The discrete straight and bending (bending angle: 45°) lines with β-BBO crystals (the width of lines: 5 μm) were patterned by laser irradiation with P = 0.8 W and S = 4 μm/s at the surface of 8Sm₂O₃-42BaO-50B₂O₃ glass. It is possible to form β-BBO crystalline dots initially at a given place by laser irradiation without moving but cracks are frequently induced around crystalline dots after stopping or moving of laser irradiation. Therefore, in this study, β-BBO crystal particles synthesized by the crystallization of the glass in an electric furnace were used as the initial nucleation site. That is, laser was first irradiated (focused) onto a β-BBO crystal particle placed at the glass surface and then scanned with the scanning speed of S = 4 μm/s.

The azimuthal dependence of SHG signals for the straight and bending lines consisting of β-BBO crystals is shown in Figure 1. The formation of β-BBO crystals in these lines has been confirmed in the previous paper (e.g., Ogawa et al., 2013). The POM photographs for these lines are included in Figure 1. The maximum SH intensities for the straight line are observed at the rotation angles of ~0° and ~180°, and the minimum SH intensities are located at 90° and 270°. In β-BBO, the presence of [B₃O₆]^3– anionic hexagonal groupings slightly distorted with a threefold axis is the origin of the large second-order nonlinear optical coefficient (d₂₂ ~ 2 pm/V). The effective second-order nonlinear optical coefficient, d_eff, is given by the equation of d_eff = d₂₂cos²θ. It was confirmed that the SH intensity for the straight line shown in Figure 1 changes as a function of cos²θ, indicating that β-BBO crystals in the straight line are highly oriented and grow with the c-axis orientation along the laser scanning direction (e.g., Honma et al., 2003; Ogawa et al., 2013). The c-axis orientation of β-BBO crystals has been already proposed in the previous papers (e.g., Honma et al., 2003; Ogawa et al., 2013).

On the other hand, as can be seen in Figure 1, the maximum SH intensities for the bending line are observed at the rotation angles of ~150° and ~345°, and the minimum SH intensities are located at ~50° and 255°. In particular, when compared with the straight line, it is found that the rotation angle providing the maximum SH intensity in the bending line shifts toward the lower angle with the magnitude of ~30°. Furthermore, it should be pointed out that the profile of SH intensities against the rotation angle in the bending line is broad when compared with the straight line. It is regarded that the bending line with the bending angle of 45° consists of two components of straight line part and bending line part against the linearly polarized incident laser for SHG measurements, i.e., the components of two rotation angles of θ and θ + 45°. In other words, the SH intensity for the bending line would be expressed as a sum of two contributions (functions) of cos²θ and cos²(θ + 45). This would be the reason for the shift of the peak position of the maximum SH intensity and the broadness of the profile of SH intensity in the bending line compared with the straight line. Indeed, the profile of SH intensity for the bending line was well fitted with a function of f(θ) = cos²θ + cos²(θ + 45). The results shown in Figure 1 also indicate that the c-axis orientation of β-BBO crystals is kept even in the bending line.

The azimuthal dependence of SHG signals for the spiral line consisting of β-BBO crystals is shown in Figure 2. The POM photographs for this lines and the SH wave images (the intensities of green light with λ = 532 nm) observed are included in Figure 2. SHGs are detected at all rotation angles, and any specific (critical) angles providing maximum or minimum SH intensities are not observed. In β-BBO crystals, strong SHGs are observed when the direction of the electric field in the linearly polarized incident lasers (E) is parallel to the direction of the polarization in [B₃O₆]^3– units (P_o), i.e., E//P_o. In the spiral line with the c-axis orientation of β-BBO crystals, the configuration of E//P_o is always achieved at any angles, and as a result, it is expected that similar SH intensities are detected in all rotation angles as shown in Figure 2. The results shown in Figure 2 also demonstrate that the c-axis orientation of β-BBO crystals is kept even in the spiral line.

