High-power laser-induced dose deposition in distilled water
Part of Laser Applications
This article was first published on this website in May 2007
Copyright © Tiberius Brastaviceanu . All rights reserved.
This text is distilled from: The role of photoionization during self-focusing of a powerful fs laser pulse (790nm) in liquid water; spatial distribution of the free electron population
Department of Nuclear Medicine and Radiobiology, Sherbrooke University, Canada
This work is based on my research at Sherbrooke University under the supervision of Daniel Houde, all the results and the analysis presented here are part of my thesis. Fore more information you can get the entire thesis (written in French) here: part 1, part 2. See also paper book, get it on OpenThesis.
Abstract
In this paper we characterize the spatial distribution of the solvated electron population generated during the propagation of an intense 100fs laser pulse, at 790nm, in liquid de-ionized water, in the self-focusing regime. This characterization is constructed from direct measurements of solvated electron absorption (at 720 nm), 50ps after the passage of the ionizing laser pulse. Our experimental results are in very good agreement with predictions of models on nonlinear propagation, self-focusing, and supercontinuum generation [2]. The solvated electron are distributed in a filamentary fashion along the trajectory of the ionizing pulse. The filaments have very similar characteristics, the product of their diameter and the average electron density is practically the same for all the filaments generated by a single laser pulse. We estimate the average electron density inside the filaments to be in the order of 1017 electrons/cm3.
Background
It is well known that a femtosecond laser beam with sufficient intensity undergoes self-focusing in materials that presents a positive Kerr nonlinearity. In the case of a multimode pulsed laser beam, the intensity is redistributed during the nonlinear propagation, accentuating irregularities on the transversal plan of the pulse (a plan perpendicular to the direction of propagation). Thus, the light converges around the intensity picks that are above the self-focusing threshold, forming areas of very high intensity. These areas of high intensity swipe the space as they propagate within the laser pulse, and give rise to what has been called light filaments. Moreover, optical studies [11] show that during the process the intensity is clamped (at around 1012 W/cm2 in the case of water).
Until recently, it was not clear what mechanism was responsible for stopping the catastrophic collapse of the laser pulse, and limiting the intensity reached during the non-linear propagation. Bloembergen [3] proposed for the first time that in the sub-ps time regime, photoionization plays a major role in stopping self-focusing. The explanation goes as follows: As a very intense laser pulse enters a material possessing a positive Kerr nonlinearity, the self-focusing effect already begins to reshape the intensity distribution on the transversal plan. Following the initial intensity spatial irregularities, the light converges around the intensity picks that are above the self-focusing threshold. As the intensity increases progressively during propagation, the threshold of multiphoton/tunnel ionization (MPI), and avalanche ionization (AI) is reached. These two photoionization mechanisms take place simultaneously in experimental conditions close to ours [2, 6]. Their relative importance to the overall accumulation of quasi-free electrons depends on the local intensity, as well as on the pulse duration. As the intensity increases even more further down the propagation path, under the influence of the self-focusing "force", the local plasma becomes denser. We have to mention that the plasma has an effect on the propagation of the laser pulse. In fact, the accumulation of quasi-free charge changes the local optical properties of the medium, by inducing a negative change to the local refraction index. This effect opposes the non-linear Kerr effect, which induces a positive change to the local refraction index. At a given intensity level, the effect of the plasma on the refraction index, should balance the Kerr effect, and the self-focusing stops. At this moment we say that a core is formed, where the intensity has attained its maximum. As the laser pulse propagates further, energy is dissipated within the core by photoionization and other non-linear processes (frequency conversion processes). The self-focusing doesn't stop everywhere when the core is formed! Only where the equilibrium condition between plasma, and the non-linear Kerr effect is satisfied, that is within the core. Thus self-focusing continues around the core, directing light into the core, and replacing whatever energy is "last" there. In this manner, the equilibrium condition can be sustained within a very confined area during a certain distance of propagation. The core is maintained until all the surrounding energy is depleted, and cannot sustain self-focusing anymore. The spatial area swiped by it forms the light filament. On the trajectory of the core, the local properties of the material can be affected, temporarily or even permanently. This gives rise to what we call fossil filaments.
There is a direct correspondence between a light filament and a fossil filament, they share the same space. The fossil filament is whatever material change is left behind, if any, after the passage of the core. It can be observed long after the pulse has passed though the material sample. The light filament can be observed only by looking directly at the light pulse.
