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We reveal stress fields induced by femtosecond laser irradiation by investigating the topography of surface relaxation of a cleavage of silica plates in which irradiation was performed, varying intensity, laser polarization and displacement of the writing beam. The stress field appears to depend on the writing parameters differently according to the laser intensity. For pulse intensity larger than 0.1 µJ, a first shear stress developed. Above 0.25 µJ, another shear stress appears that is dependent on the direction of writing and coupling with a phase matching condition between the pump wave and the third harmonic.
©2003 Optical Society of America
1. Introduction
Femtosecond laser writing of refractive index structures in wide bandgap insulators is a promising method because of the weak dependence on the material composition. Several publications show that it is possible to change the refractive index either in pure or doped silica, in fluoride or in chalcogenides1–5. The magnitude of the index change is very large, a few 10-3 up to a few 10-2 1. On the other hand, it is a unique solution for writing optical waveguides in volume1 if it is possible to understand and thus to manage all the effects induced by the irradiation. Sudrie et al. show that interaction with silica glass is dependent on the laser intensity6. Above a first damage threshold (0.1 µJ/pulse with a pulse duration of 160 fs focused inside fused silica with a microscope objective ×20, NA 0.50)6, the interaction is rather soft and leads to a permanent change of index1,5, to birefringence5, and to densification7,8. The intensity dependence of the index change seems to reveal a two-photon absorption process at 800 nm in a lead doped glass9. Above a second threshold (0.25 µJ/pulse, 160 fs, ×20; NA 0.50)6, a high order avalanche process occurs and the medium is strongly perturbed probably via a process similar to a high density plasma formation followed by local melting. At this point, the absorption of the incident light becomes very important10.
This avalanche regime leads to quite different interaction processes which modify the glass differently. In particular, it seems that below the first damage threshold, the index change is not stable but relaxes following third order kinetics correctly explained by Auger electronic processes9. The lifetime is of the order of a few seconds for intensity below the threshold whereas it is permanent above. Another difference is the engraved birefringence6. It is weak between the two damage thresholds whereas it is very strong above the second one. Since some authors have considered that the refractive index change would arise from densification7,8, we have performed observation of surface relaxation after cleavage. As a matter of fact, a non uniform densification induces stresses that can be relaxed after cleavage, leading to characteristic topography11.
2. Experimental details
The experiments were performed in plates of pure silica glass (synthetic fused silica Herasil) of 500 µm thick and 20 mm in diameter. The writing parameters are shown in Fig. 1.
Fig 1. configuration of the experiment on the left of the figure. Direction of clivage of the sample on the right.
Considering that the propagation vector is along direction, the beam was focused 250 µm below the entry surface avoiding in such a way damage induced by an interaction of the laser with a surface that exhibits a lower damage threshold. The sample was moved along a direction perpendicular (let us say x) to the beam either in one sense or in the other, thereby tracing continuous lines. The polarization lied either along y, (perpendicular to the beam and the sample displacement) or along x, (parallel to the sample displacement).
The experiments were performed in two samples. Parallel lines were written as it is drawn in Fig. 1. They were divided in sets of six or ten lines by moving the sample from line to line. In one sample (S1/S2) the polarization was only perpendicular but the power density and the distance between lines were varied. In the other one (S3/S4), it was either perpendicular or parallel to the direction of writing. The intensity of the beam was varied from a set to another one from a Pmax=220 mW (1.1 µJ/pulse, repetition rate 200 kHz) and then decreasing using neutral filters of transmission as follow 0,88, 0,66, 0,55, 0,36, 0,21, 0,12, finishing again with Pmax in order to test the reproducibility and for easy tracking. The polarization was parallel to the displacement of the sample (x) in a first packet (P1). Then, another packet (P2) was realized with polarization perpendicular to the displacements. For these two packets, the lines were performed by moving the samples alternatively in one sense and in the other one. The distance between lines was 50 µm. Investigations in the first sample (S1/S2) showed that for closer distance, there is an overlap of the induced effects between lines.
After writing, the sample was cleaved after scratching linearly its surface with a W needle. The cleaved faces was then observed with a phase shift interferometric microscope from Phase Shift Technology (Tucson, Texas). The observable vertical shift is 30 µm and the precision is better than 1 nm. The horizontal precision is of the order of 2 µm in the surface plane. The topographies are coded in wrong colors. Both faces of the clivage were observed in order to see the complementary characteristics of the glass relaxation.
