*3.2. Refractive Index Profiling*

Figure 5 exhibits depth profiles of the refractive index in undoped YAG crystals at various ion fluences. The data in the TM configuration are shown, while those in the TE mode are mentioned later. A chained horizontal line at 1.8295 indicates the index in the unirradiated state at the wavelength of 632.8 nm from literature [16]. After the irradiation to 1 <sup>×</sup> <sup>10</sup><sup>11</sup> ions/cm<sup>2</sup> , a very weak and broad enhancement peak was observed at 6 µm in depth with the full width at half maximum (FWHM) of ~4 <sup>µ</sup>m. Since the deviation from the unirradiated value was so small for the data at 1 <sup>×</sup> <sup>10</sup><sup>11</sup> and 3 <sup>×</sup> <sup>10</sup><sup>11</sup> ions/cm<sup>2</sup> that the deviation from the unirradiated value was plotted with five times magnification around the unirradiated value. *Quantum Beam Sci.* **2020**, *4*, x FOR PEER REVIEW 8 of 13

**Figure 5.** Depth profiles of refractive indices of YAG irradiated with 200 MeV Xe14+ ions to various fluences ranging from 1 × 1011 ions/cm2 to 5 × 1013 ions/cm2, determined by the prism coupling and the end-face coupling method. All the polarizations are in the transverse magnetic (TM) configuration. A chained horizontal line indicates the index in the unirradiated state of 1.8295 at the wavelength of 632.8 nm from literature. Since the deviation from the unirradiated value was so small for the data of 1 × 1011 and 3 × 1011 ions/cm2, the deviations were 5 times multiplied and added to the unirradiated value. For references, the depth profiles of electronic and nuclear stopping powers *S*e and *S*n are plotted with the right axis in the units of keV/nm. A horizontal broken line denotes the threshold *S*<sup>e</sup> value for the track formation in YAG. **Figure 5.** Depth profiles of refractive indices of YAG irradiated with 200 MeV Xe14<sup>+</sup> ions to various fluences ranging from 1 <sup>×</sup> <sup>10</sup><sup>11</sup> ions/cm<sup>2</sup> to 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> , determined by the prism coupling and the end-face coupling method. All the polarizations are in the transverse magnetic (TM) configuration. A chained horizontal line indicates the index in the unirradiated state of 1.8295 at the wavelength of 632.8 nm from literature. Since the deviation from the unirradiated value was so small for the data of <sup>1</sup> <sup>×</sup> <sup>10</sup><sup>11</sup> and 3 <sup>×</sup> <sup>10</sup><sup>11</sup> ions/cm<sup>2</sup> , the deviations were 5 times multiplied and added to the unirradiated value. For references, the depth profiles of electronic and nuclear stopping powers *S*e and *S*n are plotted with the right axis in the units of keV/nm. A horizontal broken line denotes the threshold *S*e value for the track formation in YAG.

Figure 6 shows four different images (i)–(iv) at four different fluences (1 × 1011, 1 × 1012, 1 × 1013, and 5 × 1013 ions/cm2). From left to right, (i) the experimental index depth profiles used for the endsurface intensity calculations, which are the same as shown in Figure 5, (ii) the optical microscopy images of the end-surface without the guided light, (iii) experimental, and (iv) calculated results of the spatial distributions of the guided light intensity at the end-surfaces. In the optical images of the end-surfaces without the guided light (ii), the near surface regions exhibit different color compared with the bulk parts, which are ascribed to the different indices induced by the ion irradiation. Color changes are stronger for higher ion fluences. Figure <sup>6</sup> shows four different images (i)–(iv) at four different fluences (1 <sup>×</sup> <sup>10</sup>11, 1 <sup>×</sup> <sup>10</sup>12, 1 <sup>×</sup> <sup>10</sup><sup>13</sup> , and 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> ). From left to right, (i) the experimental index depth profiles used for the end-surface intensity calculations, which are the same as shown in Figure 5, (ii) the optical microscopy images of the end-surface without the guided light, (iii) experimental, and (iv) calculated results of the spatial distributions of the guided light intensity at the end-surfaces. In the optical images of the end-surfaces without the guided light (ii), the near surface regions exhibit different color compared with the bulk parts, which are ascribed to the different indices induced by the ion irradiation. Color changes are stronger for higher ion fluences.

