1. Introduction

Femtosecond (fs) lasers have been attractive to fabricate a variety of optical elements in transparent dielectrics due to the unique characteristics of ultrashort duration and ultrahigh peak intensity [1–7]. During the interaction between a tightly focused fs laser and the glass materials, it is well known that nonlinear effects play important roles in energy transference and structural modification. For example, depending on the magnitude of single pulse energy, there have two kinds of absorption mechanism for structural modification. For high energy pulse, a mass of free electron plasma will be first excited via multiphoton or tunneling ionization at the beginning of the pulse, and then the following pulse energy will be further absorbed via one-photon absorption mechanism of inverse bremsstrahlung heating [8]; but for low energy pulse, structural modification can also be achieved with absence of plasma due to an incubation effect resulting in reduction of the ionization threshold [9]. Between pulses, energy relaxation of the heated electrons will take place in the form of lattice deformation through an electron-phonon collision process. Once the absorbed energy in the focal point cannot dissipate or diffuse timely to the outer before the arrival of the next pulse, an increasing amount of energy will continuously accumulate in the irradiated region where a high temperature elevation forms [10,11]. This heat mechanism has been widely accepted for achieving the three-dimensional crystal precipitation inside the glasses [12–17].

However, self-focusing and spherical aberration, as two common optical effects in the case of a tightly focused fs laser irradiating into glass, will cause intensity redistributions along the light propagation direction, which make the associated phenomena more complicated. For example, some literatures have reported that the fs laser-induced temperature fields became asymmetric in isotropic glass and elongated along the light propagation direction [17–19]. Meanwhile, an anisotropic heat diffusion dynamics has also been proposed to explain the aspect ratio of the elemental migration traces under the laser-driven temperature gradient field [5,20]. Since fs laser-induced crystal precipitation depends strongly on the heat accumulation, the asymmetry of temperature distribution would have a significant effect on nucleation and growth of crystals.

Dysprosium molybdate Dy₂(MoO₄)₃ (DMO) is a member of the RE₂(MoO₄)₃ (RE: trivalent rare earth ions) family which owns the characters of ferroelectricity, ferroelasticity, and nonlinear optical properties [21]. Since the DMOs have exhibited a comparatively large electro-optic effect [22–24], therefore they hold considerable technological promise for device application. However, high-quality DMO is always difficult to be obtained until a direct laser writing (DLW) technique was applied to its fabrication. A few molybdate crystals in the same isostructure, e.g., Gd₂(MoO₄)₃, Dy₂(MoO₄)₃ and Sm₂(MoO₄)₃, have been achieved on the surface of the glasses via a so-called “transition metal atom or rare earth metal atom heating technique” for laser hosts, tunable waveguides, tunable fiber gratings [25–28]. But this technique is hard to directly write crystal pattern inside the glasses, which prevents their device application in three-dimensional architecture.

In this study, our results show that the fs laser induced temperature distribution could make important influence on the asymmetry of the modified region and on the crystalline phase transformation. We investigate the spatial distribution of the crystalline phase by using micro-Raman spectra and show that the formation of the DMO crystals, no matter for α-phase or β'-phase, strongly depends on the temperature field induced by fs laser irradiation. We further present that the transformation from β-phase to α-phase occurred in the lower part of the modified structure, which was mainly because of the asymmetry of the temperature distribution. The involved mechanism was discussed from two aspects of self-focusing and spherical aberration. In addition, the results of the electron probe micro-analyzer (EPMA) mapping also reveal that the O ions migrate outward from the focal center while the Mo ions have the opposite movement after the laser irradiation. This migration process partly supports the crystal phase transformation from a perspective of material composition.

2. Experimental

The glass sample was prepared using a conventional melt quenching technique. The mixed materials with the composition of 21.25Dy₂O₃-63.75MoO₃-15B₂O₃ (mol %) about 20 g in weight were melted in a crucible at 1100°C for 45 min in air. Then the melt was poured onto a steel plate and cooled down to the room temperature. The glass transition (T_g) and melting temperature (T_m) were determined by using the differential scanning calorimetry (DSC) (NETZSCH DSC 404C) at a heating rate of 10 K/min. The glass pieces were annealed near T_g~491°C for 4 h to reduce the residual stress. All the samples were cut and optically polished.