Although it is considered a fact that photoionization takes place during propagation of a high power laser pulse, to our knowledge there is not direct experimental proof that clearly demonstrates the major role played by this effect during self-focusing in condensed matter. Our goal is to perform a direct measurement of the solvated electron distribution on the trajectory of the laser pulse, and to show the close relation between the plasma generation and the self-focusing phenomena.
Measurement
The electrons generated by photoionization of liquid water solvate within one picosecond after the passage of the laser pulse. It is also believed that the salvation shell is formed only a few nm away from the birthplace of electrons [reference]. We are able to detect and characterize the spatial distribution of these solvated electrons after the passage of the ionizing laser pulse with femtosecond time resolution. For this purpose, we used a pump-probe experimental setup (Figure 1). The probe (100fs, 720nm) is the second harmonic of the idler from an OPA, and the pump, or the ionizing pulse (100fs, 790nm), is the residual pump of the same OPA. The OPA is pumped by 70fs, 1mJ laser pulses generated by a mode-locked Ti:Sapphire laser from Spectraphysics (Tsunami), amplified with a Ti:Sapphire regenerative amplifier (Spitfire). Our experimental setup was designed to detect the absorption of solvated electrons at different locations in space, and at different delays after the passage of the pump pulse. The diameter of the probe beam at the place where it crosses the pump beam is between 50 and 30 microns. This represents our spatial resolution.
Figure 1
This article was first published on this website in May 2007
Our experiment is performed in a 5 mm quartz cell with 1 mm window, in liquid de-ionized water. Figure 2 shows the two laser beams crossing each other within the water cell. The red one is the probe at 720nm, and the bright white one is the pump at 800nm. The color white comes from supercontinuum generation.
Figure 2
Experimental results
First, we should mention that during our experiment we observed supercontinuum generation. In Figure 2, we can actually see that the pump beam, at 790nm, appears bright white. This phenomenon is caused by a mix of nonlinear optical effects that take place during propagation of light at very high intensity levels. In Figure 3 we have the supercontinuum from the water cell (Figure 2) projected on a white screen, at different input intensities of the pump.
Figure 3
Figure 4 and 5 show the kinetic properties of the solvated electron population generated by the pump pulse. The absorption of solvated electrons were measured at different delays at an arbitrary location along the trajectory of the pump (chosen to optimize the absorption signal). Each point on the graphic is the average of a large number of consecutive measures. Figure 4 shows that the absorption signal exhibits a temporal behavior very similar to what was reported by C. Pepin et al. [9]. It is worth mentioning at this point that the characteristics of the ionizing pulses used in these two situations are not the same: 790nm and 100fs in our case, and 620nm and 150fs in the case of C. Pepin et al.. Moreover, our pulse was produced by the laser system described above, whereas C. Pepin et al. used a dye laser system (Rhodamine 6G and DODCI). The similarity of these two kinetics shows that the evolution of the absorbing species is not affected by these differences. This is understandable if we assume that the photoionization process doesn't disturb the local structure of the medium.
Figure 4
Figure 5 shows the same kind of measures at different wavelengths of the probe (the pump is kept at 790nm and et constant intensity). As expected, the temporal behavior of the absorbing species doesn’t vary with the probing wavelength.
Figure 5
In Figure 6, we present five horizontal scans that were made at different pump intensities. These scans are made by measuring the absorption of solvated electrons at different points along the propagation path of the pump, at a given delay. The wavelength of the pump and probe were 790nm and 720nm respectively. Each point on the graphic is the average of a large number of consecutive measures. This graphic is a direct indication of photoionization along the trajectory of the pump pulse. We see that for high intensities values, solvated electrons are present on a distance of a few millimeters. The higher the intensity, the longer the absorption (along the propagation path). But the elongation with the increase of input intensity is unidirectional, towards the laser source. As we will see later, this behavior is expected if one interprets these results in the context of self-focusing.