From the c-axis orientation of β-BBO crystal lines demonstrated in Figures 1 and 2, it is considered that the preferential crystal growth direction is the c-axis. β-BBO with a crystal structure of R3c has the lattice parameters of a = b = 1.2547 nm and c = 1.2736 nm (Eimerl et al., 1987), indicating that the difference in the lattice parameters is very small. As well known, however, β-BBO has a large anisotropic structure, in which planar [B₃O₆]^3– units stack along the c-axis direction, and Ba²⁺ ions are located between stacked [B₃O₆]^3– units. The thermal expansion coefficient (α) of β-BBO is α = 4 × 10⁻⁶/K for the a-axis and α = 36 × 10⁻⁶/K for the c-axis, indicating that the chemical bond strength between Ba²⁺ and planar [B₃O₆]^3– units is weaker than that between [B₃O₆]^3– units. In other words, it is expected that the modification in the bonding distance between Ba²⁺ and planar [B₃O₆]^3– units is more flexible. These structural features of β-BBO would induce the c-axis orientation even for the bending and spiral lines as shown in Figures 1 and 2. That is, it would be possible to change or rotate gradually the c-axis direction at the bending or curved points.

The nucleation and crystal growth rates of β-BBO crystals in 8Sm₂O₃-42BaO-50B₂O₃ glass have not been reported so far. It is well known that a glass with the composition of 40BaO-20TiO₂-40SiO₂ displays the highest internal nucleation (I) rare for fresnoite Ba₂TiSi₂O₈ crystals so far measured in inorganic glasses (Cabral et al., 2003), i.e., I~ 10¹⁷/m³s. This nucleation rare of I ~ 10¹⁷/m³s equals to I ~ 0.1/μm³s. The maximum steady-state nucleation rates (I_max) for 51 silicate glasses with different compositions have been summarized as a function of reduced glass transition temperature (T_gr) (T_gr = T_g/T_m, T_m is the melting temperature) (Fokin et al., 2003). The silicate glasses summarized have mainly the values of I_max = 10⁹–10¹³/m³s, corresponding to the values of I_max = 10⁻⁹–10⁻⁵/μm³s. The value of I_max ~ 10/mm³s, corresponding to 10⁻⁸/μm³s, has been reported for lithium disilicate (Li₂O·2SiO₂) glass (Deubener, 2000). In the laser-induced crystallization, only spatially limited region, i.e., the region of 10–20 μm, is heated locally, and furthermore, the keeping period for high temperature in a given laser-irradiated position is short due to the laser scanning with speeds of S = 1–10 μm/s and also to the heat dissipation to the surrounding glassy part (not laser-irradiated part). These features of small heating region and short keeping time at a fixed region would result in the small probability of nucleation during laser scanning. Indeed, highly (c-axis) oriented Li₂Si₂O₅ crystal lines have been patterned in Li₂O·2SiO₂ glass without causing any new nucleation during laser scanning (Honma et al., 2008a,b). The results shown in Figures 1 and 2 propose that at least, at the laser irradiation condition of P = 0.8 W and S = 4 μm/s, only the crystal growth of β-BBO is taking place during the laser scanning in 8Sm₂O₃-42BaO-50B₂O₃ glass without causing any nucleation, and this would be one of the key points for the laser patterning of β-BBO crystals with high orientation. It should be pointed out that highly oriented Ba₂TiSi₂O₈ crystal lines have been patterned by laser irradiation in 40BaO-20TiO₂-40SiO₂ glass, although Ba₂TiSi₂O₈ nanocrystals are formed by heat treatment in an electric furnace (Enomoto et al., 2007; Honma et al., 2008a,b; Maruyama et al., 2008). Similar behaviors have been observed in the laser patterning and nano-scaled crystallization of the formation of nonlinear optical BaAlBO₃F₂ crystals in 50BaF₂-25Al₂O₃-25B₂O₃ glass (Shinozaki et al., 2012). In the crystallization of CaF₂ in CaF₂-Al₂O₃-SiO₂-based oxyfluoride glasses, however, it has been reported that lines consisting of CaF₂ nanocrystals have been patterned by laser irradiation as similar to the case in heat treatment in an electric furnace (Kanno et al., 2009; Shinozaki et al., 2013). That is, lines consisting of the assembly of CaF₂ nanocrystals have been patterned, but the patterning of highly oriented CaF₂ single crystal lines have not been reported so far. The nucleation and crystal growth behaviors in the laser-induced crystallization, therefore, depend not only on laser irradiation condition but also on glass composition.

The laser-induced crystallization technique proposed and applied in our group is based perfectly on the thermal effect (heating) as similar to the crystallization in an electric furnace. Therefore, basically, the crystalline phase formed in the laser-induced crystallization in a given glass is the same as that formed in the crystallization in an electric furnace. In this sense, it should be emphasized that even in the laser-induced crystallization, the design of the system and composition of base glasses is still a key point for the patterning of crystals with high qualities. That is, even in the laser-induced crystallization, the design and control of the morphology of crystals depend largely on the chemical composition of a given glass.

