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The refractive index changes in doped silica are investigated. We observed that the permanent isotropic index change threshold (T1) is not significantly dependent on the doping. We show that strong birefringence (permanent linear birefringence) exists in doped silica but its threshold (T2) exhibits significant dependence on the used dopants. In our conditions, comparing with silica (0.31 μJ/pulse here), for 1.5 at% Ge-doped silica the T2 threshold is smaller (0.14 ± 0.05 μJ/pulse). For a silica doped with 0.3 at% of fluorine, T2 is close to 1.20 ± 0.05 μJ/pulse. An interpretation is given not only about threshold variation but also about RIC for energies beyond. It is based on the overcoming of relaxation time in the volume interaction.
©2011 Optical Society of America
1. Introduction
Silica-based glasses are the backbone for many of today’s rapidly expanding photonics applications. Current advanced femtosecond laser systems offer a myriad of possibilities to modify glassy media; from surface ablation, annealing, to 3D refractive index modification (positive or negative index change with isotropic or anisotropic properties) depending on the laser parameters [1]. Recently, new unique properties of laser induced glass modifications have been discovered, like chirality [2,3], directional dependent writing [2–4], oxidation-reduction [5], glass decomposition [6], nanocluster precipitation and shaping [7] and elemental distribution with a sub-wavelength resolution [6,8]. To our knowledge, no other technique holds the same potential to realize 3D multi-functional photonic devices, fabricated in a single step in such a wide range of transparent materials. It exhibits enormous potential in the development of a new generation of powerful components for micro-optics, telecommunications, 3D optical data storage, imaging, biophotonic and many more [5,9,10].
One of the most investigated aspects of ultrafast laser writing is refractive index modification in silica glass. The stability and anisotropy magnitude of the induced modification have been investigated as a function of the laser pulse energy and duration, numerical aperture, writing speed and etc. From these results, at least 3 “damage” thresholds in pure SiO2 glass can be identified according to the energy. Below the first threshold, T1, (e.g. 0.085 ± 0,015 μJ/pulse, 800 nm, 160 fs, 100 kHz, 0.5 NA [3,11,12]), the increase of the index relaxes following third order kinetics typical for the Auger electron process [4]. The photo-induced refractive index change decays to the initial value within a few seconds followed by permanent transmission decrease [13]. Above the first threshold T1, permanent changes are detected: transmission decreases, the refractive index is isotropically increasing until the second threshold T2 is reached [5]. The thermal stability is increased but moderate. In undoped fused silica the maximum refractive index change is up to 3-6 × 10−3, which is much larger value than typically induced by UV nanosecond lasers [14,15]. Above the second damage threshold, T2, (e.g. 0.31 μJ/pulse, 800nm, 160fs, 100kHz, 0.5 NA, polarization parallel to the scanning direction [11]), the properties of the modified region are quite different (type II). The refractive index change magnitude can be as large as 10−2 [16] and remain even after two hours of annealing at 1000°C [17]. The most striking feature is high anisotropy of this modification [16] which originates from sub-wavelength atomic density nanogratings induced inside irradiated volume [8]. It has been shown by Bricchi et al. [16] that both eigen index values decrease. We have proved recently that nanoplanes of these gratings consist of porous matter produced by a decomposition of SiO2 into SiO2(1-x) + x.O2 [6].
Although numerous results have been already reported on pure silica, only few publications have examined the effect of silica doping [18–20] and a systematic study has not yet been conducted. It is known that it is possible to modify many types of glasses with a femtosecond laser however the dependence of modification thresholds on chemical composition is not clear. For instance, nanogratings and related form birefringence are spectacular effects but they are found only in fused silica. In another popular glass (BK7) no such structure has been detected [21], despite strong damage occurring under ultrashort laser irradiation. In SiO2-SnO2, (16 mol %) no birefringence has been detected as well, additionally the refractive index change is always positive whatever the pulse energy in contrast to pure silica [22]. It is thus clear that a characterization of the response to the femtosecond irradiation of the key materials already developed and used for photonics applications is required. Flexibility of multi-component glasses will allow tuning of glass properties including not only photosensitivity but also thermal stability, viscosity, thermal expansion coefficient and etc. From an experimental point of view, this issue can be addressed by measuring the energy damage thresholds as a function of material chemical composition. Specifically in this paper, we present measurements of the T1 and T2 as defined by isotropic and birefringence appearance in a preform fabricated by means of the Modified Chemical Vapor Deposition (MCVD) with a Ge doped core and F, P doped cladding. Here, we carry information by measuring the index change quantitatively according to pulse energy and suggest a robust interpretation.
