Femtosecond laser-induced refractive index changes in lithium niobium silicate glass were explored at high repetition rate (300 fs, 500 kHz) by polarized light microscopy, full-wave retardation plate, quantitative birefringence microscopy, and digital holographic microscopy. We found three regimes on energy increase. The first one corresponds to isotropic negative refractive index change (for pulse energy ranging 0.4-0.8 μJ/pulse, 0.6 NA, 5μm/s, 650μm focusing depth in the glass). The second one (0.8-1.2 μJ/pulse) corresponds to birefringence with well-defined slow axis orientation. The third one (above 1.2 μJ/pulse) is related to birefringence direction fluctuation. Interestingly, these regimes are consistent with crystallization ones. In addition, an asymmetric orientational writing effect has been detected on birefringence. These topics extend the possibility of controlling refractive index change in multi-component glasses.
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Modifying glass in three dimension (3D) with femtosecond (fs) laser dates back from 1996, when Davis et al.  reported fabricating waveguides inside various glasses (e.g. silica, Ge-doped silica, and borate) by tightly focused fs laser. Since then, fs laser micromachining has received intensive attention in optics [2–4]. In silica glass, at low repetition rate, without crystal formation, depending on the pulse energy delivered to the glass, three regimes of modifications with three thresholds have been defined on pulse energy increase . Note that the transition energy threshold between each regime is not specified, because the onset at certain threshold depends on the glass chemical composition [6, 7], focusing geometry , and the laser parameters (e.g. pulse duration  and repetition rate ).
A first threshold is the one related to the generation of isotropic refractive index change without obvious structural damage. The contrast of the refractive index change can be either positive or negative depending on the materials. The refractive index change can reach the maximum at 3-6 × 10−3 in fused silica, which is large compared to the one induced by UV nanosecond laser . This modification can be erased by heating the sample at temperature large enough (e.g. 1 hour at 900 °C) . The energy operating window for the first regime is narrow but increases in width for the shortest pulse duration . Poumellec et al. [5, 7] proposed that this modification can be explained by the change of the fictive temperature of material. This modification can be used to fabricate low loss optical waveguides .
A second threshold is the generation of form birefringence. This anisotropic refractive index change magnitude can reach as high as −0.1 . This birefringence can be explained by a self-organized quasi-periodic nanostructure formation (i.e. nanograting), consisting of thin planes of low refractive index, characterized by silica decomposition, surrounded by thick zones of unchanged refractive index . This assembly behaves as a uniaxial birefringent matter [2, 13]. Such kind of structures have applications in polarization converters, microfluidic, and nanofluidic channels . So far, the nanograting is investigated inside a limited number of materials (e.g. fused silica  and borosilicate glass ). In addition, narrow range of pulse durations (150-200 fs) is required to observe the birefringence in some multi-component glasses (e.g. Borofloat 33 glass) . It is worth noting that the birefringence threshold is significantly dependent on doping (e.g. fluorine, phosphorous, or germanium) . Vangheluwe et al.  demonstrated a silver ions-assisted nanograting formation at the glass surface: significant lowering of the threshold of nanograting formation and better quality nanogratings.
A third threshold is the voids formation (disruptive modification) . At high pulse energy, a void surrounded by a high refractive index crust occurs. This phenomenon can be explained by the Coulomb repulsion between the ions after electron excitation, which generates pressures larger than the material Young modulus . This leads to a shockwave, resulting in a less dense or hollow core in the focal volume surrounded by a dense shell . This kind of modification has potential applications in 3D optical storage .
For high repetition rate (ca. > 100 kHz) in fs laser irradiation, the time between successive laser pulses is shorter than the one for heat to diffuse away (typ. μs scale). A thermal accumulation in the focal volume occurs [3, 20]. Heat accumulation causing glass local melting, nanostructures may be erased . However, the high temperature achieved during a time longer than the diffusion time, may induce crystallization in suitable glasses. Especially, obtaining nonlinear optical crystals in materials by fs laser irradiation has received intensive attention due to the potential applications in active optical devices (e.g. frequency converters) .
