**5. Conclusions**

The evolution of the depth profiles with the fluence of the refractive index in YAG crystals were studied under 200 MeV <sup>136</sup>Xe14<sup>+</sup> ion irradiation by the prism-coupling and the end-face coupling methods, in which various WG modes were detected. The index depth profiles were determined so that the observed WG modes were reproduced. Since the index can be changed with the damage and/or the stress change induced by the irradiation, the index depth profiles provide the depth profiles of damage and/or stress changes induced by ion irradiation and the evolutions with the ion fluence.

At the lowest fluence of 1 <sup>×</sup> <sup>10</sup><sup>11</sup> ions/cm<sup>2</sup> , a weak index enhancement was induced at the depth of 6 µm, which does not match either of *S*<sup>e</sup> maximum nor *S*<sup>n</sup> maximum. With increasing the fluence, the peak turns to decrease. At 1 <sup>×</sup> <sup>10</sup><sup>12</sup> ions/cm<sup>2</sup> , the index enhancement is induced at the index plateau near the surface. The enhancement soon turned to decrease with the fluence. Then both the surface plateau and the 6 <sup>µ</sup>m dip reduce the index with the fluence. At the highest fluence of 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> , a new dip appeared at the depth of 13 µm, which matched to the peak of *S*n.

Index changes were perceived at three different depth regions; (i) a sharp dip at 13 µm in depth, which is ascribed to the nuclear stopping *S*<sup>n</sup> peak, (ii) a plateau near the surface at 0–3 µm, which can be ascribed to the electronic stopping *S*e, since *S*<sup>e</sup> has a very broad peak at the surface, and (iii) a broad peak at 6 µm in depth. Since the last peak is ascribed to neither of *S*<sup>e</sup> nor *S*<sup>n</sup> peak, it could be attributed to the synergy effect of *S*<sup>e</sup> and *S*n.

**Author Contributions:** Conceptualization, XRD measurements, Manuscript writing, H.A.; Sample preparation, F.C.; SHI irradiation, N.O. and N.I.; Refractive index measurements, R.L. and F.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was supported by JSPS-KAKENHI Grant Number 18K04898.

**Acknowledgments:** A part of the study was supported by the Inter-organizational Atomic Energy Research Program through an academic collaborative agreement among JAEA, QST, and the Univ. of Tokyo. Also the other part was carried out under the Common-Use Facility Program of JAEA. The authors are grateful to the staff of the accelerator facility at JAEA-Tokai for their help. The authors thank China Scholarship Council for supporting RL to stay for one year in NIMS, Japan.

**Conflicts of Interest:** The authors declare no conflict of interest.