2. Experimental details
The experiments were performed in an optical fiber preform plate of 1 mm thickness and 20 mm in diameter. The chemical analysis of the preform cross-section was made by EPMA (Electron Probe Micro Analyser) (Fig. 1 ). The core is mainly germanium doped silica except the center which is doped predominantly with fluorine. The cladding is equally co-doped with phosphorus and fluorine. The fluctuations seen on the chemical composition profiles are well correlated with the MCVD layers. The homogeneous concentration of fluorine in core-cladding is caused by its higher diffusion compared with phosphorus, which as a result marks the layers. This occurs also for the cladding-tube interface which contains only fluorine. In the experiments we took advantage of these peculiarities for determining modification thresholds dependence with doping.
Fig. 1 Chemical analysis profile of the preform used in our experiments. Si and O contents are not shown. The Ge-doped part is the core of the optical fiber preform. The increase in F concentration indicates the preform center. Chlorine (in pink) is shown to remain at very low level. The analysis has been made by EPMA.
The laser used in the experiments was a Ti sapphire operating at 800 nm, 160 fs, and 100 kHz repetition rate. The × 20 microscope objective with NA 0.50 was used for writing in the preform plate. In the experiment 31 lines were drawn 200 μm below the entry surface with a pulse energy ranging from 2.6 μJ down to 55 nJ. The sample was moved along a direction perpendicular (let us say x) to the beam tracing continuous lines from the center (Ge doped core) to the peripheral (pure silica substrate) of the fiber preform. The polarization laid along x, i.e. parallel to the sample displacement. The distance between the lines was 50 μm.
After femtosecond laser irradiation, the photo-induced macroscopic structural modifications were inspected by quantitative phase microscopy (QPm) and retardance imaging system (ABRIO, CRI inc.) both based on the Olympus BX51 optical microscope. The circularly polarized light (515 nm), generated by passing the white light through the green band-pass filter and circular polarizer, was used for illuminating the sample. The transmitted light was collected by the microscope objective and passed through the liquid crystal (LC) based compensator, which can change the polarization state of the light with no moving parts and most importantly with no image shift. As a result four intensity images were recorded for various birefringence settings of the compensator and then processed using a special algorithm embedded in the commercial software. Birefringence information including retardance (R), which is defined as: R = Β·d (Β is the birefringence in the (x, y) plan and d is the thickness of the birefringent material) and azimuth angle (slow axis between horizontal) can be calculated. QPm measurements were realized using in natural light configuration with × 20 focusing objective mounted on a piezo stage. A quantitative phase mapping of the structures was produced using QPm software (Iatia vision sciences). The photo-induced refractive index change was estimated from, where is the phase shift (in radians) of the non-polarized light at 550 nm and L – the thickness of the structure along the light propagation direction.
3. Results
As described in the introduction, we define the first damage threshold T1 as the pulse energy above which appears a permanent isotropic index change. Notice that we performed multiple (typ. 1000) pulses threshold measurements. Usually, it gives rise to a converging lens effect and thus to a higher luminosity. The second threshold T2 is (as defined in this paper) the pulse energy above which a strong linear birefringence appears and can be easily seen in crossed Nicol polarizer configuration or using retardance imaging system.
