We present direct laser writing of channels in chalcogenide glass under light filamentation conditions. Because of the intrinsic properties of the filament, the positive refractive index profile of the channels exhibits a cylindrical symmetry of high quality. The role of the repetition rate is also investigated. It is shown that if the time separation between pulses is shorter than the lifetime of the plasma, the free carriers accumulate and induce a larger variation of the refractive index.
© 2011 OSA
Direct laser writing [1, 2] is actually recognized as a mature technique for the fabrication of integrated photonic devices in dielectric media. One of the major interest in this technique is the localization on the microscale of controlled refractive index modification (Δn), arising from the nonlinear character of the interaction between femtosecond laser pulse and the media. The immediate consequence is the capability of true 3D structure engineering . Single step process, rapid prototyping, short processing time are obviously few other advantages of this technique among others.
Direct femtosecond (fs) laser writing (DFLW) has been demonstrated in a large variety of materials including polymers [4, 5], crystals [6, 7], ceramics  and glasses [9–11]. A particular class of glass is the chalcogenide one (ChG) characterized by large nonlinear optical coefficient  and broad transmission window from visible to infrared  where they are used for spectroscopic applications [14, 15]. DFLW experiments in ChG have been widely reported for a broad range of parameters including composition, pulse energy and repetition rate, see [16–20] to cite a few.
Various studies have been reported on laser repetition rate influence on Δn, all having highlighted the role of heat accumulation at MHz regime [21, 22]. However Δn has been shown to result also from the formation of plasma during laser filamentation . The phenomenon of filamentation results from a dynamical equilibrium between different effects [24, 25]. First, the laser beam self-focuses in the media because of the optical Kerr effect. When the intensity of the beam is high enough, self-focusing will collapse, resulting in a plasma formation. But the generated free carriers induce a negative refractive index variation that will tend to defocuse the beam. So the natural divergence of the beam can be compensated by the combined action of these effects over distances as long as several kilometers in air . In condensed matter like silica, the length of the filament is only of centimeter scale  and can induced a refractive index variation, as already mention. In ChG, the filamentation is made easier because of the high nonlinear refractive index and Δn induced by laser filament in ChG has been observed very recently by two groups [28, 29].
In this paper, we present a study of Δn produced by femtosecond laser filament in ChG with various repetition rates and intensities. We demonstrate that the free carrier density can be increased by several orders of magnitude if the time separation between laser pulses is shorter than their lifetime. The consequences on Δn are investigated.
First a measurement of this lifetime is presented and the phenomenon of accumulation of charges when the sample is irradiated by a pulse train is evidenced. As the intensity is increased above the filament formation threshold, a permanent refractive index variation Δn is observed. An excellent cylindrical symmetry of the Δn profile is observed and explained by the intrinsic properties of the filament. The dependence of the diameter and the magnitude of Δn with the femtosecond pulse intensity and the repetition rate are presented. The results are interpreted taking into account the charges accumulation effect.
2. Plasma lifetime measurement
2.1. Experimental setup
The investigated glass composition is 90 [(GeS2)0.8 – (Ga2S3)0.2] – 10 CsCl which shows a large transmission range extending from visible (∼ 500 nm) up to midinfrared (∼ 11.5 μm). All details on the sample preparation and properties can be found in .
The experimental setup used for the free carrier lifetime measurement is depicted in figure 1. First a femtosecond (fs) pulse is focused into the sample by a lens of 50 mm focal length. The beam waist is about 6 μm. Its polarization can be managed by used of half and quarter waveplates. The pulse duration and central wavelength are measured to be 280 fs and 800 nm, respectively. All the experiments have been performed at intensities below the threshold of permanent refractive index modification (less than 63 GW/cm2, see figures 6c and 6d).
The fs beam is combined on a dichroic mirror with a continuous wave (CW) laser at a wavelength of 1.55 μm. The beams overlap and are focused simultaneously in the sample. Some optics are used (not shown in figure 1) to mode match the CW beam with the fs one. After the sample, the beams are separated once again and the CW one is partially blocked by an aperture before to be focused on an ultrafast photodiode (Femto HSA-200M-IN). The transmission signal is recorded with a data acquisition board connected to a computer.