The glass sample was placed on a computer controlling XYZ stage. A regeneratively amplified Ti: Sapphire laser (RegA 9000, Coherent Inc.) with 150 fs, 250 kHz, 800 nm mode-locked pulses was focused inside the glass via a 100 × objective lens with a numerical aperture of 0.8. The incident light power can be continuously adjusted by using a neutral density filter. After the laser irradiation, a micro-Raman spectrometer (Renishaw inVia) was used to measure the laser-modified region by a 514 nm laser excitation. The elemental redistribution mapping was performed through an electron probe micro-analyzer (EPMA: JEOL, JXA-8100). All the measurements were carried out at room temperature.

3. Results and discussion

Figure 1 shows the optical microscope images of the modified regions, which were irradiated for 30 seconds by focusing 400 mW fs laser at different focal depths inside the molybdate glass. It is clear that the volume of the formed microstructure is much larger than the laser focal spot, which is due to the induced heat accumulation accompanied with heat diffusion. Some dark regions appear inside the modified structure, which mostly come from the Rayleigh scattering of fs laser-induced defects, bubbles or even crystallites [17]. Since the quantity of these defects is partly in terms of the glass temperature, the inhomogeneous dark regions from top to bottom indicate that more energy is accumulated in the lower part of the modified structure.

 

Fig. 1 Optical microscopic images of the induced microstructures after 400 mW fs laser irradiated 30 s at different focal depths inside the molybdate glass, (a) topview and (b) sideview. (c) Transmittance of the glass sample.

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The topview image displays a group of the induced circular structures in which the focal point is surrounded by a continuous deformation. This multiple-ring pattern in Fig. 1(a) is usually considered from the center temperature elevation and the repeated shock waves during a long time irradiation. During this process, a continuous energy deposition in the center region might cause glass melting, volume expansion and further a lowering of viscosity, meanwhile the radial heat flow also increased the temperature of the surrounding matter and led to the deformation area expanding. Hence, a circular temperature field formed in the fs laser-irradiated region. Another important factor to influence the induced pattern is the formed structural strain resulting from plastic deformation. The fast expansion of the heated material produced an outward pressure in the deformation area. Once the irradiation stopped, a rapid cooling led to a sharp increase of viscosity of the molten fluids, which prevented the compressed materials to recoil from the periphery to the center. As a result, the strains were inevitably to be generated in the frozen region where the lattice’s distortion or displacement may possibly appear [10,11]. These lattice defects would benefit for nucleation of the DMO crystal. The detailed reason will be discussed in the following context.

Unlike the circular symmetry of the cross-section perpendicular to the incident direction, the longitudinal laser-modified structures become gradually elongated and narrower when the focal depth increases. Figure 1(b) shows the dependence of the longitudinal profile on the focal depth. The mechanism of the elongated structures is explained from two aspects of self-focusing and spherical aberration, which produce light intensity redistribution of the incident pulse. When an fs laser is focused into the glass via an objective, the index mismatch between air and glass will lead to an aberration which distorts the wave front of the converging spherical wave, and causes significant stretch of the intensity distribution along the beam propagation direction on the focal axis [29,30]. We have calculated this intensity redistribution and found it would make an obviously longitudinal elongation with the focal depth increasing [31]. Like for the self-focusing, it is an optical Kerr effect induced by the change in refractive index of materials exposed to intense laser. This effect may cause long filament propagation inside the laser-modified structure as if the light travels a focusing lens. Its appearance depends on the instantaneous power of the incident pulse and has a threshold of P_crit = (3.77λ²)/8πn₀n₂ [32]. Figure 1(c) shows the transmittance of the glass sample with two obvious absorption peaks respectively at 807 nm and 901 nm, which indicate the initial glass has an intensive linear absorption about the incident 800 nm light. Therefore, when the focal depth increases further, more energy is lost ahead of the focal region. This results in weakening of self-focusing and reduces its influence on the intensity distribution. The two kinds of intensity modulation produce an asymmetric energy deposition elongated along the light propagation direction, which further built an asymmetric temperature gradient field in glass. As a result, the olive shapes are formed in the longitudinal profile of the modified structure.

Figure 2(a) shows micro-Raman spectra of the fs laser-irradiated region at 120 μm beneath the glass surface. This irradiation lasted for 60 seconds and the incident power was 250 mW. The plotted curves I and II denote the Raman spectra from two sampling points I and II, which respectively locate in the middle part of each of two lines A and B, see the inset in Fig. 2(a). Both two spectra indicate that crystallization have occurred in the irradiated glass. By comparing with the known spectra [25–28], we find that several obvious peaks should attribute to the bending or stretching vibrations in Mo-O bonds of MoO₄ tetrahedral of β'-DMO crystal, in which REO₇ polyhedra and MoO₄ tetrahedra link together to form a crystal unit cell. As for specific belongings, the 327 cm⁻¹ peak corresponds to the bending mode of Mo-O bond, while the 744 cm⁻¹, 827 cm⁻¹ and 850 cm⁻¹ peaks correspond to the antisymmetric Mo-O stretching vibration, both of the 946 cm⁻¹ and 963 cm⁻¹ peaks correspond to the symmetric Mo-O stretching vibration.