**Figure 6.** (Left to right) Index profiles used for the calculations of the intensity profile at the endsurfaces; optical microscopy images at the end-surface without wave guiding laser; experimental spatial intensity profiles of the wave guiding laser at the end-surface; and corresponding calculation results, for four different ion fluences (**a**) 1 × 1011, (**b**) 1 × 1012, (**c**) 1 × 1013, and (**d**) 5 × 1013 ions/cm2. The **Figure 6.** (Left to right) Index profiles used for the calculations of the intensity profile at the end-surfaces; optical microscopy images at the end-surface without wave guiding laser; experimental spatial intensity profiles of the wave guiding laser at the end-surface; and corresponding calculation results, for four different ion fluences (**a**) 1 <sup>×</sup> <sup>10</sup>11, (**b**) 1 <sup>×</sup> <sup>10</sup>12, (**c**) 1 <sup>×</sup> <sup>10</sup>13, and (**d**) 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> . The spatial intensity profiles were calculated by the beam propagation method (BPM) using BeamPROP code.

spatial intensity profiles were calculated by the beam propagation method (BPM) using BeamPROP code. As shown in Figure 6a, the wave guiding is induced even at the lowest fluence of 1 × 1011 ions/cm2, since the guided light is buried beneath the surface. The irradiation made index enhancement of 0.001 around the depth of 6 μm as shown in Figure 5. Even though the very small change in the index, the wave guiding was confirmed from the experimental emission image at the end-surface. Furthermore, As shown in Figure 6a, the wave guiding is induced even at the lowest fluence of 1 <sup>×</sup> <sup>10</sup><sup>11</sup> ions/cm<sup>2</sup> , since the guided light is buried beneath the surface. The irradiation made index enhancement of 0.001 around the depth of 6 µm as shown in Figure 5. Even though the very small change in the index, the wave guiding was confirmed from the experimental emission image at the end-surface. Furthermore, the calculation shows that the observed index profile predicted the same emission image from the small change of the index profile.

the calculation shows that the observed index profile predicted the same emission image from the small change of the index profile. The peak at 6 μm reduced the height at the fluence of 3 × 1011 ions/cm2. At 1 × 1012 ions/cm2, the peak further decreased and turned to a dip. Simultaneously, the index at the surface region (0–3 μm in depth) became slightly higher than the unirradiated value. However, the index at the surface region turned to decrease and became lower than the unirradiated value at 3 × 1012 ions/cm2. Likewise, the bottom value at the dip at 6 μm further decreased. Since the index at the surface region steeply decreased at 1 × 1013 ions/cm2, the low index region near the surface and the 6 μm dip were almost merged. The WG function of SHI-irradiated YAG crystals is also confirmed at 1 × 1012 and 1 × 1013 ions/cm2, as shown in Figure 6b,c. The spatial images of the guided light at the end-surface by The peak at 6 <sup>µ</sup>m reduced the height at the fluence of 3 <sup>×</sup> <sup>10</sup><sup>11</sup> ions/cm<sup>2</sup> . At 1 <sup>×</sup> <sup>10</sup><sup>12</sup> ions/cm<sup>2</sup> , the peak further decreased and turned to a dip. Simultaneously, the index at the surface region (0–3 µm in depth) became slightly higher than the unirradiated value. However, the index at the surface region turned to decrease and became lower than the unirradiated value at 3 <sup>×</sup> <sup>10</sup><sup>12</sup> ions/cm<sup>2</sup> . Likewise, the bottom value at the dip at 6 µm further decreased. Since the index at the surface region steeply decreased at 1 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> , the low index region near the surface and the 6 µm dip were almost merged. The WG function of SHI-irradiated YAG crystals is also confirmed at 1 <sup>×</sup> <sup>10</sup><sup>12</sup> and <sup>1</sup> <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> , as shown in Figure 6b,c. The spatial images of the guided light at the end-surface by experiments are well matched with those calculated from the index profiles. Similarly, the microscopy images show further color changes due to the further index changes.