3. Results
Figure 2 shows the surface topography at the place of a set of 6 lines exemplifying the various variations of the surface level. The trace of the laser is easily detectable by the strong shift of the surface level along the laser pathway (arrows). It always begins at the distance from the entry surface of the sample with a very good reproducibility. The trace is marked in Fig. 2 due to a discontinuity of the level change on each side of the trace. This is shown by the cross profile in Fig. 2(b). The surface level is higher on the left hand side of the trace whereas it is lower on the right hand side. The length of this strong interaction is about 20 to 30 µm for laser intensity Pmax. It is still the same for Pmax/2 but decreases to 25 µm for Pmax/5 and then disappears. This strong interaction line is followed by a weaker one clearly marked by a change of sense of surface level shift. The profile in Fig. 2(b) shows in this case that the discontinuity is smoothed. Figure 3 is the topography of the same set on the second half of the cleaved sample (S2). Figure 3(c) show profiles across the lines between lines 3 and 4 of sample S1 and S2. The picture is about the same leading to the conclusion that both parts are complementary at the actual level of precision (50 nm). It is worth noticing that the precision of the equipment is about two orders of magnitude lower and thus that this actual precision is due to the bad quality of the cleavage in a such perturbed glass.
Fig. 2. Four lines from a set of 6 lines in sample S1 obtained with P=Pmax, polarization perpendicular to , same sense of writing. The laser input is at the top of the figure. a - topography b - profile A and B. The objective was ×20, NA 0.50.
Fig. 3. (b) Comparaison of level profile in zone b of Figs. 2(a) and 3(a). For comparison purpose, the profile of the Fig. 3 has been inverted and shifted in position.
Fig. 3. (c) Comparaison of level profile in zone c of Figs. 2 and 3 between line 3 and 4. For comparison purpose the profile of the Fig. 3 has been inverted and shifted in position. No trace of densification can be detected.
In the above figures, the objective used in the microscope was ×20. In Fig. 4, a ×40 objective is used allowing to see better the trace of the laser and the colateral effects.
Fig. 4. Topography with an objective ×40. Polarization perpendicular to . Details along the trace of the laser. Lines L5 and L6 were writing with the laser moving in opposite directions. P=Pmax.
The first observation we can perform is that the trace seems to be not straight. In fact, the propagation is straight but the level shift produced along the interaction of the laser with the matter is largely non-linear and follows the structure heterogeneity of the glass. The head of the strong interaction is composed by small dash of 5.2 µm long perpendicular to the trace and distant from each other of 3.5 µm. As a matter of fact, this strong corrugation or localized points are not reproducible from line to line. It is worth noticing that the density of strong interaction is larger and wider at the beginning of the trace than along the tail. The observation of the other face of the sample exhibits the complementary level shift.
The second observation is the colateral level shift that appears like wings of opposite color, aside the main trace. It is enhanced in Fig. 5.
Fig. 5. Topography obtained from the SEM in secondary electron mode and with interferometer with an objective ×40. Polarization perpendicular to . Details along the trace of the laser. P=0.88 Pmax.
In these pictures, there appears at the beginning of the trace an upward shift on the left and a downward shift on the right. Then, these wing pairs change signs several times along the trace until they finish with a downward shift on the left and an upward shift on the right. Six couples in inversion are detected. We have measured such inversions in all our experiment more or less easily. It was always easier to measure at the beginning than at the end of the trace. The distance between the inversions is a little bit larger at the beginning than at the end. It is about 15 µm and then about 10 µm.
Fig. 6. Difference of the topography when the polarisation is rotated for lines written alternatively. P=P max. On the left, it is perpendicular to the laser displacement. On the right, it is parallel to the displacement. Observe the double spatial period at the entrance of the laser on the left whereas it is simple period on the right grating. The focusing point has been put further in the glass for the set on the left than on the right for clear tracking.
Figure 6 shows the difference of the topography when the polarisation is rotated. The set on the left has been achieved by writing lines when the laser polarization is perpendicular to X˗, the set on the right with polarization parallel to . The sense of sample displacement is alternate for both sets. As we can see, a simple periodicity of level shift is measured when the polarization is parallel to the displacement (set on the right) whereas it is more complex when the polarization is perpendicular (set on the left). In this case, a double periodicity is detected at the beginning of the laser trace, i.e., the color is uniform in the space between two traces. However, after 3/4 of the trace, this periodicity is lost and the wings at the end are again the same as for set on the right of Fig. 6. The observation of the face of the other sample half exhibits the same topography complementary to Fig. 6.
Fig. 7. Topography below the second damage threshold, P=Pmax hrough an objective of ×2.5 instead of ×20 perpendicular polarisation, same sense of writing. (a) One face of the two halves of the cleaved sample. (b) The other half. (c) Comparison of level profile in the two halves of the same sample at zone c in Figs. 7(a) and (b). For comparison purpose the profile of the Fig. 7(b) has been inverted and shifted in position. The positions 0–30 µm are out of the filament corresponding to the reference level for calculation of the level change. From these profiles, we can deduce that one half of the sample exhibits a modulation 25 nm smaller than the other half. Several measurements performed gave an uncertainty of 5 nm.
Finally, Fig. 7 shows the topography when the power is below the second damage threshold. In that case, strong interaction marking the trace of the laser does not exist but there is still a discontinuity of surface shift. We have noticed that the topography amplitude is slightly larger for the Fig. 7(a) (-340 nm) than for Fig. 7(b) (+315 nm). Lastly, below a power of 0.1 Pmax nothing is detected, this corresponds to 0.1 µJ/pulse.