As indicated in the above section, through the use of optimal laser power and scanning speed, it is possible to depress nucleation during laser scanning and to induce homogeneous crystal growth providing the patterning of highly oriented β-BBO crystal lines in 8Sm₂O₃-42BaO-50B₂O₃ glass. Here, the nucleation and crystal growth behaviors of β-BBO crystals in the laser-induced crystallization are discussed more in detail by patterning crossing lines. A schematic illustration for crossing line experiments is shown in Figure 3. First, a discrete straight line consisting of highly oriented β-BBO crystals was patterned by laser irradiation with P = 0.8 W and S = 4 μm/s in 8Sm₂O₃-42BaO-50B₂O₃ glass, in which a β-BBO crystal particle synthesized by the crystallization of the glass in an electric furnace was used as an initial nucleation site. Then, the second laser irradiation with P = 0.8 W and S = 1–4 μm/s was carried out against the first line with the crossing angle of 90° (perpendicularly). In the second line patterning, any β-BBO crystal particles were not used, and thus, the laser irradiation does not induce any crystallization before crossing against the first line but just only the change in the glass structure (refractive index change).

The POM photograph for the crossing lines is shown in Figure 4. In the POM observations, the crossed polarizer and analyzer were used, and the appearance of bright and homogeneous interference color indicates the formation of nonlinear optical crystals. On the other hand, structurally isotropic glassy materials do not give any interference color. It is, therefore, concluded from the POM photograph in Figure 4 that, in the second lines with the laser scanning speeds of S = 1, 2, and 3 μm/s, the formation of crystals is induced after crossing against the first crystal line, although any crystals were not formed before crossing. In the second line with S = 4 μm/s, any crystallization was not induced even after crossing. These results indicate that nucleation and crystal growth behaviors at the crossing region depend on the scanning speed of the second line patterning. That is, the scanning with low speed is more effective for the nucleation and crystal growth at the crossing region.

The micro-Raman scattering spectrum at room temperature for the crystalline part in the second line (P = 0.8 W, S = 1 μm/s) after crossing is shown in Figure 5. The Raman bands are assigned to β-BBO crystal (Suzuki et al., 2012), indicating that nonlinear optical crystals (i.e., β-BBO) formed in the second line after crossing is the same as that in the first line consisting of β-BBO. As can be seen in Figure 5, the intensities of Raman bands in the second line (b) are much larger than those in the first line (a). The first line consisting of β-BBO crystals was patterned with the condition of P = 0.8 W and S = 4 μm/s. On the other hand, the second line was patterned with P = 0.8 W and S = 1 μm/s. As shown in Figure 4, the formation behavior of β-BBO crystals after crossing depends on the laser scanning speed. The Raman scattering spectra shown in Figure 5, i.e., the difference in the Raman band intensity between the first line (a) and the second line (b), therefore, suggest that the amount of β-BBO crystals increases with the decrease in the laser scanning speed from 4 to 1 μm/s, and also, their quality might be improved in the condition of low laser scanning speed. Considering crystal growth kinetics in glass, low laser scanning speed, i.e., keeping high temperature for long period, would be favorable for crystal growth. Of course, however, optimal laser irradiation condition (optimal laser power and scanning speed) is required for the pattering of homogeneous crystal lines (Honma et al., 2005; Inoue et al., 2015).

The micro PL spectrum at room temperature for the second line after crossing is shown in Figure 6. Four luminescence peaks are observed at ~565, ~600, ~645, and ~705 nm. These are typical emissions of Sm³⁺ assigned to ⁴G_5/2→⁶H_J, i.e., ⁴G_5/2→⁶H_5/2 at 565 nm, ⁴G_5/2→⁶H_7/2 at 600 nm, ⁴G_5/2→⁶H_9/2 at 645 nm, and ⁴G_5/2→⁶H_11/2 at 705 nm. Since there is no peaks at around 683 nm (⁵D₀→⁷F₀), 725 nm (⁵D₀→⁷F₂), and 760 nm (⁵D₀→⁷F₃) attributing to Sm²⁺, samarium ions exist at trivalent Sm³⁺ in the second line after crossing. That is, there is no change in the valence of Sm ions during laser irradiation. The first and second lines show strong PL intensities compared with the glassy part (not laser-irradiated part), suggesting that some Sm³⁺ ions are incorporated into β-BBO crystals. It is, therefore, considered that Sm³⁺-doped β-BaB₂O₄ crystals are formed in the lines patterned by laser irradiation. It is noted that the intensities of PL spectra in the second line (b) (S = 1 μm/s) are much larger than those in the first line (a) (S = 4 μm/s), as similar to Raman scattering spectra (Figure 5). The PL spectra shown in Figure 6, therefore, suggest that the amount of Sm³⁺-doped β-BBO crystals formed in the second line after crossing is larger than that in the first line. The incorporation of Sm³⁺ into β-BaB₂O₄ crystals has been also proposed even in the discrete straight line (Honma et al., 2004).

