The spatial distribution of the second-order nonlinearity induced in thermally poled Infrasil silica samples is recorded after thermal annealing experiments. Two regimes have been studied: short and long poling durations. For short poling durations, the observations are in good agreement with a model where only one ion type recombines inside the depletion region. The nonlinear distribution and erasure observed for the other case are well explained by considering the addition of another positive-charged ion injected during the poling process. This second ion acts as a barrier during thermal annealing and reduces the mobility of the first one.
© 2006 Optical Society of America
Thermal poling has proved to be a reproducible method for inducing second-order nonlinearity (SON) in silica glasses . It consists of heating the sample to ≈ 300°C and simultaneously submitting it to a high bias of several kilovolts. After a few minutes, the sample is cooled down to room temperature and the voltage is removed.
The thermal poling process induces SON in a thin layer just beneath the surface in contact with the anode. Cations migration is usually assumed to be responsible for this phenomenon [2, 3, 4]. In the first stage of the poling process, the most rapid ion (say Na+) drifts towards the cathode, leaving a depletion layer negatively charged just beneath the anode. In this case, the spatial profile of the χ (2) susceptibility proves to exhibit a quasi-triangular shape [5, 6] which is the signature of a homogeneous concentration of negative charges. The magnitude of the nonlinearity increases until an optimal poling duration t opt for which the χ (2) susceptibility is maximal. The optimal duration t opt is for example equal to ≈ 10 min at 250°C in Infrasil samples. For t > t opt, charge injection (or ionization) phenomena take place and contribute to the decrease of the SON magnitude and the increase of the nonlinear width [2, 6, 7]. The width growth is then fixed by the movement of the slow ion (say H+), whose mobility is several orders of magnitude smaller than that of the rapid ion [2, 6].
The possible use of poled components in telecommunication networks raises an important question about the long term stability of the induced SON. The relaxation time of the SON has been investigated above room temperature, showing an Arrhenius dependence and an activation energy of about 1.3 eV in silica glasses . Furthermore, isothermal annealing experiments have been performed at high temperature in a large variety of glasses, with different chemical compositions in order to obtain information about the charge recombination processes that explain the χ (2) decay when the glass temperature is elevated . The time evolution of the second-harmonic (SH) signal generated within the poled sample for a fixed angle of the pump beam is mainly used to probe the SON during thermal annealing experiments [8, 9]. In such experiments, the square root of the SH intensity is generally assumed to be proportional to the product χ (2)×w, where w is the width of the nonlinear layer. The width w is assumed to be constant [8, 9] because w is not available in real time with a SH experiment.
The observations reported above show that the chemical composition of the poled glass depends strongly on the poling process duration: samples poled for t>t opt contain a significantly high amount of injected charges as compared to samples poled for t<t opt. As a consequence, the thermal stability of the induced χ (2) should depend on the poling duration since the mobilities of the two charges brought into play (H+ and Na+) are significantly different.
Moreover and having in mind the microscopic mechanisms occurring during the poling process, a complex behavior of the SH signal versus the annealing time can be found. Indeed, the SON profile (the magnitude of the χ (2) but also the width w) may change during the annealing experiment, leading to complex changes in the SH signal. Therefore, in order to correctly interpret the experimental results, the knowledge of both the poling duration and the SON spatial distribution in the course of the thermal annealing are required.
The purpose of the present work is to investigate the time evolution of the SON profile during thermal annealing experiments. A model with two positive charge carriers is used to explain the experimental observations.
2. Experimental results
The samples under study consist of 1mm-thick Infrasil silica disks cut from the same silica rod (to ensure a constant chemical composition from sample to sample). The experiments have been performed in air atmosphere, at a temperature of 250°C. Two poling durations were chosen: 5 min (<t opt, sample A) and 100 min (>t opt, sample B) . This unusual temperature (250°C instead of 280–300°C ) contributes to a decrease of the kinetics of the poling process (the ion mobilities are significantly reduced as compared to at higher temperatures) and to an accurate determination of the nonlinear profiles for short poling times. A DC voltage of 4 kV has been applied across the sample via pressed-on p-doped silicon electrodes.