Firstly, the femtosecond laser written line structures were inspected using the retardance imaging system. The color scale (i.e. disk in the up-left corner) indicates the orientation of the birefringence slow axis (the large index neutral axis) while the magnitude (i.e. color intensity) is correlated to the retardance level. The appearance of bright blue lines indicates the anisotropic modification (above T2) (Fig. 2a ). Qualitative characterization (Figs. 2a and 2b) with the Abrio system revealed some color contrast in the background, which is due to residual radially symmetric stress field related to inhomogeneous thermal expansion coefficient distribution induced by the MCVD manufacturing process [23,24]. This effect is especially noticeable around the preform center, where the birefringence is particularly large due to the strong chemical contrast. Then, concerning the lines, it can be seen that the slow axis is perpendicular to the lines’ orientation (i.e. blue color). Notice that these lines have been written with laser polarization parallel to the scanning direction. If we write lines with a laser polarization perpendicular to the scanning direction, the lines will appear in red color. This confirms that the principal axes are determined by the laser polarization.
Fig. 2 Quantitative birefringence cartography in optical fiber Ge-doped preform core in Fig. 2a and (F, P)-doped cladding and pure silica tube in Fig. 2b. The blue lines correspond to various writing pulse energies ranging from 55nJ up to 2.6μJ. The color scale indicates the slow axis orientation.
By correlating, the energy damage thresholds determined from Figs. 2a and 2b as a function of material chemical composition profile (as shown in Fig. 1), we are then able to determine the T2 threshold according to the doping. Comparing with silica (0.31 μJ/pulse here), for 1.5 at% Ge-doped silica the threshold T2 is several times smaller (0.14 ± 0.05 μJ/pulse) as shown in Fig. 2a. For a silica doped with 0.3 at% of fluorine (see arrows in Fig. 2b), the second threshold T2 is close to 1.20 ± 0.05 μJ/pulse. The addition of 0.3 at% of phosphorus to 0.3 at% F doped silica (see left arrows in Fig. 2b) degrades the second damage threshold from 1.20 to 0.25 ± 0.05 μJ/pulse. Under optical microscope working in transmission mode the lines written below the second threshold could be also detected. The contrast in the optical image arises from an isotropic variation of refractive index. In this way, we deduce that the first threshold is not influenced significantly by the doping and is always fixed at 0.095 ± 0.005 μJ/pulse.
Subsequently, from these quantitative cartographies, the retardance dependencies on the writing pulse energy for different composition are plotted in Fig. 3 from 0.055 up to 2.6 μJ. In pure silica (blue curve), there is a sharp increase of the birefringence around 0.31 μJ that indicates the T2 threshold already observed in Fig. 2a. In Ge-doped silica (black curve), we can see a continuous increase of retardance even at large pulse energies. We note that the maximum photo-induced retardance in slightly (1.5 at%) Ge-doped SiO2 is much higher (230 nm retardance at 2.6 μJ) than in pure SiO2 (140 nm at 2 μJ).
Fig. 3 Average retardance (in nm) over the interaction length t (i.e. the laser trace) according to the writing pulse energy for various chemical compositions.
Average index changes have been also inspected by quantitative phase microscopy (QPm) (Fig. 4 ). As it can be seen, at high pulse energy (above 0.31 μJ/pulse in silica) we can observe dark lines indicating that the average refractive index value (in the xy plan) has decreased when compared to the pristine silica background. It is worth noticing that the threshold of negative index change appearance coincides with the T2 threshold whatever the doping may be (see Fig. 5 ).
Fig. 4 Optical image of the Ge-doped, (F, P) co-doped, F-doped and silica in the (x, y) plane (i.e. through the sample) recorded with quantitative phase measurement (QPM) microscope. The black lines correspond to negative index changes whereas the bright ones are for positive index changes.
Fig. 5 Pulse energy versus numerical aperture diagram in log-log scale defining regions with different kinds of laser interaction with silica. Laser parameters: 0.1-17 μJ, NA = 0.01-1, 160 fs, 200 kHz, 800 nm. N.B.: the blue discontinuous line marks the position of our today experiments.
In contrast, the lines appear slightly brighter for lower pulse energies indicating an increase of the refractive index below T2. From these measurements we can thus plot the phase shift with respect to the writing pulse energy (Fig. 6 ). However, as the observations in the (x, y) plane give us only an average index change measurements along the interaction length (i.e. focus + subsequent filament), the photo-induced index change cannot be estimated straightforward from the phase shift measurements. Indeed, we need to know the length L of the laser tracks in the z direction. In addition it is known that the interaction is not homogenous especially above T2 i.e. there is a laser track comprises of head (where nanogratings [8] and related form birefringence appear) and a subsequent tail (where refractive index increase can be expected) [6].