4. Discussion
Changes of index in silica induced by irradiation with the femtosecond laser have been reported in several papers1,7,12. Authors investigated the magnitude, the kinetics, the stability, the anisotropy according to the power density and the polarization of the laser. They have pointed out three regimes with two damage thresholds.
- Between the two damage thresholds, the index change is permanent and isotropic6, the thermal stability is moderate. The second damage threshold is located at 0.25 µJ/pulse, 160 fs, using a microscope objective (×20; NA 0.50). The maximum index change is 6×10-3 6, 3×10-3 in fused silica12. This is very large compared to UV induced one13.
- Above the second damage threshold, characteristics are quite different. The index change magnitude can be as large as several times 10-2 and resists during two hours at 1000°C14 or 900 °C6. The writing kinetics is a higher order multiphoton process, involving more than 4 photons. The index change is highly anisotropic14,6 and this is the most striking feature. The principal axis is determined by the laser polarization. We have not detected blue luminescence in our experiment but other authors15 measured an anisotropic emission in blue and red indicating that anisotropic defects are created.
More precisely, Sudrie has studied the localization of the anisotropy6 along the trace of the laser. It is mainly in the head where the interaction is strong. This is quite consistent with our observation.
We have pointed out a trace of the laser which is composed by two effects: a strong interaction on the laser pathway, a weak interaction antisymmetric on each side of the trace.
The strong interaction is detected only when the input power is larger than the second damage threshold, whereas the weak interaction is detected between the two damage thresholds. The strong interaction is revealed by a topography complementary on each face of the cleavage. The magnitude of the level shift is of the order 0.2–0.3 µm. If it was arising from specific volume change, it would be an upward or a downward level shift, the same on each face of the sample for a decrease of density and vice versa. What we detect, here, is therefore the result of a fragile fracture of a transformed glass. Nevertheless, we cannot exclude a change of density because this one would lead to smaller shift (1% change of index, lead to about 1% change of density on a depth of a few µm, that means a few 10 nm of surface level shift). As a matter of fact, Hosono et al have reported a change of specific volume correlated with the change of index when writing a grating in silica2,7,8.
This interaction is antisymmetric and reveals a periodic non-linear optical interaction with a spatial period of 5.2 to 3.5 µm about (Fig. 5). It is existing whatever the writing sense or the laser polarization but it is more contrasted when the polarization is perpendicular (Fig. 5).
The weak interaction is the antisymmetric change of the surface level on each side of the trace (wings on the figure) separated by a discontinuity on the trace of the laser. The profile on each face of the sample is again complementary. This is the result of a shear stress occurring all along the trace of the laser. At the beginning of the trace, this shear stress depends on the laser polarization combined with the sample movement. The first pair of wings corresponds always to an upper shift on the left and a lower shift on the right when the polarization is parallel to the sample movement whatever the writing sense. On the contrary, when the polarization is perpendicular, shear stress sign combined with the sense of writing (Fig. 6). This leads to a frequency doubling in the diffraction efficiency that is pointed out in16. The shear stress behavior at the end of the trace is independent of the laser polarization or of the sense of writing. There is always a lower surface level shift on the left and an upper surface level on the right. This reveals a shear stress that is always of the same sign. It occurs with exactly the same sign for power density smaller than the damage threshold.
Between the head and the end of the trace, we can observe a change of sign of the shear stress. Once when the polarization is parallel to the sample displacement or several times when the polarization is perpendicular. This is a most striking feature. The periodicity of 10–15 µm indicates the occurrence of phase matching between ω and 3ω. As a matter of fact, third harmonic generation has been detected during the irradiation. The computed mismatch, considering the linear refraction index, is close to this coherence length: λ/(n800nm-n800/3)=17 µm (data are from Heraeus documentation).
We think that there are in fact two processes leading to shear stress, one above the second damage threshold and another one for lower optical power density. The origin of the shear stress remains a mystery. It reveals a chirality in the interactive process which is obviously non-linear. Figure 8 shows that below the second damage threshold, the matter is dragged with the laser displacement just after the focusing point whereas it is not so large above the damage threshold.
6. Conclusion
In measuring the surface topography of a cleaved silica sample after writing lines in varying direction of writing, polarization orientation, and power density, we have pointed out three kinds of interaction:
- Below and above the second damage threshold, a shear stress is developed which is weakly dependent on the power density. It reveals a chirality in the interaction process.
- Above the second damage threshold, two processes occur. The first one, highly birefringent, is a strong interaction which modifies the structure of the glass and is probably related to the oriented partial fusion. Attempts to detect a crystallization failed at the moment. A softer interaction occurs which gives rise also to shear stress, but is dependent on the laser polarization and writing direction. Its aspects along the laser pathway reveal that it is connected to a phase matching condition, probably occurring between the pump light and the third harmonic.
The investigation of theses processes is still in progress by performing complementary experiments.
References and links
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