**1. Introduction**

Optical waveguides (WGs) are elements to confine light wave inside and to guide the waves along them, which are considered as important parts for future optical integrate circuits [1]. Some special WGs possess additional functions such as lasing [2,3], the second harmonic generation [3,4], and the photorefractive effect [3,5]. While the most known WGs are optical fibers, here we discuss WGs of the slab type, which consist of thin film layer(s) on a substrate (See Figure 1). The optical WGs of the slab type are easily formed, when a transparent material B (guiding layer), having the highest index (*n*B), is sandwiched with materials A (cladding layer: *n*A) and C (substrate layer: *n*C), both having lower indices than the material B (the guiding layer), i.e., *n*A, *n*<sup>C</sup> < *n*B. At the boundaries A–B and B–C, the total reflections are repeated with the reflection angles higher than certain values. Light could be confined in the material B due to the total reflections at both the boundaries A–B and B–C. The material A (cladding layer) can be replaced by air or a vacuum, since either of them has the index of ~1, i.e., lower than most of the guiding layer material B. Consequently, the simplest WGs consist of two layers: (i) a higher index layer deposited on a lower index substrate can act as a slab-type WG. (ii) another strategy is to decrease the refractive index of a certain depth region of a transparent material without decreasing the index of the shallower layer.

*Quantum Beam Sci.* **2020**, *4*, x FOR PEER REVIEW 2 of 13

**Figure 1.** Schematically depicted cross-section of a slab waveguide consisting two layers: An upper layer with higher refractive index and lower one with lower index. Air (or vacuum) on the upper layer acts as a cladding layer. At light-propagating angles at discrete values, the total reflections are induced at the boundaries between air and the layer 1 and between layers 1 and 2. Consequently light in the layer 1 is confined inside of the layer 1 and guided along the inside of the layer. **Figure 1.** Schematically depicted cross-section of a slab waveguide consisting two layers: An upper layer with higher refractive index and lower one with lower index. Air (or vacuum) on the upper layer acts as a cladding layer. At light-propagating angles at discrete values, the total reflections are induced at the boundaries between air and the layer 1 and between layers 1 and 2. Consequently light in the layer 1 is confined inside of the layer 1 and guided along the inside of the layer.

Ion irradiation can realize the latter structures (ii). According to the Lorentz–Lorenz's (LL) formula (Equation (1)), the relative change of the refractive index Δ*n*/*n* is described as the following relation [3], Ion irradiation can realize the latter structures (ii). According to the Lorentz–Lorenz's (LL) formula (Equation (1)), the relative change of the refractive index ∆*n*/*n* is described as the following relation [3],

> ݊ ∝ െ

∆݊

$$\frac{\Delta n}{n} = \frac{\left(n^2 - 1\right)\left(n^2 + 2\right)}{6n} \left[ -\frac{\Delta V}{V} + \frac{\Delta \alpha}{\alpha} + F \right] \tag{1}$$

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or approximately

or approximately

$$\frac{\Delta n}{n} \propto -\frac{\Delta V}{V} \tag{2}$$

ܸ (2)

expected that the ensemble of Frenkel pairs, i.e., pairs of vacancies and interstitial atoms, could induce local volume expansion (Δ*V* > 0), which results in the index reduction (Δ*n* < 0) in some transparent solids. Moreover, lattice expansion and contraction (Δ*V* > 0 and < 0) results in the index reduction and enhancement (Δ*n* > 0 and < 0), respectively. Of course, ion irradiation could exchange atomic arrangements so that newly formed chemical bonds may change the (bond) polarizability α, i.e., the second term of Equation (1). Furthermore, some phase transitions, e.g., amorphization, could suddenly change the relative index (the third term of Equation (1)). where ∆*V*/*V*, ∆α/α, and *F* denote relative changes of volume, of polarizability, and of other factors such as phase transition, respectively. From the first term in the right side of Equation (1), it is expected that the ensemble of Frenkel pairs, i.e., pairs of vacancies and interstitial atoms, could induce local volume expansion (∆*V* > 0), which results in the index reduction (∆*n* < 0) in some transparent solids. Moreover, lattice expansion and contraction (∆*V* > 0 and < 0) results in the index reduction and enhancement (∆*n* > 0 and < 0), respectively.

