# Design and Construction of a Variable-Angle Three-Beam Stimulated Resonant Photon Collider toward eV-Scale ALP Search

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## Abstract

**:**

## 1. Introduction

## 2. Kinematics in Three-Beam Stimulated Resonant Photon Collider, ${}^{\mathrm{t}}\mathrm{SRPC}$

## 3. Basic Design to Realize Variable Collision Angles

## 4. Concrete Designs for the Large- and Narrow-Angle Setups

## 5. Verification of the Rotary Stage System

## 6. Realistic Sensitivity Projections

## 7. Conclusions and Future Plans

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Concept of a three-beam stimulated resonant photon collider (${}^{\mathrm{t}}\mathrm{SRPC}$) with focused coherent beams [21]. The two focused creation laser beams (green) at the incident angle ${\theta}_{c}$ produces an ALP resonance state and the focused inducing laser beam (red) stimulates its decay. The creation photons have different energies ${\omega}_{1}$ and ${\omega}_{2}$ from the central value of ${\omega}_{c}$ and different incident angles ${\vartheta}_{1}$ and ${\vartheta}_{2}$ from ${\theta}_{c}$, respectively. Similarly, the inducing laser (red) with a central wavelength of ${\omega}_{i}$ has part of the beam with ${\omega}_{4}$, increasing the emission probability of the signal photon of ${\omega}_{3}$ (blue) via energy-momentum conservation.

**Figure 2.**Two proposals for variable angle mechanisms. The green beams are creation lasers, the red beam is an inducing laser, and the blue beam indicates signal photons.

**Left**: parabolic mirror type where the collision angle is changeable by changing the incident position of lasers.

**Right**: rotating stage type where the collision angle is changeable by assembling a beam focusing system on multiple rotary stages.

**Figure 3.**Variable angle mechanism using a rotary stage. The incident angle is varied by rotating a stage assembling a beam-focusing system with a periscope (PS) and a parabolic mirror (PM). By using a periscope (PS), the angle is changeable only by rotating the periscope (PS) and the mirror (M) on the x-axis rail stage in front of PS. By setting the parabolic mirror’s focal point at the center of the rotary stage (RS), the collision point remains fixed even when the incident angle is varied. The focal spots can be checked using a monitoring camera.

**Figure 4.**Side views of designed variable-angle three-beam stimulated resonant photon colliders for large-angle (

**left**) and narrow-angle (

**right**) setups. Detailed explanations are found in the main text.

**Figure 5.**Collisional geometries viewed from the top. (

**a**) Large-angle setup from ${\theta}_{c}=24.8$ deg (

**left**) to ${\theta}_{c}=47.9$ deg (

**right**) and (

**b**) narrow-angle setup from ${\theta}_{c}=9.3$ deg (

**left**) to ${\theta}_{c}=24.8$ deg (

**right**). The details can be found in the main text.

**Figure 6.**

**Left**: top view of the camera system on the top layer of the rotary stages to monitor focal spots of all the three lasers c1, c2, and i.

**Right**: picture assembling all the components for the large-angle setup. The details can be found in the main text.

**Figure 7.**Picture of large-angle setup (

**left**) and focal images of three individual beams (

**right**) when lasers with a common beam diameter of 5 mm are focused into IP at ${\theta}_{c}=24.8$ degree. In the picture, the optical paths of the three beams, consisting of the creation beam (c1), the creation beam (c2), and the inducing beam (i), as well as the signal photon line (s) are drawn. The middle column shows the images of three individual lasers when they hit the crossed point between two thin target wires of a 10 $\mathsf{\mu}$m diameter.

**Figure 8.**Picture of large-angle setup (

**left**) and focal images of three individual beams (

**right**) when lasers with a common beam diameter of 5 mm are focused into IP at ${\theta}_{c}=35.5$ degree. The other details are the same as in Figure 7.

**Figure 9.**Picture of large-angle setup (

**left**) and focal images of three individual beams (

**right**) when lasers with a common beam diameter of 5 mm are focused into IP at ${\theta}_{c}=47.9$ degree. The other details are the same as in Figure 7.

