, R – reference beam splitter

(non-polarizing), D – deviation of the beam, B – balancing, to provide same

path length inside material, I – injection of the laser beam. Exceptions are LMM and UMM – main mirrors and RRP – reference roof prism.

Figure 4.5: The final interferometer Layout in a true to scale scheme. The optics is realized by substrates (grey boxes) with parallel and flat surfaces that got different coatings: full mirror (solid black lines), polarization dependant mirror (dotted line), non-polarizing semi-mirror (dashed line) or anti-reflection (no line). Retarder plates are not drawn. All beams lie within a plane, except the second half of the reference beams, that are shifted through the roof prism RRP by 7 mm to a parallel plane. See Figure 4.4(b) for the direction of the light. The coordinate system is described in subsection 2.1.6.

With these deviations the proposed layout is difficult to build, as each optics is used for several beams. Hence, there are more alignment constraints than free parameters, and no deviation can be compensated. Possible substrates for the reflection surfaces are flat cuboid substrates. They can be produced sufficiently flat, such that the beam is not deviated. If placed in a 45°-angle they displace the beam and can provide all necessary reflective properties by different coatings (none, polarization dependent and full reflection). Furthermore a stable mounting (see section 4.1.8) is easier with this solid cuboid-shaped substrates. The layout provides the possibility to be upgraded with an additional beam to monitor the effective length of the goniometer arm. However, at the current stage this does not seem to be necessary, and is not scheduled so far.

Further variations of the basic layout were studied. The one described in step four and Figure 4.5 was chosen as best compromise. It was found to be the only one providing all of the following advantages.

• The beams towards the retro reflectors are symmetric. If all four beams to the retro- reflectors have the same distance to the goniometer axis, systematic effects can be studied much easier, and some drift effects are even compensated by this symmetry. • Frequencies are separated spatially throughout the interferometer. The alternative separation by polarization can never be perfect and would hence cause periodic non-linearities.

• A more stable laser than those based on the Zeeman-effect can be used.

• No heat sources inside the interferometer. Any AOM inside the interferometer would cause thermal gradients and eventually interferometer instability.

• The layout can easily be equipped with reference beams.

• There are no surfaces perpendicular to the beam. Consequently there are no residual reflection which would cause periodic non-linearities.

However, it implies also some negative aspects.

• There are additional optics necessary to make all paths to be of the same length. Even though the total path length difference (Bsig−Bref)−(Asig−Aref) would be

balanced, small asymmetries introduced during the mounting process would cause asymmetric drifts. This would reduce the auto-compensation feature.

• The optical paths are not of the same length. As the interferometer is operated in vacuum only, this is less critical. Only small residual effects caused by the beam divergence remain. To monitor these effects over time, the length of the reference beams was chosen to be asymmetric as well.

4.1. INTERFEROMETER

• Parallel flat optics can shift the optical path length when rotated around an axis which is not parallel to the beam. This effect is much stronger when the substrates are passed in an 45° angle than passing them perpendicular. Consequently the substrates must be fixated rigidly concerning rotation. However, the reference beams compensate most of this effect.

• The retarder plates can not be fixed onto the main optics – as it would be possi- ble with beam splitter cubes. Consequently the retarder plates require individual mountings. Fortunately they are very thin, consequently any drift has no significant influence on the optical path length. And finally most retarder plates are monitored by the reference beams. A small influence on the polarization does not matter, as polarization is only used for intensity optimization.

Auto compensation

One big feature of the layout is the auto-compensation of drifts of the optics. If any of the main optics (polarizing beam splitter or main mirror) drifts, the interferometer of one goniometer axis will provide a false readout. However, exactly the same drift is also seen by the other interferometer side since it uses the same element. This will result in the same false readout. Consequently the difference is independent from any drift. As the Gams

spectrometer depends only on the angle of the two crystals relative to each other, the total result does not depend on any drift. However this is only true, if both goniometer arms are of the same length. If they are not, any drift is suppressed by the ratio between the arm length difference and the average arm length. Considering the design of the interferometer arm and the retro reflectors, achieving the same interferometer arm length, i.e. distance of the optical centre or the corner cubes, should be feasible within 0.1 mm or better. Together with an arm length of 300 mm this results in a drift suppression of 1/3000 or better. Considering the target accuracy of 2_×10−8 _{this means e.g. for the main mirror}

a possible drift of _∼ 50 nm without consequence. Without the compensation effect a stability of_∼20 pm would be required.