Just after poling, the poled silica plates were kept in the oven at the same temperature than that of the poling process and the voltage was subsequently switched off. At this stage, the samples were still in contact with the electrodes that were both grounded (short-circuit configuration). This procedure ensures an accurate control of the annealing duration and avoids a new heating from room temperature to the work temperature. After the chosen annealing duration (ranging from 5 min to 100 min), the samples were removed from the furnace and cooled down rapidly to room temperature by immersion in a tank containing water. This procedure guarantees a decrease of the temperature in the depletion region from 250°C to room temperature within only a few seconds.
Afterward, each sample has been characterized by means of the layer peeling method described in ref. . Basically, this method consists in recording the peak power of the SH signal generated within the nonlinear region for a fixed angle of the pump beam, as the sample anodic surface is etched with hydrofluoric acid. The removed glass thickness is deduced from interferometric measurements, allowing a spatial resolution of about 100 nm .
The SON spatial distributions recorded just after poling are displayed in Fig. 1 for both samples A (Fig. (a), curve ( ◦)) and B (Fig. (b), curve ( ◦)). As expected, the NL distributions exhibit two different behaviours depending on the poling duration. For sample A (short poling duration), the NL profile is almost triangular. The χ (2) magnitude peaks at about 0.5 pm/V and the NL width w is equal to about 2 µm. Note that this short width can be explained by the short poling duration and the low temperature used during the experiment . The SON distribution recorded just after poling in sample B is more complex: the χ (2) increases until≈700 nm where its value is maximal (0.4 pm/V). Then the χ (2) decreases and becomes approximately constant between 2 µm and 6 µm. The SON vanishes after a total thickness of 8 µm which proves to be the typical value for these poling parameters .
The time evolution of the SON profiles recorded after thermal annealing depends strongly on the initial poling duration:
- Case of short poling durations: As can be seen in Fig. 1(a), the χ (2) distributions for the samples annealed for 5, 15 and 30 min also exhibit a quasi-triangular shape (except in the first tens of nanometers near the surface of the sample) with a decreasing width as the annealing time increases. It is worth noticing that, even after an annealing time 6× the poling duration, a SH signal continues to be generated by the sample.
- Case of long poling durations: Figure 1(b) shows that the χ (2) profiles obtained for the samples annealed for 15 and 30 min proves to be made of 2 quasi-triangles with a steep slope near the surface. The sample annealed for 100 min leads to a SON with a triangular profile. The widths are respectively equal to 5 µm (15 min), 4 µm (30 min) and 0.5 µm (100 min).
3. Modeling and Discussion
As shown in Fig. 1, both the magnitude of the χ (2) susceptibility and the NL width w decrease during the annealing experiments. Moreover, the time evolution of w exhibits a different behavior depending on the initial poling duration, and the assumption that w is constant can only be made as a first approximation. While the time evolution of the χ (2) profile can easily be explained by the migration of 1 positive charge carrier for short poling durations , the complex behavior observed in the case of long poling durations requires a model where at least two positive charges are taken into account.
3.1. Charge migration model
The charge migration model reported in ref.  has proved to be efficient to obtain the time evolution of the χ (2) spatial distribution during the poling process. Basically, the local electric field E DC within the glass is calculated using a set of partial differential equations where ionic conduction and diffusion of two positive charge carriers are taken into account. The associated negative charges are assumed to be motionless within the glass matrix.
The injection phenomenon is modeled via the following equation:
where σ is the injection rate, x the position across the sample (x=0 corresponds to the anodic surface) and p H+ the concentration of the slow ion, assumed to be H+ for clarity.
The χ(2) susceptibility is then obtained from E DC through equation χ (2)=3χ (3) E DC with χ (3)=2×10-22 m2/V2 .
The mobility µ of each ion and the injection rate σ used to perform the simulations for the poling experiments (before annealing) are summarized in Tab. 1 together with the initial concentration of charges c 0. These parameters have been successfully used in Ref.  to reproduce the time evolution of the χ (2) spatial distribution in the course of the poling process for 500 µm-thick Infrasil silica samples.
The thermal annealing experiments are modeled as follows:
- Both the initial electric field and charge distributions are calculated for poling durations of 5 min and 100 min with the applied voltage set to 4 kV.
- The voltage is then set to zero.
- The time evolution of the charge distributions during annealing are modeled with the same partial differential equations, the charge distributions obtained previously being used as starting point.