The principle of the experiment is the following. As the fs beam is focused in the sample, it induces free carriers that modify locally the refractive index according to :
The black line of the figure 2 represents an example of this transmission signal after a single pulse excitation. It consists in a fast decrease before the transmission exponentially returns to the initial level. We point out that the maximum temporal resolution of our experiment is 0.8 μs and so, faster component of the phenomena could not be observed.
The red curve on the figure 2 is obtained when the sample is illuminated by a pulse train having a time separation between pulses shorter than the free carrier lifetime. In these conditions, charges are excited before the previously excited ones relax. Therefore the charges accumulate and the density saturates at a level much higher than the contribution of a single pulse.
This effect is more significant at higher repetition rate. The figure 3a shows the results obtained at 20, 50 and 200 kHz. From these results, charge density dependence on the repetition rate is strongly evident.
When the pulse train stops, the charges relax and the density exponentially decays as shown on figure 3b. This decay is fitted to obtain the lifetime of the free carriers. Knowing this lifetime, the response of a single pulse excitation can be calculated. The contributions of N pulses delayed by the appropriated time, are then summed to determine the enhancement factor due to the repetition rate and relative to a single pulse. We find a lifetime of 3.35 ± 0.05 ms (independently of the repetition rate) and an enhancement up to more than 500 at 200 kHz repetition rate.
This lifetime is fairly long relative to other material. As an example, it has been shown recently that permanent Δn due to plasma in silica glass has a dynamics of the 10 μs scale and subsequent cooling within 100 μs . Nevertheless, the lifetime of photo-excited charge carriers (electrons and holes) deduced from drift mobility and photoconductivity experiments in chalcogenide systems was found to vary significantly, e.g. from 100 ns (As2Te3) to 1–10 ms (As2Se3 or sulfur) [32–34]. Millisecond dynamics was also reported for the decay of luminescence excited by photons having the band-gap energy . Also, the atomic displacements in chalcogenide glasses have similar time scale. Phase-change optical memories based on Ge-Sb-Te or Ga-La-S thin films exhibit the astonishingly rapid nanosecond crystallization of nanosized amorphous ’marks’ in a polycrystalline layer [35–37]. The underlying mechanism of the observed plasma lifetime needs therefore further investigation.
2.3. Role of the temperature and polarization
If the temperature increase is high and ∂n/∂T is significant, thermal lensing and heat accumulation  have to be taken into account. In this case, a signal similar to what is reported here would be observed. Therefore we have to pay attention if thermal effect influences or not our observation. Several arguments indicate that it does not.
First if the influence of the temperature is high, it should result in Δn having spatial extension larger than the focal volume (especially in the transverse direction) and also in a dependence of its diameter with the intensity what is not observed here (see figure 6c and related discussion). [20, 22, 38]. Moreover the sample has been heated at the glass transition temperature Tg for 5 hours and we do not observed any modification in the written structure. This indicates that the permanent Δn is not resulting from a stress but rather structural modification .
Finally it has been shown that ionization mechanism is polarization sensitive . Therefore we have recorded the magnitude of the signal as a function of the polarization state of the fs beam at a repetition rate of 200 kHz. As it can be seen from the figure 4, the observed signal is larger for linear polarization than for circular one. The dependence is relatively small compared with silica glass because the order N of the nonlinear absorption of our glass (N = 2) is much smaller (N = 6 in silica) . Nevertheless such a dependence can not be explained in terms of thermal effect.
Therefore we can conclude that the temperature increase does not affect significantly our observations.
3. Refractive index contrast measurement
Because of the high nonlinear refraction index of the glass , the filamentation of the fs beam is possible even at a moderate intensity. As the plasma density becomes very large in the filament, a permanent refractive index is resulting. The figure 5a shows the image of Δn obtained by static exposure of the sample to 200 000 pulses at a repetition rate of 50 kHz and focused with a lens of 25 mm focal length. The reconstruction of Δn is done by Quantitative Phase Imaging technique followed by an Abel inversion . It can be seen from this figure that the length of Δn is much longer than the Rayleigh length (zR = 35 μm) and that its diameter is nearly constant along the refractive index modification, then confirming the presence of the filament.
