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 (
nB), is sandwiched with materials A (cladding layer:
nA) and C (substrate layer:
nC), both having lower indices than the material B (the guiding layer), i.e.,
nA,
nC <
nB. 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.
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],
or approximately
where Δ
V/V, Δ
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 (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)).
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.
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 (
Sn) 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 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).
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 (
Sn) but also the electronic energy loss (
Se) 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 Au
5+ irradiation to 8 × 10
14 ions/cm
2, 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 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 Xe
14+ ions, at various fluences ranging from 1 × 10
11 to 5 × 10
13 ions/cm
2.
4. Discussion
As shown in
Figure 5, the index dip at 13 μm in depth was only observed at the high fluence of 5 × 10
13 ions/cm
2 and higher fluence (not shown in this paper) by end-face coupling, which well matches at the peak of the nuclear energy loss
Sn. Consequently, the index reduction at 13 μm in depth is ascribed to the damage induced by the nuclear energy loss. Since
Sn is much lower than
Se, 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 Se, which has the highest at the surface. Consequently, both Se and Sn contribute the index reduction. However, the origin of the dip/peak at 6 μm in depth is not clear. Neither of Se nor Sn has a peak around 6 μm. Rather, Se decreases and Sn 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
Se 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
Se gradually decreases with making a track. The
Se 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
Se but
Sn.
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 Se and Sn, respectively. However, the origin of the dip/peak at 6 μm is not clear. Neither of Se nor Sn 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 Se and Sn, a possible candidate could be the synergy effects between Se and Sn. 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 × 10
11 ions/cm
2, a weak index enhancement, i.e., compressive stress, is generated around 6 μm in depth due to the synergy effect. At 1 × 10
12 ions/cm
2, 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 μm by
Se, but turns to decrease at higher fluences, i.e., the defect formation. At 5 × 10
13 ions/cm
2,
Sn also contributes the index change via the defect formation. This kind of complex evolutions are only accessible by the index profiling.
5. Conclusions
The evolution of the depth profiles with the fluence of the refractive index in YAG crystals were studied under 200 MeV 136Xe14+ 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 × 1011 ions/cm2, a weak index enhancement was induced at the depth of 6 μm, which does not match either of Se maximum nor Sn maximum. With increasing the fluence, the peak turns to decrease. At 1 × 1012 ions/cm2, 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 μm dip reduce the index with the fluence. At the highest fluence of 5 × 1013 ions/cm2, a new dip appeared at the depth of 13 μm, which matched to the peak of Sn.
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 Sn peak, (ii) a plateau near the surface at 0–3 μm, which can be ascribed to the electronic stopping Se, since Se 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 Se nor Sn peak, it could be attributed to the synergy effect of Se and Sn.