Figure 2 shows the theoretical SON spatial distributions for both sample A (Fig. 2(a)) and sample B (Fig. 2(b)). The initial NL distributions correspond to the curves with open circles. Note that the mobility of the rapid ion has been divided by a factor 4 in the case of sample B to reproduce the time evolution of the experimental data. This change in mobility will be explained and discussed later in the paper (in section 3.3).
3.2. Case of short poling duration
The use of poling durations shorter than t opt allows to limit the charge injection that can occur at the anodic surface of the sample . In this case, the depletion region, that is, the region from where the rapid charge carrier has moved away, contains a homogeneous concentration of negative charges . This phenomenon explains the triangular shape of the nonlinearity before annealing (curve (◦), Fig. 2(a)).
During thermal annealing, Fig. 2 shows that both the magnitude of the χ (2) susceptibilities and their widths decrease without a significant change of the shape of the nonlinearities. It is noticeable here that the experimental data shown in Fig. 1(a) are in good agreement with the theoretical ones both in terms of χ (2) magnitudes and NL widths.
This behavior can be explained as follows: during the annealing experiment, the voltage is removed and the two surfaces of the sample are at the same potential. In this case, a negative electric field appears outside the sodium depleted region due to the zero potential condition  as can be seen in the scheme of the theoretical electric field plotted in Fig. 3. This reversed electric field makes the sodium cloud drift towards the anode. As a consequence, the sodium ions can recombine with the negative charges in the depleted region, contributing to a decrease of the internal electric field, and thus a decrease of the magnitude of the χ (2) susceptibility. The reversed field drops as the negative charges are neutralized. As the drift becomes slower, a residual SH signal can be generated for times much longer than the poling time.
This phenomenon is depicted in Fig. 4 where the time evolution of the theoretical charge concentrations is shown for both sodium and hydrogen ions. The top Fig. (Fig. 4(a)) yields the initial charge distribution just after poling. The sodium concentration (hydrogen concentration) corresponds to the curve in black line (dashed line). As can be seen, the region located within the first 1.7 µm is free of sodium. Note that although the poling duration is short, a small amount of hydrogen has been injected within the first 500 nm under the anode.
As expected, sodium moves towards the anode and fills the depletion layer progressively (Fig. 4(b,c,d,e)). Hydrogen ions however continue to move in the opposite direction (towards the cathode) until they reach the edge of the sodium cloud where they begin to be motionless. The hole in the sodium concentration that can be seen in Fig. 4(e) is compensated by the hydrogen wall so that the material is neutral. This movement of hydrogen in the opposite direction is explained by the positive electric field remaining within the depleted region (see Fig. 3).
The bulk electric field magnitude (the electric field outside the depletion region) is written in Fig. 4 for each case and is a decreasing function of the annealing time as expected since the negative charge number decreases as the sodium cloud moves towards the anode.
Although the mobility of H+ is 3 orders of magnitude smaller than that of Na+, the charge movement in the depletion region is appreciable. This is explained by the magnitude of the driving field that makes H+ drift, which is hundreds of times larger than the reverse field in the bulk.
3.3. Case of long poling duration
In the case of long poling durations, charge injection cannot be neglected and the concentration of hydrogen is comparable to that of sodium . The recorded electric field exhibits then a more complex behavior as well as the χ (2) susceptibility.
The initial theoretical NL distribution is shown in Fig. 2(b) (open circles). The NL coefficient is maximal near the surface, becomes approximately constant between 3 µm and 8 µm and then decreases to zero after 8 µm. One can notice also a good agreement between the theoretical and experimental data except just beneath the anode where surface effects are maximal .
Contrary to short poling durations, the profile of the nonlinearity is modified during thermal annealing, as observed experimentally. For long annealing times, the theoretical χ (2) susceptibility also exhibits a triangular profile as can be seen experimentally in Fig. 1(b) (100 min).
To account for the experimental time evolution, the mobility of the rapid ion had to be divided by a factor 4 comparing to the value used for short poling durations. Indeed, a simulation with the same mobility leads to a too rapid decrease of the χ (2) susceptibility. From this information, it can be deduced that the formation of the depletion layer in the presence of charge injection makes a more profound change on the glass structure, reducing the mobility of the Na+ ions compared to the case of one charge carrier movement. In particular, hydrogen ions are likely to occupy the negative sites used by the sodium ions while they drift towards to anodic surface during annealing, making the Na+ ion migration more difficult. Such phenomena have already been highlighted in a large variety of silica based glasses [2, 9, 14].