Fs laser-induced nonlinear optical crystals in glasses can date back to 2000, when Miura et al.  reported the space-selective growth of β-BaB2O4 inside BaO-Al2O3-B2O3 glass at the focal point. To date, various choices of nonlinear optical crystals have been reported [21, 23, 24]. Amongst them, glasses producing LiNbO3 seem interesting for collecting refractive index change [25, 26] and second harmonic generation (SHG) . Fan et al. [26, 28] reported the refractive index change in Li2O-Nb2O5-SiO2 (LNS) glass after fs laser irradiation at low repetition rate (i.e. 1 kHz), without crystallization. This is interesting in cladding elaboration but not for SHG. Recently, we found that at high repetition rate (e.g. 300 kHz), according to pulse energy, three regimes of structural modifications on pulse energy increase can be achieved: one regime during which the fictive temperature of the amorphous phase is changed inducing a larger sensitivity to chemical etching (i.e. HF); a second regime where textured nanocrystals embedded in lamella-like amorphous phases is produced; and a third regime for which the crystallization is dependent on the writing configuration (the parameter couple: direction of writing-laser polarization direction). Moreover, in regime 2 due to the formation of textured nanocrystals embedded in self-assembly amorphous walls, a form birefringence appears . However, for further application, it is necessary to know more on refractive index change in LNS glass with crystallization.
Herein, we check the tunability in the same time we extend the observations to larger repetition rate (500 kHz) for obtaining well-defined birefringence along scanning direction, which is promising for the fast fabrication. The refractive index of irradiated line in LNS glass was investigated systematically by polarized light microscopy, full-wave retardation plate, quantitative birefringence microscopy (QBM), and digital holographic microscopy (DHM). The nonlinear response of irradiated line was determined by polarization-direction dependence of SHG (i.e. SHG intensity of irradiated line varying with the probing laser polarization angle) . This topic is of importance in the fabrication of multi-functional optical devices.
LNS glass with chemical composition of 33Li2O-33Nb2O5-34SiO2 (mol%) was fabricated from Li2CO3, Nb2O5, and SiO2 by conventional melt quenching method . A commercial Yb-doped fiber amplifier fs laser (Satsuma, Amplitude Systèmes Ltd.) with central wavelength of 1030 nm, pulse duration of 300 fs, and repetition rate of 500 kHz was used as radiation source.
An aspheric lens (numerical aperture, NA = 0.6) was used to focus the laser pulses 650 μm below the glass surface. Lines were achieved by continuous scanning irradiation in the plane perpendicular to laser propagation direction (i.e. XY plane) at a speed of 5 µm/s. The distance between each line is 50 µm. The laser polarization was linear and parallel to scanning direction. Pulse energy was controlled by a combination of a half-wave plate and a polarizing beam splitter cube, ranging from 0.4 to 2.2 μJ/pulse, by steps of 0.2 μJ/pulse. The pulse energy was measured by a laser power energy meters (Ophir Laser measurement P/N 7Z01601), after the beam having passed through lens in air. It is worth noting that the threshold for obtaining crystals inside LNS glass is defined by listing the irradiation conditions (e.g. laser wavelength, repetition rate, NA, focus depth, and scanning speed). In fact, this is not a bulk or surface laser-induced damage threshold but a threshold of glass permanent transformations. A more accurate method to determine the threshold of glass transformations under fs laser irradiation was described in .
Polarization-direction dependence of SHG of irradiated lines was performed below the energy threshold for glass modification with the same laser. Details of the experiment are given in . Optical path differences ranging from a fraction of a wavelength up to several wavelengths can be estimated by full-wave retardation plate method. A full-wave retardation plate (530 nm, Olympus U-TP530) was used to determine slow axis orientation of irradiated line in XY plane. Before attempting an analysis of birefringence, irradiated lines were oriented with the neutral axis in a diagonal position with respect to the microscope polarizer and analyzer. The full-wave retardation plate was inserted at diagonal position with reference to the microscope polarizer/analyzer direction. The quantitative birefringence properties of irradiated lines were measured in XY plane by QBM. Details of QBM measurement (operating wavelength of 515 nm) are shown in . DHM was performed by transmission configured digital holographic microscope (DHM) T 1000 models, with operating wavelength of 666 nm in University of Southampton.
