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Abstract
We investigate, for the first time to our knowledge, the impact of poling duration and duty cycle on second order non-linearities induced in poled silica multi-layer structures. We observe that the magnitude of the induced non-linearity, as determined through second harmonic generation, is strongly dependent on the duty cycle of the doped-undoped region in the layers with the highest non-linearity being observed with thick undoped layers. We also observe that multi-layer structures pole in a fraction of the time required for bulk samples. We utilize a charge migration model to explain these phenomena.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Silica is a widely used material in optical components as a consequence of its many desirable linear optical properties [1]. While silica’s centro-symmetric structure is usually desirable, it does mean that it lacks a second order non-linear (SON) optical susceptibility. The absence of a SON means that important non-linear processes like the electro-optic effect and second harmonic generation (SHG) are absent in silica [2]. In order to break the symmetry, methods such as optical and thermal poling have been shown to be successful in creating an ‘artificial’ SON in silica [3–7]. It is believed that thermal poling, a process where glass is heated and subjected to a large electric field, causes charge migration of positive impurity ions within the material [3]. This migration leaves behind a depletion region of negative charge, resulting in a separation that creates a built in internal electric field, ${E_{DC}}$, once the glass is cooled. The internal electric field combines with the third order susceptibility of the material to produce an effective SON:
This is the maximum value of the SON when an incident field is aligned with ${E_{DC}}$ [8]. Research has shown that the depletion region, and the resulting non-linearity, occupies a small region no larger than a few microns near the anode [3,9]. There has been a significant effort within the research community to utilize poled glass in non-linear optical applications [10–15]. Unfortunately, this effort has been somewhat limited by both the small extent of the non-linear region and the 1 pm/V magnitude of ${\chi ^{(2 )}}$ that is achievable in silica. The small magnitude and thin poling region require longer interaction lengths of the incident radiation with any embedded waveguide, which introduced additional complications with phase matching and pulse walk-off. In an effort to understand, and perhaps to improve upon, the effect of poling in glass researchers have studied the process extensively [16–23]. A myriad of experiments and theoretical models have been introduced that consider various poling conditions and materials constituents. To date it has not been possible to significantly improve on the magnitude of the non-linearity.
Research in poled silica fiber and waveguides has shown that second order non-linearities tend to form at the interface between the doped core and undoped cladding region [24–27]. These results suggested that migrating charges build up at the interface between media of different composition, causing a local increase in the electric field and a resulting increase in the SON. Another possible explanation for the induced nonlinearity is that defects at the interface between the doped and undoped region could reorient in the electric field.
In two separate studies our group sought to utilize this effect to increase the depth of the non-linear region in poled silica [28,29]. In our first study, through introducing an alternating multi-layer stack of doped and undoped silica, we were able to show a modest increase in the overall non-linearity (measured by SHG created in a Maker fringe apparatus). This study also showed that with a 2-sided multi-layer structure, it was possible to produce a non-linearity on the cathode side of the sample, unlike what could be achieved with bulk silica. We followed this up by dramatically increasing the number of layers to 40 × 75 nm, which resulted in a 204-fold increase in SHG. It is unlikely that there was a significant increase in the SON of each individual layer, so these results suggested an increase in the extent of the non-linear region in the silica. A larger non-linear region would allow for enhanced overlap between the non-linearity and the core mode of an embedded waveguide, making non-linear processes more efficient. We followed up these studies with the demonstration of an intrinsic non-linearity that is present in unpoled multi-layer stacks, possibly on account of symmetry breaking at the interface between doped and undoped layers [30].
In this study we explore the timescales associated with the induced nonlinearity in both poled bulk and multi-layer structures. In addition to this we investigate the impact of duty cycle on the on the induced non-linearity. We observe that the poling timescales for multi-layer structures is much smaller than with bulk silica and demonstrate a strong dependence of the induced non-linearity on multi-layer duty cycle. In addition to the data we present a theoretical model that helps explain the smaller poling duration in multi-layer stacks and the impact of varying the layer duty cycle.
2. Experiment
Thin film structures of alternating doped and undoped layers were deposited by PECVD at 350°C and a deposition rate of ∼100 nm/minute on double side polished 500 µm JGS2 wafers (University Wafer: 150 ppm OH- and 20-40 ppm impurity content). The doped layers were phosphorous doped with a concentration of 2 wt%. No post deposition anneal was performed on the samples. The different multi-layer stacks developed are shown in Fig. 1. The two configurations were a 1 µm(un-doped)/200 nm(doped) structure shown in Fig. 1(a) and (a) 200 nm(un-doped)/1µm(doped) structure shown in Fig. 1(b). The samples we considered in this study contained 8 layers (4 un-doped and 4 doped).
Fig. 1. Multi-layer structures: a) multi-layer structures consisting of alternating 200 nm thick P-doped and 1 µm thick undoped silica layers. b) multi-layer structures consisting of alternating 1 µm thick P-doped and 200 nm1 thick undoped silica layers.
These samples were thermally poled at a temperature of 350°C by placing an electric field of 6 MV/m across the sample. The poling duration was varied from 1 minute to as much as 60 minutes (in the case of bulk silica samples). In order to study the transient nature of the poling process these samples were removed immediately from the heat source after poling rather than leave the voltage on while the sample slowly cools with the heating element. It is not clear what impact the rapid removal would have on the poling, however, all samples were subjected to the same procedure.