Fig. 6 Average phase shift (in rad) over the interaction length t according to writing pulse energy for various chemical compositions. The up-right inset corresponds to low writing energies from 0.1 up to 0.4μJ.
4. Discussion
To summarize, we have measured the chemical dependence of isotropic and anisotropic index change and in particular the thresholds T1 and T2 in MCVD perform taking advantages of its Ge, P, F profile. In such sample, we have written a series of lines with pulse energies ranging from 55 nJ to 2.6 μJ from the center (Ge doped core) to the peripheral (substrate pure silica tube). Then, we have observed the index change by means of transmitted natural, polarized light, birefringence quantitative measurements and QPm. Correlating the chemical profile (Fig. 1) with our measurements; we have thus deduced the variation of the T1 and T2 energy thresholds. Table 1 summarizes these results.
Table 1. Dependence on T1 and T2 Thresholds on Dopinga
T1 is independent on doping, T2 decreases strongly on Ge, P doping, increases on F doping. An important role in the interaction process might be played by self-focusing (SF) [13], in particular when the pulse energy overcomes the SF threshold and a filament appears. For comparison purpose, the corresponding SF values are reported in the right column of Table 1. As it is well known self-focusing is defined by the linear and the non-linear n 2 indices. It should also be noted that self-focusing depends only on the peak power in the beam [13], but not intensity; thus the critical self-focusing threshold does not depend on the focusing strength. As it can be seen, n 2 increases only slightly with the presence of either Ge or F [25] when compared to pure SiO2. The self focusing effect is roughly the same whatever the doping (at the level used in our sample). On the contrary, the appearance of a linear birefringence is strongly dependent on doping. Especially in F-doped silica, the threshold energy for self-focusing is 3 times lower than T2, indicating that self-focusing does not play a detectable role in the formation of index anisotropy.
Despite the mechanism of photo-induced modification formation in silica glass is not understood, T1 (i.e. appearance of permanent isotropic index change) was suggested to be related on point defects distributed isotropically or with a weak anisotropy [26]. Indeed, point defects such as NBOHC (Non Bridging Oxygen Hole Center), SiE’ (Si dangling bonds), peroxy linkage or radical, and interstitial oxygen (atoms or molecules), bond angle tetrahedral rotation [27], density change [28] have been identified in luminescence, electron paramagnetic resonance (EPR), Raman spectroscopy and other studies [29,30] of fused silica. In contrast, T2 is defined by the appearance of a new nanostructure (i.e. nanoplanes of low atomic density) and should be related with some kind of phase transition.
4.1 T1 interpretation
For understanding the independence of T1 on doping for large number of pulses (typ. 1000 pulses) we have to analyze precisely what is the basis of T1, which is defined here through the appearance of permanent isotropic index change. In other papers [13] it is defined through attenuation permanent variation in the near IR but it is actually the same threshold. What we call threshold corresponds to the clear intersection between two lines in a given plot of the property according to the pulse energy. Isotropic index changes or attenuation decrease are both arising from extended glass modifications. On the other hand, in the first femtoseconds after the pump pulse beginning, the energy absorbed from the femtosecond laser pulse leads to formation of excited electrons that relax first into self-trapped excitons (STE) on the 100’s femtosecond timescale and then annihilate or transform into point defects later on [31], following the reaction scheme sketched for the Ge doped silica case:
Glass modifications are the result of STE relaxation. Two ways of STE decay are possible: a simple radiative recombination with a photon emission (lifetime of nanoseconds at room temperature [31]) or a non-radiative one by coupling with lattice phonons. Alternatively, STE can transform into point defects (e.g. GeODC(II)) [32] but its yield is small [33]. On the other hand, the permanent attenuation in the IR lies in a wavelength range where there is no point defect absorption [34] and thus the transparency loss is thus resulting of long or medium range structural modifications but not from point defects. We speculate that such glass transformation results from non-radiative relaxation of excited electrons by coupling with the lattice. This coupling corresponds to an increase of non-equilibrium temperature of the lattice that can reach several thousands of degrees in the illuminated area just limited by thermal conduction. The temperature increase during a time long enough