At the fluence of 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> , the index further decreased. Moreover, a new dip appeared at 13 µm in depth, which could be ascribed to the collisional damage, because the depth of the dip well matches with the peak of the nuclear energy loss *S*n. As shown in Figure 6d, the index profile of the sample irradiated with 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> exhibits interesting waveguiding different from other fluences. Two WG modes are propagated in shallow and deep layers, which were, respectively, formed by the electronic and the nuclear damages. The two-branch guiding at the end-surface was also confirmed by the calculations. The calculated emission image is very similar with the experimental one. well matches with the peak of the nuclear energy loss *S*n. As shown in Figure 6d, the index profile of the sample irradiated with 5 *×* 1013 ions/cm2 exhibits interesting waveguiding different from other fluences. Two WG modes are propagated in shallow and deep layers, which were, respectively, formed by the electronic and the nuclear damages. The two-branch guiding at the end-surface was also confirmed by the calculations. The calculated emission image is very similar with the experimental one.

*Quantum Beam Sci.* **2020**, *4*, x FOR PEER REVIEW 10 of 13

experiments are well matched with those calculated from the index profiles. Similarly, the

at 13 μm in depth, which could be ascribed to the collisional damage, because the depth of the dip

Figure 7 shows the incident polarization dependence of the output power at the end-surface of the WGs. These data were collected with rotating a half-wave plate in the end-face coupling schematically shown in Figure 3c. The low fluence samples (1 <sup>×</sup> <sup>10</sup><sup>11</sup> and 1 <sup>×</sup> <sup>10</sup><sup>12</sup> ions/cm<sup>2</sup> ) show the "8"-shaped (i.e., dipole-shaped) polarization angle dependence. While the strongest power was observed for the TM polarization, little signal (no WG modes) was observed for the TE polarization. Contrary, the high fluence samples (1 <sup>×</sup> <sup>10</sup><sup>13</sup> and 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> ) exhibit nearly isotropic angle dependences, i.e., the output power almost does not depend on the polarization angle. At the moment, the mechanism has not been clarified yet. It should be noted that Figure 4 showed that the low fluence samples (1 <sup>×</sup> <sup>10</sup><sup>11</sup> and 1 <sup>×</sup> <sup>10</sup><sup>12</sup> ions/cm<sup>2</sup> ) are cubic symmetry crystals but the high fluence samples (1 <sup>×</sup> <sup>10</sup><sup>13</sup> and <sup>5</sup> <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> ) are amorphous. Amorphization could be an origin of the change of the polarization angle dependence. However, the detailed mechanism is under investigation. Figure 7 shows the incident polarization dependence of the output power at the end-surface of the WGs. These data were collected with rotating a half-wave plate in the end-face coupling schematically shown in Figure 3c. The low fluence samples (1 × 1011 and 1 × 1012 ions/cm2) show the "8"-shaped (i.e., dipole-shaped) polarization angle dependence. While the strongest power was observed for the TM polarization, little signal (no WG modes) was observed for the TE polarization. Contrary, the high fluence samples (1 × 1013 and 5 × 1013 ions/cm2) exhibit nearly isotropic angle dependences, i.e., the output power almost does not depend on the polarization angle. At the moment, the mechanism has not been clarified yet. It should be noted that Figure 4 showed that the low fluence samples (1 × 1011 and 1 × 1012 ions/cm2) are cubic symmetry crystals but the high fluence samples (1 × 1013 and 5 × 1013 ions/cm2) are amorphous. Amorphization could be an origin of the change of the polarization angle dependence. However, the detailed mechanism is under investigation.

**Figure 7.** The total output power of the waveguide through the end-surface was plotted with changing the polarization angle of the incident laser. The incident laser power was set to 1.8 mW. The samples were irradiated with 200 MeV Xe14+ ions at four different fluences; 1 × 1011, 1 × 1012, 1 × 1013, and 5 × 1013 ions/cm2. **Figure 7.** The total output power of the waveguide through the end-surface was plotted with changing the polarization angle of the incident laser. The incident laser power was set to 1.8 mW. The samples were irradiated with 200 MeV Xe14<sup>+</sup> ions at four different fluences; 1 <sup>×</sup> <sup>10</sup>11, 1 <sup>×</sup> <sup>10</sup>12, 1 <sup>×</sup> <sup>10</sup><sup>13</sup> , and 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> .

