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We study experimentally the physics of the generation of permanent material restructuring, for the case of fused silica after excitation with intense femtosecond pulses and filaments, in the bulk of the medium. Using a powerful time and spectrally resolved holographic technique we monitor the temporal material evolution from the initial electronic excitation through its successive relaxation stages and up to the final permanent amorphous lattice state. A complete physical model is formulated from the experimental data.
©2011 Optical Society of America
1. Introduction
The fabrication of embedded optical elements in the bulk of transparent glasses involving the controlled modification of their amorphous structure was proven to be a great challenge in the past [1]. To this end various optical and particle sources have been used without noteworthy success. Even powerful laser sources have proven inefficient for such processes. The main reason for this has been the long laser pulse lengths, picoseconds and above, that lead to either damage of the material surface or breakdown, cracks and material explosion in the bulk. All these undesired effects originated from the use of relatively long pulses driving electron avalanche effects, which consequently lead to catastrophic and uncontrolled results [2,3].
Things have significantly changed with the use of ultrashort pulses. There in contrary to what discussed above the electron avalanche effects are minimal allowing, finally, the creation of specific lattice rearrangements in the bulk of the medium. This advance has enabled the fabrication of various optical elements and photonic circuits in the bulk of optical glasses, like waveguides, gratings and many others [4–8]. It is worth noting here that the use of femtosecond lasers has additional advantages, owing to the multi-photon character of the excitation, as we will see in the following, allowing incomparable control in the whole process and the fabrication of sub-wavelength structures at the same time [8–13].
Although in the last decade a plethora of applications have been demonstrated using this technique the physics leading to the material restructuring is still up-to-date a subject of intense study and debate [4,14–18]. The reasons for this are numerous but in general can be grouped in two categories. The first is related to the large variety of materials that have been used in the different studies, including pure, defect free, glasses like fused silica and crystals like sapphire, impurity containing glasses like BK7, up to chalcogenide glasses and others with very low band gaps. It is evident that one cannot propose a single physical model to explain the induced changes in all different glass categories. The second reason is the different laser systems used and especially their repetition rate. As we will demonstrate in the following, physics can be significantly different when using low repetition rate systems, where single shot electron plasma effects dominate as opposed to high repetition rate systems where thermal accumulation effects cannot be neglected and can in many cases be dominant [19].
In this study we focus our interest in the category of pure glasses and low repetition rate laser systems in order to avoid thermal effects. The material chosen is ultrapure fused silica and the laser system is operated in few Hertz repetition rate. Already in a previous study we had demonstrated the important link of the initially excited plasma density with the induced permanent structure [20]. We now employ a powerful temporal and spectrally resolved holographic probing technique [21] to monitor the material evolution starting from its initial laser pulse excitation and going through all the intermediate stages up to the final permanent material restructuring. Using these experimental data we present a precise physical model of the process.
2. Experimental setup
For the experiments a femtosecond laser system delivering pulses at 248 nm is used for the material excitation. This is a hybrid femtosecond distributed feedback dye – KrF Excimer laser where a XeCl Excimer laser oscillator beam is used to pump a series of dye lasers and produce 450 fs laser pulses at 496 nm, which then are frequency doubled in a nonlinear β-barium borate (BBO) crystal and triply amplified in the KrF cavity of the Excimer laser. The whole system operates at a few Hertz repetition rate allowing for single shot experiments. In our experiments, the UV 248 nm, 450 fs pump laser pulses were tightly focused in the bulk of the fused silica samples (Corning Suprasil), at a depth of 300 μm, using a Schwarzschild 25x, 0.4 NA reflective objective. The pump pulse energy (65 μJ) and focusing conditions were chosen as to create permanent modifications in fused silica as described in [20,22].
In order to monitor the evolution of the material changes from short (<1 ps) to very long delays (>100 ns) we have used two different schemes regarding the probing and detection. For the short delays, from a few fs up to ~70 ns, we used the residual beam of the laser system after the BBO, at 496 nm and 450 fs, as a probe as shown in Fig. 1(a) . The diffracted probe beam was remotely imaged by a linear CCD camera (12 bit, 1024x768 pixels, 4.6 μm2/pixel) using a bi-telecentric optical system [21]. The delay in this case was controlled using an optical delay line. On the other hand in order to probe at later times (up to a few msec) we used CW lasers as probe (633 nm, 543 nm, ~1m coherence length) as shown in Fig. 1(b). While the same optical system was used to remotely retrieve the in-line holographic images of the perturbed CW probe beams the CCD camera was replaced by a gated Intensified CCD camera (ICCD, 16 bit, 690x256 pixels, 26 μm2/pixel). In this scheme the delay between the probe images and the pump pulses was controlled with a pulse delay generator that synchronized the delay between the ICCD camera time-window and the pump laser system. In our experiments the integration time-window of the ICCD camera was fixed at 200 ns.