can lead to glass melting and to a change of average disorder i.e. a change of glass fictive temperature [35]. We can define this temperature (Tc) by saying that the relaxation time defined by the ratio between the viscosity (η) and the shear modulus (G) [36] should be smaller than the time during which the matter overcome this temperature. This can be written as:On the other hand, the time-temperature profile of the irradiated area is mainly defined by the amount of energy density released in the lattice during the laser pulse divided by the specific heat capacity [37]. This energy comes from excited electron-relaxation and not directly from pump pulse that is not completely absorbed by the matter through electron excitation. As a matter of fact, the energy releases by a STE is at least equal to Eg but less than 2Eg as no avalanche is detected in our conditions [32,38]. Let assume that this energy is roughly the same whatever the doping (so a = constant and 1<a<2). So, finally the released energy density (W) is expressed as the product of (a), of the forbidden energy gap Eg of the glass and of the STE concentration at the end of the pulse i.e. .The STE concentration is obtained by time integration of the MPI (multiphoton ionization) rate. It yields approximately where σn is the multiphoton absorption cross section, τ is the duration of the pulse, NO the state density at the top of valence band and Ith the light intensity corresponding to T1 energy. It comes thus:
As mentioned above, only a fraction of the incident pulse energy (T1) is absorbed by the matter i.e. a part is reflected by the plasma [39]. Let us write αT1. Due to focusing and taking into account the absorption length, we have: where S(NA, Ith) is the average cross section of the focal volume alike the expression given by Schaffer et al. [13] valid for NA>0.1. α, is a priori unknown but assumed constant in this paper. It has been determined by considering that the Eq. (1) is fulfilled with the minimum energy T1 = 0.1µJ in pure silica. We found α = 23%. This appears consistent with time-resolved absorption measurements performed in similar experimental conditions [40].
Equation (1) itself has been solved by taking into account the data available in the literature for the glass considered in this paper and by solving the time dependent Fourier equation after a time long enough after the pulse. More details will be published elsewhere. Equation (1) is thus the intersection of the two curves types of curves plotted in Fig. 7 . This graph compares the temperature dependence of the relaxation time for the different sample compositions of this paper based on viscosity measurements and shear modulus data [41] change and the cooling profile modeling after single pulse irradiation [37]. For pure silica, the estimate of the fictive temperature is thus around 2490°C. If we decrease the incident pulse energy, there is of course no more intersection, but if we increase the pulse energy, the fictive temperature decreases slightly to 2250°C from 0.1 to 0.3 μJ.
Fig. 7 This graph compares the glass relaxation time and the cooling profile after single pulse femtosecond laser irradiation for pure and doped silica. The cooling profiles with varying incident energy are for pure silica only.
Now, if we consider the case of Ge doping at a level of 1,5 at % in silica, specific heat capacity increases by less than 2% [42], viscosity decreases by less than 3% based on our own measurements and [43], shear modulus decreases by less than 4% [41]. The thermal diffusivity is also increasing by not more than 2%. The same is for P and F doping [44]. Therefore, the critical temperature for structural modification as defined above is expected not to change significantly (less than 50°C) with doping and thus the corresponding energy density appearing in Eq. (2), from those ones we can deduce the change in intensity threshold. We have
The band gap seems to significantly decrease as the STE localize on Ge atoms even with the weak doping used in this paper [45]. As a result, the band gap decreases from 9 eV to 7.5 eV i.e. by about 17%. On the other hand, the frequency-based spectral interferometry measurements indicate that the STE concentration increases by about a factor 3 [45]. Here we used the multiphoton cross-sections for pure silica (6 photons absorption) and Ge-doped silica (5 photons absorption) that we measured using plasma density measurements in similar experimental conditions (σGe = 1.8 ± 0.2 10−55 s−1cm10W−5 and σSi = 4.5 ± 0.2 10−69 s−1cm12W−6 [38]) and the silica intensity threshold corresponding to T1 threshold in silica (≈15 TW/cm2). As a result, the variation of the intensity threshold is less than 10%. Further, as the cross section of the focal volume is not varying significantly on doping, we deduce that T1 is not varying either. This is thus consistent with the observations.