Then, the sample was cut along the direction perpendicular to the scanning direction (i.e. YZ plane) and polished to optical quality (with colloidal silica, 0.03 μm). To have a high contrast in scanning electron microscopy (SEM) observation, the above polished samples were etched by HF (10%, 2min)  Electron backscattered diffraction (EBSD) was conducted with a field-emission gun scanning electron microscope (FEG-SEM ZEISS SUPRA 55 VP).
3.1 Refractive index change observation
3.1.1 Microscopy observation in natural light
Firstly, microscopy observation using natural light was conducted to check if there is contrast between the written lines and the area not irradiated by fs laser. The factors inducing contrast may be due to the refractive index change, absorption, or scattering.
Figure 1 shows the microscopy images of irradiated lines varying pulse energy and writing orientation (N.B. in + or -X, X means the direction of writing and the sign indicates the orientation along this direction, marked by cyan arrows in Fig. 1(a)). The laser propagation direction was perpendicular to the paper plane. We note a trend of the fs laser LNS glass interaction area to increase in size with increasing pulse energy. As shown in Fig. 1(a), at 0.4 μJ/pulse, the irradiated lines are almost undetectable. At the energy of 0.6 μJ/pulse, homogeneous thin darker lines were observed. No difference of the structures was detected between the lines written in two orientations.
At 0.8-1.2 μJ/pulse, there are overlapping dots and the lines become darker with the increase of pulse energy (Figs. 1(a)-1(c)). It is worth pointing out that the morphology of the irradiated lines changes, just by reversing the laser writing orientation (N.B. a direction has two orientations), especially at 0.8 μJ/pulse. The –X writing orientation (the right line in Fig. 1(b)) is rougher than the line written in the reversed orientation ( + X writing orientation, the left line in Fig. 1(b)). This asymmetric writing for opposite orientations in LNS glass is similar to the one reported in silica glass [31, 32]. This writing orientation dependence writing is like “quill” writing, which can be explained by the anisotropic trapping of electron plasma by a tilted front of the laser pulse along the writing direction . At 1.4-1.6 μJ/pulse, the size of black dots becomes larger (shown in magnified Fig. 1(d)). At 1.8-2.2 μJ/pulse, black dot size increases further and black linear contrasts surrounding the doted lines appear (marked by green arrows for 2.0 and 2.2 μJ/pulse in Fig. 1(a) and magnified Fig. 1(e)). This may seem to be fractures in glass, produced by the material modification in the lines appearing dotted.
3.1.2 Microscopy observation with polarized light
Then, polarized microscopy was used to determine qualitatively the birefringence of irradiated lines. The images of irradiated lines were taken between two crossed polarizers (i.e. A and P, illustrated in Fig. 2) in transmission mode. As show in Fig. 2, no birefringence was obtained for irradiated lines at the pulse energies of 0.4 and 0.6 μJ/pulse. With the increase of pulse energy (i.e. 0.8 to 2.2 μJ/pulse), birefringence of irradiated lines was obtained. At 0.8-1.2 μJ/pulse, when the sample was rotated around the laser propagation direction (i.e. along Z direction), an intensity variation (period of 90°) of irradiated line was observed: intensity reaches minimum when laser polarization direction (illustrated by E in Fig. 2) is closely parallel or perpendicular to the polarizers (shown in Fig. 2(a)), but maximum when the writing laser polarization is nearly oriented to a diagonal position (illustrated in Fig. 2(b)). In contrast, the non-irradiated area is stable (totally dark). Increasing the pulse energies above 1.2 μJ/pulse, strong scattering of irradiated lines was obtained, whatever the direction of irradiated lines in respect to the polarizer and analyser.