Figure 6
Visually, the solvated electron absorption starts to appear on the graphic (the left side of the curves, being the side by which the laser pulse enters the water cell) during the scan when the intersection between the probe and pump beams is near the location where the supercontinuum white light starts to become visible. You can see in Figure 2 the location where the pump beam becomes white, closer to the entry side (both beams come from the back of the water cell). Moreover, for higher intensities the intensity of the supercontinuum light is brighter, Figure 3. We didn't quantified this, it is only a qualitative observation. But we never succeeded in measuring any absorption of solvated electron below the supercontinuum threshold, even though a serious effort was invested. Lack of evidence cannot be turned into evidence, but if one considers it with care, lack of evidence can still carry information, or provide some loose indications. Again qualitatively speaking, by looking at the intensity of the supercontinuum (generated by the pump beam inside the water cell) for every of these horizontal scans, we observed that when the absorption vanishes somewhere below 4.0mW (when it becomes impossible to detect any absorption by carefully probing different locations), we can still see a week, and sometime unstable continuum. Again, this qualitative correlation between the distribution of solvated electrons and the supercontinuum can be better understood by considering self-focusing. We now regret for not having quantify these observations, by plotting the supercontinuum intensity and spectrum with the length of the solvated electron distribution.
If we look carefully at a horizontal scan (measure of D.O. at different locations along the trajectory the pump pulse) in Figure 7, we can see that the D.O. seems to take only discrete values. Both graphics represent the same scan, only that for the one on the right side, the x axes has been compressed in order to make clearer the discreet accumulation of points.
Figure 7
A vertical scan doesn't present any structure, Figure 8, no matter how much effort we invest to maximize the sensitivity of the measure. The structure underlying the values of D.O. measured in horizontal scans can be successfully explained, as we will see later, if these results are interpreted considering self-focusing. For the moment, let's see how reproducible, and how evident this effect is.
Figure 8
Figure 7 seams to indicate that the absorption is "quantified", but we have to design a more convincing method, one that puts this idea on more solid grounds. For example, we could take all the horizontal scans presented in the Figure 6, and look for the same behavior. If we compress the x axis of this graphic it becomes hard to tell because of the accumulation and overlapping of a large number of points. What if we present these results in another way. First, we take all the points on the graphic in Figure 6, and we form all the possible unique pairs. A pair might contain two points that belong to different scans. Second, we calculate the difference between the two D.O. values for every pair. And third, we build a histogram with all the values obtained (difference between two D.O. values).
The black histogram in Figure 9 was built with all the measured absorption values from Figure 6. For the red one, we excluded the scan with the higher intensity (20.0 mW). We can see a periodic structure emerging on this later histogram. This structure is very reproducible with other sets of data. What this figure shows, is that some values of D.O. differences are more frequent then others, and the more frequent ones form a periodic structure - they are separated by the same distance on the x axes. The fact that this periodic structure is more visible on the red histogram then on the black one suggests that this structure can be affected at high intensity levels.
Figure 9
Figure 10 presents other two histograms. The one in black is constructed with points from horizontal scans at 10.5mW, 5.3mW, and 4.0mW from Figure 6. The one in red is constructed with points from a horizontal scan acquired on a different day at 11.0mW, with a very high precision, by increasing the number of individual measures averaged for one single point (to 60 000 pulses), and by imposing a very strict selection condition in order to minimize the input intensity fluctuation (only pulses within 5% of a predefined intensity value were considered). Here too the same periodic structure appears.
Figure 10
Discussion
Our experimental results prove that photoionization takes place during self-focusing on a distance that can reach up to 2mm along the trajectory of a high power laser pulse. We have mentioned above that self-focusing and supercontinuum generation have been adequately explained within the theory of nonlinear propagation of high power laser pulses. These studies predict that photoionization takes place during propagation, and that the ionization density has a filamentary spatial distribution. Our goal at this moment is to investigate the link between our experimental results (which consists of a direct measurement of the solvated electron, and a characterization of the spatial distribution of the solvated electron population) and the predictions of self-focusing and supercontinuum generation models. If we succeed in establishing a very close correlation, the role of photoionization in self-focusing and supercontinuum generation will be firmly established. As a consequence, these models can be use to control the dose distribution induced within dielectric materials by high power laser pulses in the self-focusing regime, and in aqueous solutions, to predict the outcomes in terms of photolytic effects. We have found four points of correlation, which we discuss here-below. Upon our attentive investigation we haven't found any discordance between any aspect of our experimental results and the self-focusing model.
Supercontinuum generation and photoionization
The supercontinuum generation is caused by a mix of nonlinear optical effects that occur during propagation of laser light at very high intensity levels. The power threshold for supercontinuum generation coincides very closely with the critical power of self-focusing. This very strong connection between the two effects is now very well established [1, 2, 6]. Moreover, studies suggest that the presence of free electrons, induced by multiphoton and avalanche ionization, is crucial to explain the spectrum of the supercontinuum.