As indicated in Figures 1 and 4, β-BBO crystals with the c-axis orientation are patterned in the first crystal line. Furthermore, it is found that the nucleation and crystal growth of β-BBO crystals occur effectively at the crossing region of two lines. In order to look at the crystallization behavior at the crossing region more in detail, the POM photograph focusing the crossing region in the second line patterned with S = 2 μm/s is again shown in Figure 7. It is found that the second line just after crossing has a light color, being the same as that in the first line consisting of the c-axis oriented β-BBO crystals. The same color means the same retardation, i.e., the same crystal orientation of nonlinear optical crystals. It is, therefore, considered that the orientation of β-BBO crystals in the second line after crossing is the same as that in the first line. It is seen that the homogeneous light blue color in the second line changes to other color in the part beyond the distance of about 20 μm from the crossing point. This means that the orientation of β-BBO crystals in this part changes gradually. Considering the crystal growth mechanism in the crossing line experiments, it is suggested that the side plane of the first β-BBO crystal line acts as the nucleation site for the crystallization in the second line.

The difference in the lattice parameters (a = b = 1.2547 nm and c = 1.2736 nm) in β-BBO is very small, indicating that the lattice mismatch between the c-plane and a (=b)-plane is very small. However, β-BBO has a large anisotropic structure, in particular, the stacking of planar [B₃O₆]^3– units along the c-axis direction, indicating a large difference in the atomic arrangement in the a-plane and c-plane, i.e., a large structural mismatch. It is, therefore, considered that the growth of the c-plane at the a-plane would be difficult structurally. This would be the reason that the a-plane of β-BBO crystals is created in the second line after crossing, as schematically shown in Figure 7. The relationship in the crystal growth direction at the crossing point between the first and second lines is expressed as the combination of the a-plane/the a-plane of the same crystalline phase of β-BBO, and this crystal growth is regarded as “a homo-epitaxial crystal growth” in the crossing lines of nonlinear optical β-BBO crystals patterned by laser irradiation. The preferential crystal growth direction of β-BBO patterned by laser is the c-axis. Therefore, during the crystal growth in the second line, β-BBO tends to have the c-axis orientation. It would be difficult energetically to change the crystal growth direction from the a-axis to the c-axis in an instance at a given position, but the gradual change would be expected. Consequently, the transition zone for the c-axis orientation, i.e., from the a-axis orientation to the c-axis orientation, would be created. Finally, even in the second line, β-BBO crystals with the c-axis orientation would be patterned, as schematically shown in Figure 8. The phenomenon on the nucleation and crystal growth of β-BBO crystals in the second line after crossing is illustrated schematically in Figure 9. A similar behavior of homo-epitaxial crystal growth in the crossing lines patterned by laser irradiation has been reported in the patterning of nonlinear optical BaAlBO₃F₂ crystals (Shinozaki et al., 2015). That is, the present study is the second example for the homo-epitaxial crystal growth in the crystallization of glasses, and the homo-epitaxial crystal growth is regarded as a common feature in the laser-induced crystallization in glasses.

It should be pointed out that the behavior of hetero-epitaxial crystal growth in the crystallization of glasses has been found in Li₂O-Al₂O₃-SiO₂ glasses containing P₂O₅ nucleation agent, in which the hetero-epitaxial growth of lithium metasilicate Li₂SiO₃ and lithium disilicate Li₂Si₂O₅ on Li₃PO₄ crystals is found in heat treatment in an electric furnace (Headley and Loehman, 1984). There are many glasses that show the formation of two different kinds of crystalline phases in the crystallization. In such glasses, hetero-epitaxial crystal growth might be expected largely through the control of heat treatment. However, it should be pointed out that the design and control of the nucleation site and the crystal growth direction in the crystallization in an electric furnace would be difficult. On the other hand, in the laser-induced crystallization, which enables the heating position, direction, and period, the nucleation site and crystal growth direction might be designed and controlled more effectively. In particular, crossing line experiments are proposed to be a good technique for the study of nucleation and crystal growth in glasses as demonstrated in the present study.