Channels of Δn can be written by moving the sample across the focal point and parallel to the beam propagation direction. This longitudinal scheme of writing is allowed by the very high photosensitivity of ChG resulting from the ease of plasma generation. In the experiments we have fixed the translation speed to 200 μm·s−1. As it can be seen from the figure 5b, the result is a very homogeneous Δn of magnitude and full width at half maximum (FWHM) equal to 1 ·10−3 and 2.07 μm, resp. The homogeneity is directly connected to the intrinsic properties of the filament. First, because the lowest order laser beam mode is the smaller one, it will be the first to generate the filament. All the others are then defocused by the plasma (at moderate power above the critical power for the beam collapse) and are not entering into the filament. Consequently only the lowest order mode is forming the channel, an effect known as spatial mode self-cleaning . Next the intensity is clamped in the filament  and therefore Δn is not sensitive to laser fluctuations both in shape and in power.
An example of the measured transverse profile (circles) of Δn(r) is represented on figure 6a where the red line is a Gaussian fit. The high symmetry of Δn profile is highlighted in figure 6b. The figures 6c and 6d give the evolution of the FWHM and the magnitude of Δn with the intensity of the incoming fs pulse for different values of the repetition rate (20, 50 and 200 kHz).
First for low value of the intensity, modification of the refractive index is not observed (FWHM and magnitude of Δn are equal to 0 in figures 6c and 6d). The formation of the filament requires that the power is above a critical value (Pc). This value can be calculated from :30], so that the critical power is evaluated to Pc = 18 kW. Considering a beam waist of w0 = 3 μm, laser filamentation occurs at intensities higher than 63 GW/cm2. Therefore, it can be concluded that Δn is observed only when a filament is formed.
As expected  the FWHM does not present any dependence with the intensity. The absence of dependence with the repetition rate (within our experimental spatial resolution) confirms once again the low influence of thermal effect.
The evolution of the magnitude of Δn is more complex (see figure 6d). This parameter saturates as the intensity increases at a value that depends on the repetition rate. First the saturation can easily be understood in term of the already mentioned intensity clamping effect in the filament. If it is well seen at 200 kHz, it is obviously less marked at lower repetition rate. This can be understood because the length of filament slightly increases with the intensity. Therefore the overlapping length between two filaments due to two consecutive fs pulses is longer at higher intensity. So the accumulation effect evidenced in section 2.2 is more efficient. This accumulation effect has also been shown to lead to higher free carrier density at higher repetition rate. Therefore the difference in the saturation level of the magnitude of Δn for different repetition rate could be explained by this dependence of the free carrier density.
In conclusion positive refractive index modifications of ChG under fs laser filamentation conditions are presented. The intrinsic properties of the filament lead to homogeneous Δn with a diameter independent of the intensity. Because of their very long lifetime, free carrier density can be enhanced by several orders of magnitude by increasing the laser repetition rate, the consequence being a higher value of Δn magnitude.
So the control of Δn magnitude is shown to be more easily achieved by controlling the time separation between the laser pulse or equivalently the translation speed. An increase of the laser intensity is not efficient because of intensity clamping effect and second, a too large augmentation would result unavoidably in multifilamentation and an inhomogeneous Δn structure [44, 45].
We are very grateful to Pr. Andrei Tveryanovich for stimulating discussion. O. Caulier is very grateful also to the Direction Générale de l’Armement and the Syndicat Mixte de la Côte d’Opale for financial support. The Laboratoire de Physico-Chimie de l’Atmosphère participates in the Institut de Recherche en ENvironnement Industriel (IRENI) which is financed by the Communauté Urbaine de Dunkerque, the Région Nord Pas-de-Calais, the Ministère de l’Enseignement Supérieur et de la Recherche, the CNRS and European funds (ERDF). This work was also supported by the European Commission within the framework of the Interreg IVA-2Seas (CleanTech project) programme.
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