Optics mounting and alignment for the central optical bench of the dual cavity enhanced light-shining-through-a-wall experiment ALPS II

Li-Wei Wei; Kanioar Karan; Benno Willke

doi:10.1364/AO.401346

Applied Optics
Vol. 59,
Issue 28,
pp. 8839-8847
(2020)
•https://doi.org/10.1364/AO.401346

Optics mounting and alignment for the central optical bench of the dual cavity enhanced light-shining-through-a-wall experiment ALPS II

Li-Wei Wei, Kanioar Karan, and Benno Willke

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Li-Wei Wei, Kanioar Karan, and Benno Willke, "Optics mounting and alignment for the central optical bench of the dual cavity enhanced light-shining-through-a-wall experiment ALPS II," Appl. Opt. 59, 8839-8847 (2020)

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Abstract

Any Light Particle Search II (ALPS II) is a light-shining-through-a-wall experiment seeking axion-like particles. ALPS II will feature two 120 m long linear optical cavities that are separated by a wall and support the same photon mode. The central optical bench at the core of the experiment will be equipped with a light-tight shutter and two planar mirrors for the cavities. We show that the mounting concept for ALPS II provides sufficient angular stability and verify that a simple autocollimator assisted alignment procedure for crucial components of the ALPS II optical cavities can lead to the required overlap of the cavity eigenmodes. Furthermore, we show that mounted quadrant photodiodes added to the optical bench can have sufficient stability to maintain this overlap even without a clear line of sight between the two optical cavities.

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Fig. 1. Schematic and Feynman diagram of the ALPS II experiment, in which

$\gamma$

represents a photon field,

${\gamma ^*}$

represents a virtual photon field supplied by the magnetic field

$B$

, and

$\phi$

is the axion field. M, mirror; W, wall (a light-tight shutter in practice); solid red line, axion-producing photon field; dotted red line, axion-regenerated photon field.

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Fig. 2. ALPS II control schemes on lasers and optical cavities for the TES mode and the HET mode. PDH, Pound–Drever–Hall laser-frequency stabilization technique [28,29].

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Fig. 3. Schematic of the ALPS II central optical bench. BS, beam-splitter; QPD, quadrant photo-detector.

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Fig. 4. Schematics of the optics setup for the tests. NPRO, non-planar ring oscillator; PD, photo-detector; PZT, piezoelectric transducer.

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Fig. 5.

$\Pi$

-shaped clamping frame with spring-loaded ball-tip screws. The force exerted by each screw is specified to be 8.5 N and 14 N at the beginning and the end of its 0.8 mm travel range.

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Fig. 6. Autocollimator measurement time series on the angle between a

$\Pi$

-clamped rectangular mirror and a commercial high-stability mount. Raw angle (yaw/pitch) measurements are sampled at

$\approx 110\;{\rm ms}$

intervals and plotted in black using the left

$y$

axis. Moving-averaged curves with 1000 data samples are plotted in blue using the

$y$

axes on the right for better correlation visibility. The temperature (in black) and relative humidity (R.H., in blue) data are sampled every 10 min. A strong correlation of

${-}{0.75}$

(Pearson correlation coefficient) exists between the pitch angle (averaged to 10 min sampling period) and relative humidity, to be compared with the correlation of

${-}{0.17}$

between the yaw angle and relative humidity. The correlation to temperature is

${-}{0.05}$

for yaw and

${-}{0.14}$

for pitch. The correlation calculations are not optimized with phase shifts.

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Fig. 7. Histograms of the raw angle measurements in Fig. 6. The bin width is

$0.1\;{\unicode{x00B5} \rm rad}$

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Fig. 8. Cavity eigenmode scan measurement result. The higher-order-mode spacing corresponds to

$\approx 2\;{\rm ms}$

in the scan. The higher-order-mode spacing of the test cavities is

$\approx 0.1 {\rm FSR}$

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Fig. 9. Mounted quadrant photodiode assembly. The quadrant photodiode is sandwiched between a baseplate and a cap with screws. The baseplate translates on the XY plate for alignment purposes and is fixed once aligned.