The birefringence is therefore well defined at moderate pulse energy (i.e. 0.8-1.2 μJ/pulse). To go a step further, a full-wave retardation plate (530 nm, Olympus U-TP530) was used to determine slow axis of irradiated lines at this pulse energy range. A full-wave retardation plate (denoted as λ in Fig. 3) was oriented with its slow axis in a diagonal position with respect to the crossed polarizers (illustrated by A and P in Fig. 3). The background is isotropic, appearing magenta. When line appears blue (Fig. 3(a)), it means that the slow axis of irradiated line at that place is parallel to the slow axis of the full-wave retardation plate. In contrast, if yellow (Fig. 3(b)), the slow axis irradiated line at that place is perpendicular to the slow axis of the full-wave retardation plate. This phenomenon is clearer for low pulse energy one (i.e. 0.8 μJ/pulse, shown in Fig. 3) than for the higher ones (i.e. 1.0 and 1.2 μJ/pulse, shown in Fig. 3). Thus, the large refractive index direction (slow axis) of the birefringence region is perpendicular to laser polarization direction (illustrated by E in Fig. 3) in XY plane.
It is worth mentioning that we observed a weak birefringence around the irradiated line at 1.0 μJ/pulse for –X writing (marked by green arrows in Fig. 3). This observation is much clearer at 1.2 μJ/pulse for –X writing. The line sides exhibit slow axis directions at 90° from each other (illustrated by yellow arrows in Fig. 3). To get quantitative information of the birefringence of these irradiated lines, quantitative birefringence microscopy (QBM) was then performed.
3.1.3 Quantitative birefringence microscopy (QBM) measurements
Figure 4 shows the birefringence properties of irradiated lines varying pulse energy (two lines in each energy group but different writing orientation illustrated by the cyan arrows). As shown in Fig. 4(a), no retardance was detected for the lines written at 0.4 and 0.6 μJ/pulse, but for the energy ranging from 0.8 to 2.2 μJ/pulse. Well-defined retardance of irradiated line was obtained along scanning direction at 0.8-1.0 μJ/pulse. With the increase of pulse energy (i.e. 0.8-1.0 μJ/pulse), the retardance amplitude of irradiated line increases and reaches the maximum (i.e. 87 nm). If we continue to increase the pulse energy, 1.2 μJ/pulse, the retardance decreases to 48 nm for the + X writing. At 1.4 μJ/pulse, the fluctuation of retardance amplitude is larger than for the low pulse energy ones. It is worth noting that for –X writing, for the left side of the irradiated line, the retardance along scanning direction is nearly homogeneous (illustrated by the pink arrows and the magnified inset in Fig. 4(a)). Then, increasing pulse energy further (i.e. 1.6-2.2 μJ/pulse), the retardance of irradiated line becomes fluctuating along scanning direction.
Figure 4 (b) illustrates the slow axis direction of the corresponding irradiated lines. The color in QBM image shows the slow axis direction of the irradiated line and the color of the circular legend displays slow axis direction. At 0.8-1.0 μJ/pulse, the irradiated line appears completely red and homogeneous along scanning direction, indicating that the slow axis (i.e. the largest refractive index axis) is oriented perpendicularly to the writing laser polarization direction. This is in agreement with the result measured from full-wave retardation plate by polarized light microscopy. Interestingly, we observed an occurrence of orientational dependence in the structures written along the + X and –X directions at 0.8 μJ/pulse, which can be clearly shown from the magnified image (Fig. 4(c)). The irradiated lines in both writing directions show the same profile shape (i.e. bell-shaped) but the retardance amplitude is different (shown in Fig. 4(a) bottom). The peak retardance amplitude for + X writing (38 nm) is smaller than the –X one (55 nm). It reveals an asymmetric orientational writing (AOW) effect on the refractive index change in LNS glass in heat accumulation regime.
At 1.0 μJ/pulse, for + X writing, the slow axis direction is 90° from the line (red). However for –X writing, the irradiated line is surrounded by an opposite birefringence, with retardance around 20 nm (i.e. blue, indicated by white arrows in Fig. 4(d)). This surrounding birefringence is due to stress induced by volume change in the center of the line . If we continue to increase the pulse energy, 1.2 μJ/pulse, for + X writing, the irradiated line remains nearly red, but for –X writing, the line appears with two sides with opposite birefringence (i.e. red on one side and blue on the other, marked by yellow arrows and the magnified inset in Fig. 4(b)). From the magnified image (Fig. 4(e)), we found that there is a blue area around the irradiated line, with retardance peaking at ~25 nm (marked by white arrow in Fig. 4(e)). This observation is consistent with the result recorded with full-wave retardation plate by polarized light microscopy .