Fig. 1 Pump–probe experimental setups (FS): fused silica sample, (Obj): Objective lens, (HM): in-line holographic microscope, (A) attenuator. (a) 496 nm, 450 fs probe delayed using an optical delay line, (b) 633 nm or 543 nm, CW probe. The CCD sensor is replaced by a time gated ICCD sensor.
In both cases, short pulse and CW beam, the probe beam wavefront is perturbed as it crosses the pump-altered medium. The bi-telecentric microscope system is used to remotely record in-line holographic images of the propagating probe beam at different propagation planes and for various pump-probe delays. The bi-telecentric microscope is composed by a cascade of two 4f optical systems that preserve the angular spectrum of the diffracted probe [21]. The first subsystem relays the image so that a sufficiently long working distance is ensured while the second 4f system can be freely moved along the light propagation axis. The final outcome is a spatially magnified image, at constant magnification, of any plane along the propagation of the diffracted probe beam. In the case of the 496 nm, 450 fs probe, the recorded in-line holographic images over a number of propagation planes are numerically analyzed using an iterative wavefront propagation code, which accurately retrieves the amplitude and phase of the perturbed wavefront without making any assumptions on the nature (phase/amplitude) of the probe wave perturbation. Finally, the 3D distribution of the real and the imaginary part of the refractive index perturbation is revealed using Abel inversion. A detailed analysis of the technique can be found in [21].
3. Results and discussion
A typical probe image, using the short pulse probe, arriving at the same time with the pump in the medium is shown in Fig. 2(a) . One can observe a dark string-like structure that is worth explaining. As the probe images are normalized using a reference image, without pump, the dark part of the normalized image then denotes absorption of the probe beam from the pump-altered volume. This absorption is due to the presence of the excited electron plasma, as will be explained in the following. The second observation is about the long string structure appearing in the image, which is significantly longer than the Raleigh length (~10 μm in our case). This observation is linked to the nonlinear propagation of the intense femtosecond pump pulse in the medium in the form of a filament. Ultrashort laser pulse filamentation is a well known and studied phenomenon of beam self-trapping is a narrow intense filamentary structure extending over very long distances, significantly longer than the characteristic Raleigh length. Filaments appear for input powers above the critical one for self-focusing, while trapping can be qualitatively explained as a dynamical competitive balance between linear and nonlinear effects including the Kerr self-focusing, ionization defocusing, nonlinear losses and dispersion effects [23]. In the filament’s core high intensities are reached and a plasma string is generated along its path. It is this plasma string that is actually visualized in Fig. 2(a). Performing the numerical analysis described above and using a simple Drude model to correlate the absorption with the electron density one can retrieve the 3D distribution of the plasma string electron density as shown in Fig. 2(d). According to the Drude model the presence of plasma of density ρ perturbs both the real (Δn) and the imaginary (Δκ) part of the refractive index as described by the equation [2]:
where ω is the probe frequency, τc is the electron collision time, and is the critical density above which the plasma becomes opaque for the probe (no is the refractive index of the medium, εo is the vacuum permittivity, me is the electron mass and m* a dimensionless effective mass of the electron-hole pair). The critical parameters [20] used in the Drude model are the collision time τc, the electron density ρ and the effective mass of the electron-hole pair m*. By simultaneously measuring the real and the imaginary part of the refractive index in the focal area [21] we are able to estimate the electron collision time from and use that value to Eq. (1) to estimate the ratio (ρ/m*). From our measurements the electron collision time is estimated to be τc ≈(1.26 ± 0.2) fs. In the following whenever we refer to the electron carrier density we refer to the ratio (ρ/m*). The reached values for the imaginary part of the refractive index Δκ are about (1.8 ± 0.1)⋅10−3 leading to peak electron density values of (14 ± 0.8)⋅1019 cm−3 and (6 ± 0.3)⋅1019 cm−3 average electron density in the filament volume. These electron density values are in agreement with previous experimental results and numerical simulations of laser beam filamentation in fused silica [9].Fig. 2 (a)–(c) Probe images at various delays (496 nm, 450 fs probe, 248 nm, 65 μJ, 450 fs pump). (d) Spatial distribution of time integrated maximal electron density (ρ/m*) of the plasma string in comparison to the refractive index changes (real part only) Δn (496 nm) (measured at 30 ps delay) induced by the transient defects.