During our experiment we observe that supercontinuum is generated by the pump pulse (Figures 2 and 3). We then have to conclude that self-focusing takes place within the water cell. Furthermore, Figure 6 shows that solvated electrons are present on the trajectory of the pump pulse 50ps after its passage, and this is a strong indication that photoionization takes place.
Chin's model on supercontinuum generation [reference] states that the amount of light converted into supercontinuum is closely related to the length of light filaments. White light is generated within the core, for longer light filaments we should have a brighter supercontinuum. But because photoionization is believed to play an important role in the frequency conversion processes, and in the stabilization of the self-focusing core, the length of light filaments should be matched with the length of the solvated electron spatial distribution. In other words, the light filaments should be identified with the "fossil" filaments. The phrase "the longer the light filament the brighter the supercontinuum" can be transposed into "the longer the "fossil" filament (i.e. the spatial distribution of the population of solvated electrons) the brighter the supercontinuum". This correlation was qualitatively established during our experiments. In Figure 6, the horizontal scans at higher input intensities show that solvated electrons are present on a longer distance, and for the same scans the supercontinuum is brighter. As we diminish the input intensity, the white light fades away, and the distance on which solvated electrons are detected diminishes. The disappearance of the supercontinuum is correlated with the disappearance of the solvated electron absorption signal.
Moreover, a visual inspection of the location where the solvated electron absorption first appears along the propagation path of the pump pulse (the entry side), shows that it coincides with the location where the pump beam becomes bright white (see Figure 2).
This qualitative correlation can easily be quantified by measuring the intensity and the spectrum of the supercontinuum at different intensities, and by plotting this data along with the measured length of the solvated electron distribution.
Light filaments and fossil filaments
In the previous paragraph we established a qualitative correlation between the intensity of the supercontinuum generated within the water cell by the pump pulse, and the length of the solvated electron distribution. We said that according to Chin's model of supercontinuum generation, the white light is generated within the light filament, and the photoionization plays an important role. After the passage of the laser pulse, the free electrons generated during these processes solvate, and constitute the fossil filaments. We don't know yet if the solvated electrons are distributed in a filamentary fashion, for the moment we only take into consideration the length on which they are distributed along the trajectory of the pump. So we said that the correlation between the length of solvated electron distribution and the intensity of the supercontinuum must be similar to the correlation between the length of light filaments and the intensity of the supercontinuum. And this is what we observed qualitatively. But the above reasoning becomes valid only if we establish more firmly the link between light filaments and the solvated electron distribution.
Figure 6 also shows that for higher intensities the distribution of solvated electrons is wider. It is also important to realize that the elongation of the electron distribution for higher intensities proceeds in only one direction. The position along the trajectory of the pump pulse where the solvated electron absorption ends (the write side of the scans) doesn’t seem to bee affected by the variation of the intensity. This behavior is very similar to that of the light filament traces that are directly observed by imaging the cross section of the laser beam inside the water cell, and predicted by the moving focus model on self-focusing [8]. For higher intensities the self-focusing starts earlier during propagation, but the end of the filament trace is practically fixed [2, 8, 10]. This similarity in behavior between the solvated electron distribution end the self-focusing effects again suggest a strong relation between ionization and self-focusing, and a strong link between light filaments and the solvated electron distribution.
Filamentary structure of the solvated electron distribution
The strongest point of correlation between our experimental results and self-focusing, and supercontinuum generation is the "quantified" behavior of our D.O. measures (Figure 7). The periodic structure that appears in Figure 9, and 10 suggest that the absorbent is constituted of entities that have the same spectroscopic properties. The total absorption signal is a multiple of the absorption of a fundamental entity.Unfortunately our spatial resolution is insufficient to detect any structure in the solvated electron density by scanning in the direction perpendicular to the trajectory the pump pulse (vertical scan Figure 8). Let's try to interpret this behaviour using the self-focusing scheme.
As a powerful laser pulse self-focuses, there is creation of a family of light filaments. The length of a particular filament depends on the amount of energy stored around the core, in the form of light. So by looking at this bundle of filaments, some of them are longer then others. But their diameter is almost the same, and the ionization density within each filament is the same, these two parameters being controlled by the conditions of equilibrium between the non-linear Kerr effect, and the plasma effect on the local refraction index. If the diameter and the ionization density is very similar from one filament to another, this means that once the pump pulse has passed, the plasma relaxes, and the electrons solvate and form filamentary structures with very similar spectroscopic characteristics. As we scan along the trajectory of the pump, we measure the absorption of a different number of filaments. The "quantified" behavior of the absorption values suggests that the product between the diameter of filaments and the average electron density within them is almost constant in a given experimental condition.