**Figure 10.**Incident angles of the inducing beam ${\theta}_{i}$ as a function of ALP masses ${m}_{a}$ which are determined by incident angles of creation beams ${\theta}_{c}$. Three combinations of laser wavelengths for fundamental, second harmonic, and third harmonic cases. Namely, beginning with 800 nm (Ti:Sapphire) for two creation beams and 1064 nm (Nd:YAG) for an inducing beam expressed as $800\times 2+1064$ nm (red), we extend the search to those with $400\times 2+532$ nm (blue) and $267\times 2+355$ nm (magenta). Depending on the combinations between the two angle setups and laser wavelengths, accessible mass ranges are different. This figure shows projections to cover from 0.5 to 6.9 eV.

Item | Parabolic Mirror Type | Rotary Stage Type |
---|---|---|

Adjustment | easy | difficult |

Size | large | compact (vacuum chamber compatible) |

Angle range | narrow | wide |

Focal length | angle-dependently variable | fixed |

Flexibility | low (custom-ordered mirror) | high (catalog items) |

**Table 2.**Experimental parameters used to numerically calculate the upper limits on the coupling–mass relations. $(*)$ We note that the focal length of the inducing beam in the case of the narrow-angle setup must slightly vary in principle because of the nature of the parabolic mirror. However, since the incident position with respect to the focusing mirror does not vary a lot, for simplicity, we assume a common focal length to evaluate the sensitivity.

Parameters | Values |
---|---|

Two equal creation laser pulses | |

Central wavelength of creation laser ${\lambda}_{c}$ | 800 nm ($\omega $)/400 nm ($2\omega $)/267 nm (3$\omega $) |

Relative linewidth of creation laser, $\delta {\omega}_{c}/<{\omega}_{c}>$ | ${10}^{-2}$ |

Duration time of creation laser, ${\tau}_{c}$ | 40 fs |

Creation laser energy per ${\tau}_{c}$, ${E}_{c}$ | 1 mJ |

Beam diameter of creation laser beam, ${d}_{c}$ | 0.005 m |

Focal length of narrow-angle setup | ${f}_{c}=0.18$ m |

Focal length of large-angle setup | ${f}_{c}=0.10$ m |

Polarization | left-handed circular polarization |

One inducing laser pulse | |

Central wavelength of inducing laser ${\lambda}_{i}$ | 1064 nm ($\omega $)/532 nm ($2\omega $)/355 nm (3$\omega $) |

Relative linewidth of inducing laser, $\delta {\omega}_{i}/<{\omega}_{i}>$ | ${10}^{-4}$ |

Duration time of inducing laser beam, ${\tau}_{i}$ | 9 ns |

Inducing laser energy per ${\tau}_{i}$, ${E}_{i}$ | 100 mJ |

Beam diameter of inducing laser beam, ${d}_{i}$ | $0.005$ m |

Focal length of narrow-angle setup $(*)$ | ${f}_{i}=0.19$ m |

Focal length of large-angle setup | ${f}_{i}=0.20$ m |

Polarization | right-handed circular polarization |

Overall detection efficiency, $\u03f5$ | 5% |

Number of shots per collision angle, ${N}_{shots}$ | ${10}^{4}$ shots |

$\delta {N}_{noise}$ | 50 |

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**MDPI and ACS Style**

Hasada, T.; Homma, K.; Kirita, Y.
Design and Construction of a Variable-Angle Three-Beam Stimulated Resonant Photon Collider toward eV-Scale ALP Search. *Universe* **2023**, *9*, 355.
https://doi.org/10.3390/universe9080355

**AMA Style**

Hasada T, Homma K, Kirita Y.
Design and Construction of a Variable-Angle Three-Beam Stimulated Resonant Photon Collider toward eV-Scale ALP Search. *Universe*. 2023; 9(8):355.
https://doi.org/10.3390/universe9080355

**Chicago/Turabian Style**

Hasada, Takumi, Kensuke Homma, and Yuri Kirita.
2023. "Design and Construction of a Variable-Angle Three-Beam Stimulated Resonant Photon Collider toward eV-Scale ALP Search" *Universe* 9, no. 8: 355.
https://doi.org/10.3390/universe9080355