Thus, the first stage in the material restructuring involves the laser beam filamentation and the concomitant low density plasma string. Already in a previous study we had demonstrated the important link of the plasma string density with the induced permanent structure [20]. In the following we track in time the evolution stages of the excited material up to the final lattice restructuring.
A probe image with the probe crossing the pump altered medium 0.5 ps after the one of Fig. 2(a) is shown in Fig. 2(b). There one can distinguish 2 regimes, the first one at the head of the structure is still linked to the presence of the pump beam and plasma absorption, the second one at the tail presents a pure diffracting structure without absorption. This diffraction pattern corresponds to a decreased index of refraction in the core that can be linked to the presence of electronic defects in the medium. The electronic defects persist for long time as can be seen in the probe image taken at 30 ps delay, shown in Fig. 2(c). In this image one recognizes the defect-induced diffraction pattern all along the initial plasma string path. The 3D distribution of the refractive index changes induced by the defects at this delay was retrieved by using the in-line holographic analysis described in [21] and is depicted in Fig. 2(d) in comparison with the maximal electron density distribution. The change Δn in the real part of the refractive index reaches values of about (−2.9 ± 0.1)⋅10−3 for our 496 nm probe beam. The attribution of such a change to a heating effect can be excluded due to the following reasons: firstly heating would locally increase, and not decrease, the refraction index since for fused silica [24] dn/dT ~ + 12.5 10−6 K−1, the refractive index change is rapid and occurs in sub-ps duration, and the diffraction image shown in Fig. 2(c) persisted for more than 40 ns, with no apparent increase in size that would be correlated with heat diffusion effects. Furthermore, the direct correspondence of the 3D refractive index distribution to the plasma density distribution in the plasma string is striking and along with the previous arguments supports the generation of electronic defects through an exciton self-trapping mechanism. This conclusion is in agreement with the results of Saeta et al. [15] where the sub-ps rise of the electronic defects density was measured under illumination of fused silica with UV radiation. Actually, it is well known that electrons trap in a femtosecond time scale in excitons (self-trapped excitons STEs) inside fused silica [14,15,25]. These excitons in turn relax equally in a femtosecond time scale in a variety of electronic defects, such as the E’ (oxygen vacancy) and non-bridging oxygen hole centers (NBOHC) [14,26]. Our conclusion is further supported by the emission spectrum from the irradiated region in the glass which is shown in Fig. 3 . These spectra were captured by imaging the emission from the irradiated volume of the glass into a fiber coupled spectrograph (TRIAX-320, Jobin Yvon/Spex) equipped with an intensified Charge Coupled Device (ICCD) detector. The spectrum of Fig. 3 is the result of an average of 200 time integrated spectra over 100 ms from the laser excitation. In this figure two peaks [15] corresponding to the photoluminescence at 2.8 eV, characteristic of STEs’ recombination in SiO2, and the fluorescence at 1.9 eV, characteristic of NBOHC formation are easily recognized.
To probe at longer delays we use, as explained above, CW laser probes and a gated ICCD camera. The experiments were performed at two different wavelengths 633 nm and 543 nm. In this case the lower spatial resolution of the ICCD sensor along with the inherent high frequency optical noise in the images lead us to replace the analytical in-line holographic techniques by a more simplified approach. Typical diffraction images, slightly defocused to enhance the diffraction fringe visibility, for various delays of the 543 nm probe are shown in Fig. 4(a) . The images are normalized using reference images, without pump. The square root of these normalized values corresponds to the diffraction amplitude. The amplitude is measured as the peak to peak variation along a line profile as shown in Fig. 4(b). The diffraction amplitude for both probe wavelengths as a function of the delay is shown in Fig. 4(c). The strong diffraction observed here is still due to the electronic defects, which are found to decay with a life-time of about 3 μsec.
Fig. 4 (a) Normalized probe images at various delays (543 nm, CW probe). (b) Normalized diffraction amplitude profiles at 0 μs delay measured along the dotted line of Fig. 4(a). (c) Normalized diffraction amplitude as a function of the delay for 543 nm, 633 nm CW probes. (d) Ratio of refractive index change as a function of delay. (Δn R: 633 nm, Δn G: 543 nm).