It is worth mentioning here that this behavior becomes more pronounced at smaller intensities, as we can see in the Figure 9 by looking at the difference between the red and the black curves. We believe that for higher intensities the propagation is more strongly perturbed and this prevents the formation of clearly separated filaments [5,7,8].
We have to mention that the periodic structures that appear on Figure 9, and 10 are very reproducible. In Figure 10 we present the results of a horizontal scan obtained on a different day. This particular scan was made with special care, and our goal was to increase the sensitivity of our measurement.
The picks that appear on Figure 9 and 10 are not very pronounced and this can be understood within the same framework. Every point on the graphic in Figure 6 is an average of a very large number of consecutive measures. A very small fluctuation of the pump intensity induces a slight displacement of the filaments, as predicted by the self-focusing theory. Even if we impose every strict selection conditions to reduce the input intensity fluctuations, the jitter in the filament position cannot be completely eliminated from pulse to pulse. The effect of this is that periodic structure becomes less prominent. This is how we can explain the presence of intermediary points on the right part of the Figure 7.
Photoionization density and slvated electron density
Based on the difference between two consecutive possible values of D.O., or the distance between two picks form Figure 9 or 10, we can approximate the average electron density within the filaments, if we already have the value of their diameter. We use 10 microns proposed by Chin et al. [2,4] in water using other independent measurement techniques . Using the Beer-Lambert low, our calculations give an average electron density in the order of 1017 cm-3, witch is in very good agreement with Chin's predictions based on nonlinear propagation models, and self-focusing [1,2], which is the estimated density necessary to balances the Kerr effect, and to stabilize self-focusing.
Conclusion
To our knowledge, this direct measurement of the electron density distribution along the trajectory of a powerful laser pulse that undergoes self-focusing is a premier. We have shown that photoionization takes place during self-focusing of femtosecond laser pulses in liquid water, and that it plays an important role in the stabilization of self-focusing, in the sub-ps time regime. The theory on self-focusing can be used to control and to predict the dose distribution induced by powerful laser pulses during their propagation within dielectric materials, in the self-focusing regime.
References
[1] Superbroadening in H2O and D2O by self-focused picosecond pulses from a YAIG:Nd laser; W. Lee Smith, P. Liu, and N. Bloembergen; Physical ReviewA, Volume 15, Number 6, June 1977
[2] Ultrafast wihte-light continuum generation end self focusing in transparent condensed media; A. Brodeur and S.L. Chin ; 1999 Optical Society of Smerica Vol. 16, no. 4/April 1999/J. Opt. Soc. Am. B 637
[3] Avalanche Ionisation and the Limiting Diameter of Filaments Induced by Light Pulses in Transparent Media; Eli Yablonovith and N. Bloembergen; Physical Review Letters, Volume 29, Number 14, 2 October 1972
[4] Beam filamentation and the white light continuum divergence; A.Bordeur, F. A. Ilkov, S. L. Chin; Optics communications, 15 august 1996
[5] Random deflection of the white light beam during self-focusing and filamentation of a femtosecond laser pulse in water; W. Liu, O. Kosareva, I.S. Golubtsov, A. Iwasaki, A. Becker, V.P. kandidov, S.L. Chin; Appl. Phys. B 75, 595–599 (2002).
[6] Band Gap Dependence of the ultrafast white-light continuum; A.Brodeur and S.L. Chin; Phys rev lett, Vol 80, No 20, 18 may 1998
[7] Theory and Simulation on the Threshold of Water Breakdown Induced by Focused Ultrashort Laser Pulses; Q. Freng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Roockwell, and C. R. Thompson; IEEE Journal of Quantum Electronics, Vol. 33, No. 2, February 1997.
[8] Self-Focusing: Theory; J. H. Marburger, Prog. Quant. Electr., Vol 4, pp.35-110, Pergamon Press, 1975
[9] Génération de l'électron hydraté par absorbtion multiphotonique d'impulsions laser femtoseconde de 2 eV; C. Pépin, D. Houde, H. Remita, T. Goulet, J.-P. Jay-Gerin; J Chim. Phys (1993) 90, 745-753
[10] Self-Focusing : Experimental; Y. R. Shen; Progress in Quantum Electronics, Vol. 4, pp. 1-34, Pergamon Press 1975.
[11] Intensity clamping article of Chin et al..