In this paper, however, the first term in the right side of Equation (1) is only considered as an approximation, and the second and the third terms are, at the moment, neglected. Therefore, instead of the Equation (1), the Equation (2) is used in this paper. Our main concern is the detection of the defect formation and/or the stress generation via the index changes. We will not discuss the volume Of course, ion irradiation could exchange atomic arrangements so that newly formed chemical bonds may change the (bond) polarizability α, i.e., the second term of Equation (1). Furthermore, some phase transitions, e.g., amorphization, could suddenly change the relative index (the third term of Equation (1)).

changes quantitatively. The original idea to produce optical WGs in transparent crystals by ion beams, was to utilize the nuclear stopping process of light ions, e.g., ~1–2 MeV He ions [6]. As schematically shown in Figure 2, the nuclear energy loss (*S*n) reaches the maximum at several micrometers beneath the crystal's surface, i.e., the Bragg peak, and leaves serious damage. Much shallower region than the Bragg peak is preserved negligible damage. From Equation (2), the refractive index decreases (Δ*n* < 0) around the In this paper, however, the first term in the right side of Equation (1) is only considered as an approximation, and the second and the third terms are, at the moment, neglected. Therefore, instead of the Equation (1), the Equation (2) is used in this paper. Our main concern is the detection of the defect formation and/or the stress generation via the index changes. We will not discuss the volume changes quantitatively.

Bragg peak depth due to serious damage, i.e., Δ*V* > 0, while the index almost preserves in the layer shallower than the Bragg peak. This is the WG structures of the type (ii). The original idea to produce optical WGs in transparent crystals by ion beams, was to utilize the nuclear stopping process of light ions, e.g., ~1–2 MeV He ions [6]. As schematically shown in Figure 2, the nuclear energy loss (*S*n) reaches the maximum at several micrometers beneath the crystal's surface, i.e., the Bragg peak, and leaves serious damage. Much shallower region than the Bragg peak is preserved negligible damage. From Equation (2), the refractive index decreases (∆*n* < 0) around the Bragg peak depth due to serious damage, i.e., ∆*V* > 0, while the index almost preserves in the layer shallower than the Bragg peak. This is the WG structures of the type (ii).

Since the first optical WG was successfully formed by ion irradiations [6], various studies have been developed: This methodology has been applied in various materials [3,7]. In some glasses, it was confirmed that ion irradiation induced the increase of the density, i.e., ∆*V* < 0, i.e., ∆*n* > 0 [8].

Olivares et al. clarified that not only the nuclear energy loss (*S*n) but also the electronic energy loss (*S*e) of swift heavy ions reduces the refractive index of crystals [9]. Rodriguez et al. studied ion

tracks in Nd-doped yttrium aluminum garnet (Nd:YAG) formed by 2.2 GeV Au ion irradiation, using transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS) [10]. They concluded that the ion tracks were in an amorphous phase with a hard-cylinder density distribution, other than the core/shell types. We have confirmed the refractive index changes of Nd:YAG induced by 15 MeV Au5<sup>+</sup> irradiation to 8 <sup>×</sup> <sup>10</sup><sup>14</sup> ions/cm<sup>2</sup> , and found that the amorphous phase showed a lower index [11]. *Quantum Beam Sci.* **2020**, *4*, x FOR PEER REVIEW 3 of 13

**Figure 2.** Schematically depicted depth profiles of damage induced by a few MeV light ions. The refractive index is reduced around the depth of the Bragg peak due to strong damage, while the index in shallower region seldom changes. Consequently, a slab-type waveguide is formed only by the irradiation of a few MeV light ions. **Figure 2.** Schematically depicted depth profiles of damage induced by a few MeV light ions. The refractive index is reduced around the depth of the Bragg peak due to strong damage, while the index in shallower region seldom changes. Consequently, a slab-type waveguide is formed only by the irradiation of a few MeV light ions.

Since the first optical WG was successfully formed by ion irradiations [6], various studies have been developed: This methodology has been applied in various materials [3,7]. In some glasses, it was confirmed that ion irradiation induced the increase of the density, i.e., Δ*V <* 0, i.e., Δ*n* > 0 [8]. Olivares et al. clarified that not only the nuclear energy loss (*S*n) but also the electronic energy loss (*S*e) of swift heavy ions reduces the refractive index of crystals [9]. Rodriguez et al. studied ion tracks in Nd-doped yttrium aluminum garnet (Nd:YAG) formed by 2.2 GeV Au ion irradiation, using transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS) [10]. They concluded that the ion tracks were in an amorphous phase with a hard-cylinder density distribution, other than the core/shell types. We have confirmed the refractive index changes of Nd:YAG induced by 15 MeV Au5+ irradiation to 8 × 1014 ions/cm2, and found that the amorphous phase showed a lower index [11]. As shown in Equation (2), the studies of the refractive index change provide information on the density changes, which are induced by ion irradiation, via damage or stress change. According to a naive image of WG shown in Figure 1, the waveguiding is possible for any angles higher than a certain value. However, this is not correct. Because of the interference of light, the guiding is possible As shown in Equation (2), the studies of the refractive index change provide information on the density changes, which are induced by ion irradiation, via damage or stress change. According to a naive image of WG shown in Figure 1, the waveguiding is possible for any angles higher than a certain value. However, this is not correct. Because of the interference of light, the guiding is possible only for discrete values of the angles, each of which corresponds to the WG mode. Furthermore, when the light confinement is surely maintained between the cladding and the substrate layer, the guiding is possible for inhomogeneous index profile in the guiding layer, with different distribution of the modes. Contrary, with measuring the mode angles using, e.g., the prism coupling method, the depth profile of the refractive index can be reconstructed. This paper reports the fluence dependence of the refractive index profiles of yttrium-aluminum-garnet (YAG) crystals irradiated with swift heavy ions (SHIs) of 200 MeV Xe14<sup>+</sup> ions, at various fluences ranging from 1 <sup>×</sup> <sup>10</sup><sup>11</sup> to 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> .