Above 1.2 μJ/pulse, the X writing becomes heterogeneous along scanning direction with a dominant blue. Exceptionally for 1.4 μJ/pulse and –X writing, the left side of the irradiated line is uniformly blue along scanning direction (marked by the pink arrows and the magnified inset in Fig. 4(b)), with high retardance ~40 nm. It indicates that with the increase of pulse energy, the stress-induced birefringence becomes more and more important. Then, with the increase of pulse energy (1.6-2.2 μJ/pulse) the slow axis orientation appears even more fluctuating along scanning direction (Fig. 4(b) right part). We observed also that the line width greatly increased.
3.1.4 Amplitude of the mean refractive index change
Lastly, digital holographic microscopy (DHM) was used to determine the amplitude of the mean refractive index change in the irradiated lines. Almost no phase difference between the glass matrix and irradiated line was detected for 0.4 μJ/pulse (Fig. 5(a) right). A negative refractive index change was recorded for 0.6 μJ/pulse, shown in Fig. 5(a) left. When increasing the pulse energy (i.e. 0.8 μJ/pulse, Fig. 5(b)), there is a positive peak at the center (as large as 1.75 rad for –X writing) surrounded by small negative variations. In contrast for + X writing, the phase change is smaller than the –X one. It indicates an AOW effect on the mean refractive index change in LNS glass.
At 1.0 to 1.2 μJ/pulse, the shape of the refractive index change profile is complex and exhibits pairs of positive peaks at the center surrounded by negative refractive index changes (Figs. 5(c) and 5(d)). It is worth noting that for higher pulse energy fabrication, high frequency modulation of the phase was detected, with no obvious correlation with the QBM results. This may be due to abrupt change in phase (plus scattering) that DHM method is not capable to reconstruct correctly and yields oscillations like windowing in Fourier transformation.
3.2 Second harmonic generation (SHG) observation
SHG here is a good mean for confirming that LiNbO3 crystals are formed . Green irradiation was observed during laser writing process from the pulse energy of 0.8 μJ/pulse (1030 nm, 300 fs, 500 kHz, NA = 0.6, focus depth 650 μm in glass, and scanning speed of 5 μm/s), not below. Then, it was possible to record SHG direction dependence of irradiated lines varying the probing laser polarization. For pulse energy 0.8-1.4 μJ/pulse, with a maximum in the direction perpendicular to the polarization or writing direction (as they are parallel in this experiment) and a minimum in the direction of writing. When we increase the pulse energy to 2.2 μJ/pulse, strong SHG is observed whatever the direction of probing laser polarization.
As shown by green curve in Fig. 6, at 0.8 μJ/pulse for writing along + X direction, a well-defined curve with period of 180° was observed. The minimum SHG intensity peaks when the probing laser is closely parallel to writing laser polarization direction (i.e. 172°) and the maximum SHG intensity was obtained at an angle closely perpendicular to writing laser polarization direction (82°). Interestingly, when we change the writing orientation to –X direction (illustrated by red curve in Fig. 6), the probing laser polarization is around 92° for obtaining maximum SHG intensity. So, an AOW effect on the polarization-orientation dependence of SHG intensity on probing laser polarization was detected.
Here, we defined a quantity that called “anisotropy magnitude”, deduced from the above polarization-orientation dependence of the SHG intensity curve, following the Eq. (1) below.
This was used to characterize the SHG polarization-orientation contrast. At 0.8 μJ/pulse, the anisotropy magnitude is 0.79 for + X or –X cases. It indicates that even a AOW effect on the polarization-orientation dependence SHG was observed for different writing orientations, there is no effect on anisotropy magnitude for this pulse energy (i.e. slightly above the crystallization threshold). This observation is consistent with results obtained at 250 kHz . When increasing the pulse energy to 1.0 and 1.4 μJ/pulse, anisotropy magnitude decreases to 0.51 and 0.37, respectively. Our previous work  shows influence of the second texture, oriented at 90° from the other, and becoming dominant for larger pulse energy is already detected.