The ratios calculated for other doped silica leads to the same conclusions: the energy thresholds for glass structural change are about the same. As a matter of fact, comparing relaxation time and cooling curve in doped samples, see Fig. 7 assuming the same proportion of pulse energy absorption, leads to a pulse energy threshold of 0.10μJ for Ge doped sample, of 0.095μJ of P and F-doped samples. The corresponding fictive temperatures are 2490°C and 2450°C respectively.
4.2 T2 interpretation
T2 threshold exhibits a totally different origin than T1. It is the onset of a strong linear birefringence based on the appearance of a long range microstructure i.e. the assembly of nanoplans that sometimes organize in nanogratings [8]. Nanoplanes (a few nm thick) are composed by porous matter [6] tha7t on the average has a lower atomic density than the surrounding glass. They are probably formed as a result of glass decomposition with releasing oxygen into pores [46]. The appearance of nanoplanes, the orientation of which being determined by laser polarization seems related whatever the interpretation (nanoplasma [47] or phonon-plasmon interference [48]), to plasma density or energy increase significantly larger than the average electron density. It has been noted that it needs several pulses for their observation, the number depending on the pulse energy. On the other hand, we have observed them at a repetition rate as low as 1 kHz so with pulses without other relation than some information “written” in the glass. On the other hand, they can be prolongated coherently on a long distance (several mm). It is therefore clear that the plasma micro-structure is recorded in the glass and that the corresponding information seeds the plasma structure in the subsequent pulse. Referring to the relaxation scheme already sketched for T1 interpretation above, we will hypothesize that point defects, even if they are not the most efficient relaxation pathway are good candidates for recording medium. As a matter of fact, decomposition of silica leads to SiODC(II) defect formation [49], which may behave as trapping centers and then to electron source for the next pulse. Then, in the process of multiphoton ionization, these centers with occupied level in the forbidden gap are expected to be readily ionized in first, contributing to plasma nanostructure formation. As the irradiation is going on, the process self organized into a stable structure.
It is worth noticing that point defects in Ge-doped silica is easier achieved through reduction process [50,51] and Ge itself can easily behave as a trapping centers forming Ge(1) centers [52]. We have to note also that GeODC(II), inherent to Ge doped silica is an electron source that gives rise to Ge(1) through UV absorption. The same properties stands for phosphorus doped silica [52] but not for fluorine doping, which is also recognized for hardening the glass against the ionizing radiation [53]. On the other hand, decomposition of the glass that depends on the bound energies is easier with Ge and P but not with F-doping.
Finally, as we have seen for T1, the electron density or energy in the plasma seems not being the step that determines the doping dependence of the nanoplanes formation, it is rather the ability of the glass to be decomposed and to record the plasma density spatial structure. In such a way, the branching ratio for STE’s to transform into point defects is larger for Ge and P than for F. The number of pulses of a given energy is thus varying accordingly and thus the energy for a given number of pulses. On the other hand, as the energy required for decomposing Ge doped silica is less than for pure silica, the onset energy for nanoplanes appearance is smaller. Similar remarks stand for P doping. On the contrary, doping silica with fluorine reduces defects concentrations and the structural disorder [54,55], this result in a more difficult glass decomposition and thus a higher T2 threshold.