#### only for discrete values of the angles, each of which corresponds to the WG mode. Furthermore, when the light confinement is surely maintained between the cladding and the substrate layer, the guiding **2. Materials and Methods**

#### modes. Contrary, with measuring the mode angles using, e.g., the prism coupling method, the depth *2.1. Material*

profile of the refractive index can be reconstructed. This paper reports the fluence dependence of the refractive index profiles of yttrium-aluminum-garnet (YAG) crystals irradiated with swift heavy ions (SHIs) of 200 MeV Xe14+ ions, at various fluences ranging from 1 × 1011 to 5 × 1013 ions/cm2. **2. Materials and Methods**  *2.1. Material*  Single crystals of undoped yttrium-aluminum-garnet (Y3Al5O12, YAG) with the dimensions of 10 mm by 10 mm by 1 mm were purchased from ATOM Optics Co. Ltd., Shanghai, China. The double sides of them were mirror-polished. Here the "undoped YAG" means that Nd ions or other rare-earth Single crystals of undoped yttrium-aluminum-garnet (Y3Al5O12, YAG) with the dimensions of 10 mm by 10 mm by 1 mm were purchased from ATOM Optics Co. Ltd., Shanghai, China. The double sides of them were mirror-polished. Here the "undoped YAG" means that Nd ions or other rare-earth impurities have not been intentionally doped. While the samples were single crystals in unirradiated state, they seemed to transform to polycrystalline and finally to amorphous, as shown later. The crystalline structure of YAG (Y3Al5O12) is the garnet type, i.e., in the cubic symmetry but including many atoms in a unit cell.

is possible for inhomogeneous index profile in the guiding layer, with different distribution of the

#### impurities have not been intentionally doped. While the samples were single crystals in unirradiated state, they seemed to transform to polycrystalline and finally to amorphous, as shown later. The *2.2. Ion Irradiation*

The {0 0 1} plane of the single crystals of YAG was irradiated at room temperature with 200 MeV <sup>136</sup>Xe14<sup>+</sup> ions from the tandem accelerator in the Japan Atomic Energy Agency (JAEA), Tokai Research and Development Center. The fluence ranged from 1 <sup>×</sup> <sup>10</sup><sup>11</sup> to 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> , with maintaining the

beam current density at ~60 nA/cm<sup>2</sup> , except the fluences of 1 <sup>×</sup> <sup>10</sup><sup>11</sup> and 3 <sup>×</sup> <sup>10</sup><sup>11</sup> ions/cm<sup>2</sup> at ~5 nA/cm<sup>2</sup> to avoid inaccurate fluences due to too short irradiation time. Noted that the particle current density is 1/14 of the above-described values. The beam was rasterized at ~40 Hz (horizontal) and ~2 Hz (vertical). An important point was the frequencies were approximated values, which were not commensurate. The area of 10 mm square was irradiated through a square slit.

The stopping powers and the projected range of the 200 MeV Xe ions in YAG was calculated using SRIM 2013 code [12] with the mass density of 4.56 g/cm<sup>3</sup> , and shown in Table 1. The displacement energy, the bulk binding energy, and the surface binding energy of each element used for the calculations were summarized in Table 2. The 200 MeV Xe ion provides the electronic stopping power *S*<sup>e</sup> of 24.3 keV/nm, which was much higher than the track formation threshold of 7.5 keV/nm [13].

**Table 1.** Electronic and nuclear stopping powers (at the surface), and the projected range of 200 MeV <sup>136</sup>Xe14+. ions in yttrium-aluminum-garnet (YAG) crystal, calculated by SRIM 2013. The track formation threshold and the X-ray penetration depth of the Cr Kα line used for fixed incident angle X-ray diffractometry (FIA-XRD) are also shown.


**Table 2.** The displacement energies, the bulk binding energies, and the surface binding energies of Y, Al, and O atoms in YAG crystal, used for the SRIM 2013 calculations.