As in the case of short poling durations, the time evolution of the theoretical charge concentrations is displayed in Fig. 5. Figure 5(a) corresponds to the initial state (before annealing). Figure 5(b,c,d,e) show the charge concentrations for annealing times equal to respectively 15, 30, 100 and 165 min. Curves in continuous line (dashed line) shows the sodium concentration (hydrogen concentration).
As can be seen, the initial state is characterized by a huge amount of injected charges between the anodic surface and 7.5 µm, i.e., most of the depletion region is neutralized. The depleted layer is now filled with hydrogen and only ≈ 700 nm is free of sodium (between 7.5 and 8.2 µm). The hydrogen concentration proves to be similar to that of sodium in the bulk (9.5×1022 ions/m3).
During annealing, the sodium cloud migrates toward the anode and fills progressively the depleted layer. After having passed through the hydrogen wall (Fig. 5(d)), sodium continues to migrate towards the anode and begins to fill the region now free of hydrogen (Fig. 5(d) and (e)). The hydrogen wall is quasi-motionless in this case. Having in mind this large hydrogen wall, it is now understandable that the mobility of sodium should be modified by its presence.
3.4. Theoretical second harmonic signal
It is interesting to examine the decay of the SH signal in the present erasure experiments because they shed light in the charge distribution recorded during poling for different poling times. Qualitatively, in the case of short poling times a relatively narrow depletion region is formed, but total erasure requires the movement of Na+ all the way to the anodic surface, since the negative charge distribution after poling is uniform. In the case of long poling times, the present model shows that the field is created to a large extent by a buried layer of negative charge, while the depletion region is mainly neutral. Cancellation of the negative charge at the edge of the depletion region in the latter case should lead to a large reduction of the SH signal, without the need for the Na+ to migrate all the way to the anodic surface. Examination of the experimental results of Fig. 1(a) and 1(b) confirms that the reduction of the area under the NL profile after 15 minutes erasure is much more significant in the case of long poling times. This is independent confirmation that the charge distribution recorded by poling qualitatively follows the plots shown in Fig. 4(a) and 5(a).
Based on the theoretical χ (2) distributions, the time evolution of the second-harmonic signal has been calculated in these two cases using the following equation :
where Δk is the phase mismatch, θ the internal propagation angle, l is the sample thickness and x is the position across the sample.
The internal angle has been fixed to 36° which corresponds to a typical angle of incidence of about 60°.
In Fig. 6 is displayed the theoretical evolution of the SH signal for both samples A and B. As can be seen, the SH signals exhibit different behavior depending on the value of the poling experiment. In particular, the SH signal generated within sample B proves to exhibit a more complex evolution than that of sample A. A rapid analysis of the two curves could lead to the conclusion that different mechanisms are implied during the thermal annealing whereas only the rapid ion is brought into play during this process (hydrogen can be assumed to be motionless for sample B).
The SON spatial distributions induced in thermally poled Infrasil silica samples have been determined after thermal annealing experiments performed at 250°C. Two initial poling conditions were considered: short and long poling durations. For short poling durations, the charge injection mechanisms have been minimized, leading to a homogeneous negative charge concentration in the depletion region. As a result, a single charge carrier model proves to be sufficiently accurate to describe the time evolution of the SON distribution during thermal annealing. Experimental and theoretical results concerning thermal annealing experiments performed with a long poling duration can be explained by considering the addition of another positive charge injected during the poling process. The movement of the rapid ion toward the anode during the annealing experiment can be explained by the presence of a relatively weak but important negative electric field distribution in the bulk of the poled sample. A reduction of the mobility of the rapid ion in the presence of the injected second ion species was also inferred. The charge migration model used in this context leads to the conclusion that a careful analysis of SH signals recorded during a thermal annealing experiment should be made to extract the correct activation energies of the different ions involved in the poling process.
This work was financially supported by the Region “Nord - Pas de Calais”. Gladys A. Quintero and Paula M. P. Gouvêa acknowledge fellowships from CNPq.
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