#### As shown in Figure 5, the index dip at 13 μm in depth was only observed at the high fluence of **4. Discussion**

**4. Discussion** 

5 × 1013 ions/cm2 and higher fluence (not shown in this paper) by end-face coupling, which well matches at the peak of the nuclear energy loss *S*n. Consequently, the index reduction at 13 μm in depth is ascribed to the damage induced by the nuclear energy loss. Since *S*n is much lower than *S*e, the dip appeared only at high fluences. The existence of this mode is clearly evidenced by the deep WG mode shown in Figure 6d. As shown in Figure 5, the index dip at 13 µm in depth was only observed at the high fluence of 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> and higher fluence (not shown in this paper) by end-face coupling, which well matches at the peak of the nuclear energy loss *S*n. Consequently, the index reduction at 13 µm in depth is ascribed to the damage induced by the nuclear energy loss. Since *S*<sup>n</sup> is much lower than *S*e, the dip appeared only at high fluences. The existence of this mode is clearly evidenced by the deep WG mode shown in Figure 6d.

The index reduction in the surface plateau region between 0 and ~3 µm can be ascribed to the electronic energy loss *S*e, which has the highest at the surface. Consequently, both *S*<sup>e</sup> and *S*<sup>n</sup> contribute the index reduction. However, the origin of the dip/peak at 6 µm in depth is not clear. Neither of *S*<sup>e</sup> nor *S*<sup>n</sup> has a peak around 6 µm. Rather, *S*<sup>e</sup> decreases and *S*<sup>n</sup> increases around 6 µm.

It is known that amorphous ion tracks are formed in YAG crystals. The amorphization was confirmed by XRD as shown in Figure 4. The track threshold is reported as 7.5 keV/nm. The *S*<sup>e</sup> of

200 MeV Xe ions in YAG crystal calculated by SRIM 2013 amounts to 24.3 keV/nm at the surface. With increasing the depth, the *S*<sup>e</sup> gradually decreases with making a track. The *S*<sup>e</sup> finally becomes below the threshold value of 7.5 keV/nm [13] and stops forming the tracks around the depth of ~10 µm. The threshold value of 7.5 keV/nm is indicated by a broken line in Figure 5. Deeper than the depth of ~10 µm, tracks are no longer formed. As shown in Figure 5, no index changes are induced in the region deeper than ~10 µm, except the dip at 13 µm. This is another evidence that the dip at 13 µm is not due to *S*<sup>e</sup> but *S*n.

Consequently, the index reductions at the surface plateau region and the dip at 13 µm can be described to the electronic and nuclear energy losses, because either of them matches with the maximum depths of *S*<sup>e</sup> and *S*n, respectively. However, the origin of the dip/peak at 6 µm is not clear. Neither of *S*<sup>e</sup> nor *S*<sup>n</sup> has a peak around 6 µm. Since the enhancement of the index was firstly observed, the irradiation introduces density increase around 6 µm depth. The density enhancement soon turns to the density reduction probably introduction of defects. Further the index at 6 µm decreases combined with the reduction in the surface plateau. Since the 6 µm peak matches neither of the peaks of *S*<sup>e</sup> and *S*n, a possible candidate could be the synergy effects between *S*<sup>e</sup> and *S*n. Since the synergy effects are not included in SRIM code, the deviation at 6 µm between the index profiles and SRIM calculations is a matter of course.

The refractive index profiling is a relatively new method to study the irradiation effects of SHIs, which is sensitive to defect formation and/or stress (strain) generation, and detectable the depth profiles at any fluences. Figure 5 clearly shows complex evolutions of the index, i.e., the defect formation and/or the stress generation, along the fluence. At the fluence of 1 <sup>×</sup> <sup>10</sup><sup>11</sup> ions/cm<sup>2</sup> , a weak index enhancement, i.e., compressive stress, is generated around 6 µm in depth due to the synergy effect. At 1 <sup>×</sup> <sup>10</sup><sup>12</sup> ions/cm<sup>2</sup> , the index turns to decrease, i.e., the compressive stress turns to the defect formation. At the same fluence, the index enhancement, i.e., the compressive stress is induced at 0–3 <sup>µ</sup>m by *<sup>S</sup>*e, but turns to decrease at higher fluences, i.e., the defect formation. At 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> , *S*<sup>n</sup> also contributes the index change via the defect formation. This kind of complex evolutions are only accessible by the index profiling.