4.1 Summary of the fs laser-induced refractive index change in LNS glass
Under fs laser irradiation at high repetition rate (300 fs, 500 kHz), increasing the pulse energy, we observed three regimes of refractive index change with three energy thresholds in LNS glass. The first one is defined by the appearance of isotropic negative refractive index change (0.4-0.8 μJ/pulse). The second one (0.8-1.2 μJ/pulse) is the occurrence of birefringence with well-defined slow axis, perpendicular to writing laser polarization direction in XY plane. The third regime (above 1.2 μJ/pulse) is the one with fluctuating birefringence and two textures along scanning direction, and strong optical scattering.
4.2 Refractive index change interpretation due to nonlinear optical crystal formation
To get a deeper understanding of underlying physics of the fs laser-induced refractive index change in LNS glass, SEM and EBSD were used to investigate the material structure changes (e.g. morphology and crystal distribution) of irradiated lines after polishing to expose the laser-modified area as it was already made for lower repetition rate .
Regime 1: At low pulse energy (i.e. 0.4-0.8 μJ/pulse), a needle-like morphology is observed along the laser propagation direction. Figure 7(a) displays the laser track, obtained at 0.4 μJ/pulse, with width of 0.4 μm and length of 6.3 μm. In addition, a clear boundary is observed between the glass matrix and the over-etched amorphous zone (illustrated by red arrows in Fig. 7(a)). With the increase of pulse energy (i.e. 0.6 μJ/pulse), as shown in Fig. 7(b), the width of laser track increases to 0.9 μm and length to 20.3 μm. In addition, a clearer boundary is observed, marked by red arrows in Fig. 7(b). These modifications are associated with a permanent refractive index change without crystallization . They can be explained by fictive temperature increase of the material , thus explaining the negative refractive index changes observed here. Fan et al.  evaluated the fictive temperature change of + 300 K, a free of stress volume expansion ratio ~2 × 10−2 and then the refractive index change around −1.3 × 10−2 in LNS glass. It is worth pointing that for pure silica, the refractive index change versus fictive temperature increase is positive as the volume decreases when fictive temperature increases .
Regime 2: With pulse energy increase (i.e. 0.8-1.2 μJ/pulse), a filamentary propagation is recorded (marked by yellow arrow in Fig. 7(c)). This phenomena is caused by the dynamical balance between self-focusing and defocusing due to the plasma formation, characterized by a near constant beam waist over several Reyleigh lengths . Typically, tight focusing can lead to a shorter filament. The length of filament increases with the pulse energy and the filament onset moves towards the lens direction .
Besides the over-etched amorphous area (marked by red arrows in Fig. 7(c)), a rough structure is obtained at the centre of laser-modified area. The distribution of crystals and their orientation are investigated by EBSD. By comparing the SEM image (marked by red rectangle in Fig. 7(c)) and the corresponding mapping of the crystal orientation (Fig. 7(d)), we found that nanocrystals are obtained in the rough zone. The global color of the map is nearly blue or green but not red, indicating the formation of textured nanocrystals (i.e. polar axis avoids oriented along the writing laser polarization direction as demonstrated in [30, 33]). For LiNbO3, the largest SHG intensity is obtained when probing laser polarization is oriented parallel to polar axis direction. The above texture is in agreement with the results from SHG observation: the largest SHG intensity is observed when probing laser polarization is oriented perpendicular to writing laser polarization direction. This pulse energy controlled nanocrystal formation is in agreement with previous ones obtained at 250 or 300 kHz at moderate pulse energy [27, 30, 33]. It indicates that even if we increase repetition rate as high as 500 kHz, textured nanocrystals can also be obtained. Moreover, these textured nanocrystals are embedded in self-organized amorphous nanostructures, leading to a form birefringence . This explains why the slow axis of irradiated line is oriented to writing laser polarization direction for moderate pulse energy. For details, please refer to our previous works [23, 25, 30].