 

Fig. 2 (a) Micro-Raman spectra of the unmodified and the modified regions. Curves I and II correspond to the middle parts of line A and B indicated by the arrows in insert. The irradiated power and time are respectively 250 mW and 60 s, the focal depth is 120 μm. (b) Micro-Raman spectra in the centers of the modified regions with varied irradiation times. The laser power and the focal depth are the same as in (a).

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These Raman spectra not only identify precipitation of β'-DMO crystal, a special peak at 899 cm⁻¹ appeared in curve II also indicates more information about the formed crystallites. Here, an important phenomenon needs to be pointed out in advance. The DMO is a temperature-dependent polymorphism and has multiple structural types. Generally speaking, the thermodynamically stable phase is the α-phase with a monoclinic structure (C2/c), which can be formed in a high temperature regime ranging from 800°C to 990°C. But before heating to this temperature, a metastable β-phase with a tetragonal structure (P42₁m) will be firstly formed, and tends to transform to the β'-phase with an orthorhombic structure (Pba2) when the temperature is lower than its Curie temperature of 159°C [26,27]. As the II point in Fig. 2(a) appears a Raman peak at 899 cm⁻¹, which has been identified as the indicator for the formation of α-phase crystal [26], we think that the II region should be a higher temperature region than other ones, i.e., there suffered from the maximum light intensity. In Fig. 2(b), we find that the signal intensity at 899 cm⁻¹ becomes stronger and stronger with the irradiated time increasing. This tendency indicates that the phase transformation of the DMO crystal closely depends on the fs laser-induced temperature field. During the crystallized process of the laser-heated glass, a certain amount of β-phase crystallites could transform to α-phase state in the dark region where a relative high temperature sustained for their phase transformation. In fact, this phase transformation is slow kinetically [33], therefore, the longer the irradiated time lasted, the more the crystallites from β-phase to α-phase transformed. Once the melt quenched, the residual β-phase crystallites had to transform to the β'-phase ones. In the previous report of writing crystal lines by samarium atom heat processing [26], the crystal line consisting of single β'-phase could be achieved after a continuous-wave, 1064 nm and 0.9 W YAG laser exposure at the scanning speed of 10 μm/s, whereas the crystal line written after 0.73 W YAG laser exposure at the speed of 1 μm/s contained both α-phase and β'-phase. That indicated that an increase of the deposited energy in per unit length could improve the formation of α-phase crystallites. This agrees well with our experimental results.

According to the above discussions, the dark color in the region II reflects the assembly of a mass of defects or bubbles, and their quantities to some extent depend on the induced temperature. These induced defects were the preferential nucleation sites for the β-phase crystallites, which would further transform to α-phase ones after some time irradiation. Therefore, the results in Fig. 2 prove that the asymmetry of the fs laser-induced temperature field can have important influences on crystal precipitation and on subsequent phase transformations.

Figure 3 shows the multi-point scanning Raman spectra for the DMO crystal distribution. We chose a Raman signal at 963 cm⁻¹, which is the most intense peak of the DMO crystal, to plot an intensity mapping in the cross-section of the fs laser-modified structure. The intensity distribution of Raman signal shows a circular symmetry and is a radial gradient except a depression in the focal center. That indicates that the center of the irradiated region possibly formed a porous, bubble-filled core with lower density [14,15]. In order to better understand this phenomenon, let us recall the process of heat accumulation. When a high repetition rate fs laser beam is focused inside the glass, hot electron plasma is firstly induced via multiphoton ionization. After an experience on the electron-lattice collisions and the resulting energy accumulation, the heat-affected glass will expand outwards due to a temperature elevation in the modified structure. But a fraction of overheated glass in the focal center suffers from repeated ionizations, which results in material composition changing and imbalance of the chemical elements, thus the crystal growth rate at the focal center is slower than that at the surroundings. Furthermore, the ionized materials in the focal center might well be pushed downwards by an asymmetric temperature field. This anisotropic heat diffusion produced a shift of the crystallized region from the structural center to the lower part. Therefore, much more information about the asymmetric crystallization behavior should be dug out from the longitudinal cross-section.