Additionally, using the diffraction images at different wavelengths we track the dispersion of the transient refractive index modification. Using a simple analysis and, since the diffracting object is not absorbing, the diffraction amplitude A at any propagation plane is proportional to the total phase change experienced by the probe wavefront:
where is the phase change induced in the probe wavefront after passing through the modified area, denotes the spatial distribution of the refractive index change, the amplitude of the transient refractive index change, λ the probe beam’s wavelength, x, y, z are the spatial coordinates and t is the time delay.Thus by dividing the diffraction amplitude of the two wavelengths we can retrieve the ratio of the transient refractive index changes and consequently the temporal evolution of the dispersion of the refractive index.
The ratio of the normalized refractive index modification for the two probe wavelengths (633 nm and 543 nm) is shown in Fig. 4(d). From Fig. 4(d) it is clear that the transient refractive index modification is initially strongly wavelength dependent, another firm indication that is correlated to electronic defects and not to local heating which would lead [24] to a ΔnR/ΔnG ratio of ~0.98. At later times >3 μsec the dispersion and the diffraction amplitude are considerably smaller. This enhances the idea of the transient defects initializing a reorganization of the glass network that leads to the densification of the material. From Fig. 4(c) one can see that this transformation is gradual and takes at least 3 μsec to complete. Actually, ring rearrangement in the fused silica excited area, with a significant increase of the 3-membered rings has been reported in [27] using micro-Raman spectroscopy, measurements that we have confirmed in our samples as well (not shown here). The ring reorganization and the densification have also been predicted by molecular dynamic simulations of UV-laser-induced densification of fused silica in [28]. Although our measurements clearly show that material densification is present we cannot exclude the contribution of other mechanisms, such as changes of the molar refractivity (phase changes) or the formation of defect centers.
Finally, to complete the picture of the material evolution the permanent modification of the material is studied in situ. In Fig. 5(a) is shown the length of the permanent modifications and in Fig. 5(b) the corresponding permanent refractive index modification, as a function of the number of accumulated pulses. The permanent refractive index changes were measured using the same holographic technique and the setup depicted in Fig. 1(a). It is worth noting that the diffraction images have inversed phase, which is the signature of an increase in the index of refraction in the core. The permanent refractive index modification starts from a very low value for a single laser pulse ~(2 ± 1)⋅10−4 and builds up with a decaying rate up to approximately (3.5 ± 1)⋅10−3 for 1000 pulses. The longitudinal size of the permanent modifications follows a similar behavior reaching saturation after ~300 pulses. Interestingly, for a single pulse excitation the refractive index is changing sign from a value of (−2.9 ± 0.1)⋅10−3 at short delays (30 ps) to ~(2 ± 1)⋅10−4 in the permanent state indicating the different physical origin of the refractive index change as a function of the delay
Fig. 5 (a) Permanent structure length and (b) refractive index change (at 496 nm probe wavelength) as a function of the number of pulses.
An important comment related to these results is the fact that in order to induce a permanent restructuring in the medium one needs to reach a minimum initial electron plasma density, as we have shown in a previous study [20]. This can easily be understood in the frame of the above described model as only 1 in 104 defects survive after each laser shot [25] and thus for an initial plasma density of ~1018 cm−3 only ~1014 defects/cm3 would survive, which is comparable to the natural defects in the bulk of the material. Thus material restructuring can only be observed for initial electron densities above this value in accordance with our previous work [20].
4. Conclusions
In conclusion, we have presented experimental data that reveal the complete material evolution from its initial excitation to its final lattice restructuring. Using a powerful time and spectrally resolved holographic technique we follow the laser pulse nonlinear propagation inside the medium and the concomitant electron plasma string created. It is only along this string that the material is modified. Electrons are trapped in excitons that relax rapidly in electronic defect states, which are long living and gradually decay, in microseconds, leading to a rearrangement of the material ring structure and consequently change its density. Moreover, we have provided clear evidence that under our conditions, pure fused silica and low repetition rate laser excitation, thermal effects do not play any noteworthy role. Finally, from the defect relaxation time one can estimate that thermal effects will start playing a role for laser repetition rates above 100 kHz.
Acknowledgments
This work was supported by the European Union Marie Curie Excellence Grant “MULTIRAD” MEXT-CT-2006-042683 and in part by the EU FP7 Program “LASERLAB-EUROPE” (grant agreement no. 228334).
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