For high pulse energy, the slow axis direction is fluctuating because the texture and the nanostructure are fluctuating. The dominant blue color in Fig. 4(b) is thus arising from stress birefringence, produced by specific volume change due to crystallization in the center of the line. Take silica glass for example. Fast-cooled glass (with higher fictive temperature) shows a smaller volume . In that case, the volume decreases with increase of the fictive temperature. The volume shrinks but the surrounding material resists. This induces stress field in the surrounding area but also in the radiation-affected zone. For a negative free of stress volume contraction ratio, the birefringence is with the slow refractive index parallel to the line direction . In the case of LNS crystallization, the conclusion is qualitatively the same as crystallization induces volume decrease.
Now, let us discuss the irradiated line that is composed by two sides with opposite birefringence for 1.2 μJ/pulse (marked by yellow arrows in Fig. 4(b)). The birefringence with slow axis perpendicular to the laser polarization direction (shown by the red in Fig. 4(e)) can be explained by the nanoscale periodic phase separation: textured nanocrystal embedded in nanostructured amorphous phase . In agreement with above, the birefringence with the other orientation (i.e. shown in blue in Fig. 4(e)) may be explained by the disappearance of the self-organisation of texture and nanostructure, leaving the stress field, induced by the crystallization volume change alone for producing birefringence by photoelastic effect.
Regime 3: When increasing the pulse energy above 1.2 μJ/pulse, take 1.4 μJ/pulse for example. As shown in Fig. 7(e), affected area becomes larger along laser propagation direction, with width of 4.8 μm and length of 56.0 μm. In addition, sub-micro meter scale crystals are obtained. At high pulse energy, 2.0 μJ/pulse (Figs. 7(f) and 7(g)), the interacted area becomes even larger: width of 8.0 μm and length of 66.7 μm. In addition, the crystal size becomes larger, especially in the head of laser track (with diameter as large as 2.3 μm).
As shown in the inset of Fig. 7(f), a smooth zone (marked by green arrows in the inset of Fig. 7(f)) was obtained between the HF over-etched zone and the central rough zone. The boundary between the glass matrix and the over-etched zone is marked by red arrows in Fig. 7(f). This dependence of the number of zones with the pulse energy is in agreement with previous one recorded at 300 kHz . Actually, the central rough zone is consisting of LiNbO3 crystals embedded in lamella-like frames of amorphous SiO2 . The orientation of the amorphous phase wall is perpendicular to laser polarization direction. For details of each zone’s properties, please refer to .
It is worth to point out that, in comparison with the low pulse energy, two kinds of micro-sized cracks occur within and in the surrounding material of the laser track: transversal (marked by orange arrows in Fig. 7 (f)) and longitudinal ones (marked by blue arrow in Fig. 7 (f)). The first kind may be induced by tensile or shear stress. The origin of the second one is not clear. The fractures of the second kind may explain the splitting around the irradiated lines, obtained in Fig. 1(e) and the birefringence obtained in QBM images (Figs. 4(a) and 4(b) right part).
For glass ceramic materials, the attenuation of light because of scattering is dependent on the difference in refractive index of the two phases, the size, and the distribution of crystals in the glass . Hendy  computed the scattering intensity and found that the attenuation of light because of scattering (i.e. turbidity) has a strong dependence on the average radius of the crystals in the glass (i.e. ∝ R7) at a given crystalline volume fraction. In our case, LiNbO3 is obtained embedded in amorphous phases (i.e. SiO2) [23, 25]. The refractive index difference between these two compositions is large (i.e. ~2.3 and ~1.45, respectively). The fs laser-induced large crystal size at high pulse can explain the strong scattering recorded from polarized microscopy. However, if the size of crystal is much smaller than wavelength, the low scattering loss can be maintained, thus obtaining transparent devices.
4.3 Calculation of refractive index change
Based on the results from QBM, DHM, and SEM, the refractive index of irradiated lines in LNS glass (XY plane) can be calculated as below.