 

Fig. 3 (a) The sketch map of the Raman scanning from both of topview and sideview (irradiation time: 60 s; laser power: 250 mW; depth: 120 μm). (b) Micro-Raman mapping at the 963 cm⁻¹ peak for the modified region. (c) and (d) the intensity distribution at 963 cm⁻¹ peak along the lines A and B, respectively.

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We plot the horizontal distribution of Raman signal at 963 cm⁻¹ in the different depths of the modified structure, as shown in Figs. 3(c) and 3(d). These two curves correspond to the scanning paths line A and line B described in Fig. 3(a). Both have an intensity depression in the center, which shows a little weaker crystallization than the periphery. Especially for the line B, the dark region in the middle part experiences a relatively high temperature and pressure where the transformation from β-phase to α-phase takes place. Besides, Raman signal in line B has more peaks including the ones in the same positions of line A and other two special ones with higher intensities, which are close to the contour of the inner boundary as labeled in Figs. 3(a) and 3(d). This means that the boundary of the inner region may be another favorable place with high temperature and pressure for the initial heterogeneous nucleation [17]. Since this region is located near the bottom of the modified structure, a diffraction effect resulting from spherical aberration during the laser writing might be a plausible explanation for the lateral separation of light intensity [29]. Based on this hypothesis, we suggest that this diffraction effect should also be responsible for the induced multiple-ring pattern. Following this idea, there can produce multiple heat sources including a central principal maximum and some low-level diffraction rings in the entire modified region, which result in a superimposed effect on the temperature distribution for the nucleation and growth of the DMO crystals, but the detailed mechanism still needs more investigations.

Figure 4 shows the different elemental concentration in the longitudinal cross-section of an fs laser-modified structure, which is irradiated by using 250 mW laser for 60 seconds. Figure 4(a) shows the backscattering electron image, in which a light color region is the inner of the formed structure. There the concentration of Mo element has a little increase while the concentration of O element reduces, but an opposite migration process for the two elements happens in the periphery of the focused region. As for the Dy element, there showed negligible variation between the modified region and the surroundings, so we think that Dy was insensitive in the laser-driven element migration in current glass composition. In previous studies, the mechanism of the elemental redistribution was assumed to be caused by the temperature gradient induced by the heat diffusion [12,20]. Recently, Jain et al. presented that a ponderomotive force $F_p=-\frac{e^2}{4m{\omega }^2}\nabla E^2$, a nonlinear force that a charged particle experiences in an inhomogeneous oscillating electromagnetic field, may influence the redistribution of element due to high pulse energy of fs laser [14,15]. In their opinions, a charge displacement that developed for the ponderomotive forces could drive electrons away from the center of the high-energy pulse. Therefore, at the beginning of the irradiation, the number of the liberated ions increases due to the breaking of glass network via simultaneous multiphphoton ionization. Then all the free ions have a migration tendency towards the outer region under the driving of the ponderomotive force. However, in contrast to the O ions with negative charges, the high valence Mo ions have a higher polarizability and stronger capability of charge accumulation [34], which result in a slow mobility. Meanwhile, following with the heat expansion process, some migrated O ions will be expelled into the network of the peripheral melts and further fill in the space where previously occupied by the Mo ions, thus a small portion of Mo ions will migrate towards the center as a result of glass network deformation. That produced a relatively rich center in the redistribution of the Mo element and a reverse movement for the O element. Furthermore, it is reported that the density of α-phase crystalline is larger about 25% than that of β'-phase one [35], so we think that the high concentration of the Mo element may be positive to transform β-phase to α-phase state in the richer Mo region. That means that the crystallization behavior could vary accordingly with the composition variation driven by the temperature gradient and the ponderomotive force.

 

Fig. 4 (a) Backscattering electron image and (b-d) EPMA mapping for the concentration of different elements (O), Dy and Mo) in the fs laser-modified region (irradiation time: 60 s; laser power: 250 mW; depth: 120 μm).

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4. Conclusion

In conclusion, spatial distribution of the Dy₂(MoO₄)₃ crystal in the fs laser-modified glass has been studied. According to micro-Raman spectra, we found that the DMO crystals could precipitate inside the molybdate glass and a transformation from β-phase to α-phase occurred at the relatively high temperature region. The temperature discrepancy in different parts of the fs laser-modified structure resulted from an asymmetrical intensity distribution along the longitudinal direction due to both effects of self-focusing and spherical aberration. This phenomenon will make important influences on the subsequent crystal nucleation and growth. Meanwhile, the elements migration process in the modified region has been studied through the EPMA analysis. The result shows that a high concentration of the Mo element in the center possibly promotes the β- to α-phase transformation of the DMO crystal.