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Fig. 10. Mounted quadrant photodiode modules reading comparison.

$\Delta {\rm X}$

refers to the positional readout difference in the horizontal plane, and

$\Delta {\rm Y}$

is the vertical plane;

$\Delta {\rm X}$

and

$\Delta {\rm Y}$

are zeroed to their mean values in the plot for better visualization. Air temperature and relative humidity are also shown to signify potentially increased stability of the setup when operating in vacuum.

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Fig. 11. Eigenmode content versus quadrant photodiode readings with intentional tilts introduced to curved mirror M1.

$\delta {x_{{\rm eig}}} = [{{\rm X}^2} + {{\rm Y}^2}{]^{1/2}}$

, and the origins of quadrant photodiode readings X and Y are defined with respect to the minimal

${\epsilon _1}$

measured in the cavity eigenmode scan. The same

$\epsilon$

measurements in the

$y$

axis are plotted with respect to the two quadrant photodiode measurements as the

$x$

axis. The perturbative model curve uses Eq. (2) with

${\omega _{0,{\rm eig}}} = 1008\;{\unicode{x00B5}{\rm m}}$

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Equations (11)

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\begin{aligned} P & \propto {[g_{a γ γ} \cdot \int B d L_{B}]}^{4} [β_{1 | 2} \cdot β_{3 | 4}] \\ \approx {[g_{a γ γ} \cdot \int B d L_{B}]}^{4} {[\frac{F}{π}]}^{2}, \end{aligned}

\begin{aligned} ϵ \equiv ϵ_{1} + ϵ_{2} \approx \frac{| U_{1} |^{2}}{| U_{0} |^{2}} + \frac{| U_{2} |^{2}}{| U_{0} |^{2}} \\ \approx {(\frac{δ α_{e i g}}{θ_{0, e i g}})}^{2} + {(\frac{δ x_{e i g}}{w_{0, e i g}})}^{2} + {(\frac{δ z_{0, e i g}}{2 \cdot z_{R}})}^{2} + {(\frac{δ w_{0, e i g}}{w_{0, e i g}})}^{2} \\ \leq {(\frac{5 µ r a d}{56.5 µ r a d})}^{2} + {(\frac{0.1 m m}{6 m m})}^{2} + {(\frac{1 m}{2 \cdot 106 m})}^{2} + {(\frac{0.2 m m}{6 m m})}^{2} \\ \approx 0.78 % + 0.28 % + 0.0022 % + 0.11 % \approx 1.17 %, \end{aligned}

z_{R} = 3 m, ω_{0, e i g} = 1008 µ m, a n d θ_{0, e i g} = 336 µ r a d

ϵ_{1} \leq {(\frac{5 µ r a d}{336 µ r a d})}^{2} \approx 2.2 \times 10^{- 4}

ϵ_{2} \approx {(\frac{0.5 m}{2 \cdot 3 m})}^{2} \approx 0.007.

ϵ_{k} = \sum_{i, j \in N}^{i + j = k} {\iint U_{00} (x, y, 0) \cdot U_{i j}^{*} (x + Δ_{eig}, y, δ z_{0, eig}) d x d y},

E_{1 | 2} = t_{1} \cdot E_{L} + σ_{1 | 2} \cdot E_{1 | 2},

σ_{1 | 2} = r_{1} \cdot r_{2} \cdot e x p [- α_{1 | 2} \cdot 2 L_{c}]

\sqrt{β_{1 | 2}} \equiv \frac{E_{1 | 2}}{E_{L}} = \frac{t_{1}}{1 - σ_{1 | 2}} \approx \frac{t}{1 - r^{2}} = \frac{1}{t} \approx \sqrt{\frac{F}{π}},

E_{3 | 4} = E_{R} + σ_{3 | 4} \cdot E_{3 | 4}, E_{D} = t_{4} \cdot E_{3 | 4},

\sqrt{β_{3 | 4}} \equiv \frac{E_{D}}{E_{R}} = \frac{t_{4}}{1 - σ_{3 | 4}} .

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Equations (11)

Applied Optics