More quantitatively, we may consider that birefringence is always detected above the same quantity (quoted as [B]). This minimal quantity is certainly proportional to an amount of glass decomposition which is itself proportional to the branching ratio (ε) from STE and to STE concentration ([STE]) produced by a series of pulses (N). We may write [B]~N·ε·[STE]. On the other hand, [STE]~σ·Ik where k is the number of photon in the MPI process. So, finally we get:
Again referring to the focal volume cross section, invariant on doping and to the Table 1, we find that the left term of the above equation reaches about 0.5. We deduce that N·ε ratio reaches about 0.1, meaning that the branching ratio is in the order of 10 in favor of Ge if we assume that the number of pulses is the same for both glasses.Another point to discuss is the birefringence beyond the energy thresholds. In Fig. 3, we see that retardance after a sudden increase (what is consistent with multiphoton production of birefringence in volume) the birefringence saturates. In addition, RIC is larger for Ge and smaller for F-doped SiO2. We can note that above a certain energy (0.2 μJ for Ge-doped silica or P/F doped samples but 2 μJ for F-doped silica), the plasma saturates [45] indicating that the coupled energy in the matter is thus limited. Another limitation is that glass decomposition is in itself limited and that form birefringence can increases only by increasing the number of nanoplanes in the cross section of the laser tracks (perpendicular to the propagation axis) but it is observed that their distance remain roughly the same and so this number rapidly saturates. Finally, only the increase of their length along the propagation axis might be possible but this needs light intensity increase beyond the focus. As the larger intensity is in the focus, the plasma formed reflects more and more the incoming pulse as its energy increases. A fraction of light going through to the tail of the structure is thus becoming smaller and smaller thus justifying the birefringence curve saturation.
For, isotropic index change displayed in Fig. 6, the sudden increase for low energy is consistent with multiphoton absorption. As a matter of fact, taking again the mechanism described at the beginning of the discussion, beyond the T1 threshold, the relation defines the critical temperature for the beginning of glass modification. When pulse energy increases, it is easy to see in Fig. 7 that fictive temperature does not change significantly in the interaction region but the volume satisfying the above condition increases. Then, depending on the glass modification (some examples are reported in [56]) the phase recorded through the laser track increases accordingly. However, beyond T2, the curves in Fig. 4 drop dramatically before leveling off. This corresponds to the mechanism change and the appearance of nanoplanes with lower index. The leveling is thus consistent with the one observed in Fig. 3 and the associated mechanism described above.
5. Conclusion
We show that strong birefringence, which is not observed to this date in glasses other than pure silica, appears also in doped silica. The first threshold (i.e. permanent isotropic index change) is not significantly dependent on the chemical composition, i.e. doping, in contrast to the second threshold (i.e. permanent linear birefringence). This is explained by noting that isotropic index change at low pulse energies arising from glass modification allowed when the glass is heated a time long enough for restructuration (larger than the relaxation time) and that this requested time does not change much at our doping level. On the contrary, the second threshold is related to nanoplanes of decomposed silica and produced through a mechanism that requires point or extended defects to be produced by the plasma and record its structure. The efficiency of this mechanism is thus determined by the ability of the glass to produce point defects and the energy for glass decomposition.
From a practical point of view, it appears that silica doped with small amounts of either germanium or phosphorous is a better choice for birefringence tailoring than pure silica glass, since the processing window is wider and the maximum photo-induced retardance (typ. 230nm at 550nm in one layer) is larger than in pure silica. In contrast, it is the reverse influence for fluorine doping. It is thus judicious to use Ge or P doped silica for discrete optical device fabrication when birefringence is required, such as for a retardation plate or Fresnel lens. As the retardance can be accumulated over many layers, quarter and half waveplates can be easily realized over a typical 100 microns thickness. F-doped silica is well adapted for devices based on isotropic index change such as 3D waveguides or volume Bragg gratings. Indeed, the pulse energy processing window is quite large (from 0.1 up to 1.20 μJ/pulse) which allows us to tailor the photo-induced index change profile. In addition the phase change can be as high as -π/2. This means that we can realized phase lens such as annular phase ring in two or three layers (i.e. less than 150 microns thickness).
Acknowledgments
This work has been performed in the frame of FLAG (Femtosecond Laser Application in Glasses) consortium project with the support of several organisations: the Agence Nationale pour la Recherche (ANR-09-BLAN-0172-01), the RTRA Triangle de la Physique (Réseau Thématique de Recherche Avancée, 2008-056T), the Essonne administrative Department (ASTRE2007), the Ministry of the Foreign Affairs (PHC Alliance) and FP7-PEOPLE-IRSES e-FLAG247635.
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