Where R is the retardance of the sample, which can be obtained from QBM result (measured at 515 nm); t is the thickness of the region where birefringence is produced (deduced from SEM images). na and nb are the eigen values of the refractive index in the plane perpendicular to the light propagation direction.
DHM records holograms produced by the interference between the beam transmitted through the sample and a reference beam generated inside the microscope. For the irradiated line (measured in XY plane), the averaged refractive index of the irradiated line () can be calculated based on Eq. (3)
Where Δφ is the measured phase difference between glass matrix and irradiated line (unit is in rad); λDHM is the wavelength (666 nm) used for the measurements; n0 is refractive index of the background (i.e. glass matrix without laser irradiation), which was measured by Brewster’s angle method with a continuous wave He-Ne laser at 632.8 nm: 1.937 ± 0.004. This high refractive index is due to the high content of niobium .
For 0.6 μJ/pulse, + X writing, the refractive index contrast to the glass matrix is −2.3 × 10−3, thus consistent with fictive temperature change for low pulse energy . When increasing the energy (e.g. 0.8 μJ/pulse, –X writing), refractive index change becomes positive and reaches 2.0 × 10−2 due to crystallization. We get na = 1.9604 and nb = 1.9544. This is quite interesting for further waveguide elaboration . Then for higher pulse energy, behaviour is complex but remaining at a high positive level. It is worth noting that the wavelength for the measurements QBM, DHM, and Brewster’s angle method are different, which introduces the error of the final results.
For comparison, we collected the information on refractive index change in LNS glasses according to the various laser parameters (shown in Table 1) from several authors.
We can see that at low repetition rate (i.e. 1 kHz), without crystallization, birefringence can be achieved above a certain pulse energy threshold (i.e. 0.12 μJ/pulse) . In these conditions, negative refractive index change was observed due to fictive temperature increase and related photoelastic effect . The authors evaluated the refractive index change induced by stress field to −3.0 × 10−3 for the mean refractive index change and to −2.9 × 10−3 for the birefringence with the slow axis perpendicular to the line direction.
At high repetition rate (e.g. 500 kHz in our case), below the crystallization threshold, negative refractive index change was achieved without birefringence. Birefringence appears just above the crystallization threshold with the slow axis perpendicular to the laser polarization. This can be explained by the nanostructure (periodic phase separation) of textured nanocrystals and vitreous phase [25, 30]. At high pulse energy, birefringence can still be detected, fluctuating along scanning direction. In this case, larger crystal formation and disordered texture and nanostructure do not lead to strong birefringence, leaving likely the stress at the origin of it. Additionally, there are modulations along the radius originated from crystallization density modulation. It is worth noting that the regimes defines here, based on refractive index properties, are consistent with crystallization regimes, which are defined in details in .
In conclusion, we demonstrate the multiplicity of refractive index change in LNS glass under fs laser irradiation at high repetition rate (1030 nm, 300 fs, 500 kHz, NA = 0.6, 5 μm/s, focusing depth 650 μm below the glass surface). These regimes, defined based on refractive index properties, are consistent with regimes of crystallisation. The first regime is the one with isotropic negative refractive index change (0.4-0.8 μJ/pulse), due to the change of the fictive temperature of the material. The refractive index contrast to the glass matrix can reach −2.3 × 10−3. The second regime is the appearance of crystalline lines with textured nanocrystal orientation (0.8-1.2 μJ/pulse): polar axis of nanocrystal is distributed in the plane perpendicular to writing laser polarization direction. In the plane perpendicular to laser propagation direction, form birefringence of irradiated line with slow axis perpendicular to writing laser polarization direction was recorded. The refractive index change is positive and reaches 2.0 × 10−2. The third regime (1.2-2.2 μJ/pulse) exhibits birefringence, fluctuating along writing direction, with larger crystal formation and disordered texture, leading to strong scattering. With further improvements in the fabrication techniques, the application of this work is to achieve functional optical devices such as frequency doubling optical waveguide and birefringence-based devices.
The authors thank Prof. P. Kazansky at University of Southampton for the access to QBM and DHM measurements. J. CAO is grateful for the support provided by China Scholarship Council and Université Paris Sud.
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