Following the poling the induced SON in the material is measured through SHG using a Maker fringe experiment, which is illustrated in in Fig. 2. The pulsed laser source used for SHG has a temporal pulse length of 8 ps, operating at 1064 nm (Passat Compiler). The laser had a repetition rate of 500 Hz, with a beam radius of ∼1 mm and a maximum pulse energy of 2 mJ. The laser pulses were passed through a 150 mm focal length lens L3 through the sample, which is placed at the focus on an automated rotation stage. The beam intensity was controlled with the use of a half-wave plate and a Glan-Thompson polarizer. A filter F1 was placed at the exit of the laser to filter any possible SHG generated in the source. A beam expander L1 and L2 is used to increase the spot size of the laser. A lens L4 is used to collimate the SHG at the exit of the sample and additional filters F2 and F3 as well as a prism were used to eliminate the 1064 nm pump laser beam. The SHG generated in the sample was detected with a Hamamatsu H7827-001 19 mm diameter voltage-type photomultiplier tube sensitive in the 300–650 nm range (blind at 1064 nm), connected to an oscilloscope.
Fig. 2. Maker fringe measurement apparatus consisting of Q-switched Nd:YAG laser at 1.064 µm, down collimating lenses L1: FL 5 cm and L2: FL 2.5 cm, focusing lens L3: FL 15 cm, L4: FL 10 cm lens, F1: Long-pass filter (blocks λ<800 nm), F2: short-pass filter (blocks λ>800 nm), F3: band-pass filter centered on 532 nm, M1 and M2: dielectric mirrors.
3. Numerical model
The charge distribution in the multi-layer stack was simulated by numerically solving Poisson’s equation and the continuity equation [30]. The goal with this model is to establish that a charge migration model can explain our observations regarding layer duty cycle and poling duration. In these simulations we assume a single charge carrier.
Here p is the charge density (ions/m3), ${p_{init}}$ is the initial charge density, $\mu $ is the charge mobility, e is the charge of the electron, $\varepsilon = 3.78{\varepsilon _o}$ is the dielectric permittivity of silica.
The boundary conditions employed in our simulation are like those in [30,31]. In our experiments a voltage is applied at the anode and the cathode side of the sample is grounded. This introduces the requirement that the integral of the electric field across the sample must be equivalent to ${V_{app.\; \; }}$ This means that:
In agreement with [30] the charge distribution at the anode at t = 0 is set to zero.
The value of the mobility varies, depending on the positive charge carrier. It is unclear what charge carriers are prevalent in our JGS2 substrates although they are typically metals, according to the manufacturer. Hydrogen is an impurity that is often a byproduct of the reaction in PECVD deposited thin films. For example, in previous studies in Infrasil the charge carrier was assumed to be Na+ with a mobility of is ${\mu _{N{a^ + }}} = 1.5 \times {10^{ - 15}}{m^2}{V^{ - 1}}{s^{ - 1}}$ which is roughly 3 orders of magnitude higher than Hydrogen’s mobility [30].
Once the charge distribution in the sample is calculated, and the resulting internal electric field, the induced non-linearity in the sample is calculated using Eq. (1), with,
The simulated charge distribution for a 500-micron bulk silica sample subjected to an electric field of 6 MV/m for 60 minutes is shown in Fig. 3 (a). The resulting electric field and nonlinearity is shown in Fig. 4(b) and (c), respectively. The mobile charges in this simulation were assumed to positive ions with an initial concentration of ${p_{init}} = 9.5 \times {10^{22}}ions/{m^3}$, consistent with previous studies [30]. The sample thickness is set at 500 $\mu m$, the same as our substrates. The images in Fig. 3 only show the 10 $\mu m$ near the anode side of the sample.
Fig. 3. (a) Modeled charge density distribution in bulk silica after applying a 6 MV/m electric field for 60 minutes. (b) The resulting electric field distribution near the anodic surface of the sample. (c) The induced second order nonlinearity in the sample. The peak non-linearity is approximately 0.7 pm/V, which is consistent with experimental observations.
Fig. 4. (a) Maker fringe profile for bulk silica sample in Fig. 3. The lack of fringes is an indicator that the non-linearity occupies a small region near the anode. (b) For comparison this is the expected Maker fringe profile for if the non-linearity extended throughout the entire sample.
Over time a depletion region develops near the anode, resulting in an internal electric field that persists after the applied field is removed. We see this internal electric field in Fig. 3 (b). This electric field opposes the applied field until, at equilibrium, the voltage is zero throughout the sample. Once the sample has reached equilibrium the charges will no longer migrate. With a mobility of $\mu = 2 \times {10^{ - 15}}{m^2}{V^{ - 1}}{s^{ - 1}}$, the charge migration in this simulation was arrested after 15 minutes [30]. A solution of Poisson’s equation readily yields the extent of the depletion region [31]. Following Von Hippel, the induced electric field should extend a distance of:
We see in Fig. 3, our model is consistent with the theory presented by Von Hippel [32].
Once the induced non-linearity is determined, the SHG from the Maker fringe apparatus can be determined by numerically solving [2]:
Here ${A_1}$ and ${A_2}$ is the amplitude of the fundamental and second harmonic radiation respectively, $\omega $ is the frequency of the fundamental, and ${n_{2\omega }} = 1.4613$ is the index of refraction of the second harmonic radiation. The phase matching term:
Here $\theta $ is the angle that the k-vector of the fundamental radiation makes with the normal to the sample. The Maker fringe profile for the non-linearity shown in Fig. 3 (c) is shown in Fig. 4. (a). For comparison the maker fringe pattern for a material with a nonlinearity that extends over the entire 500 $\mu m$ sample is shown in Fig. 4 (b).
With thick non-linearities we see the presence of fringes as the path length increases by multiples of the coherence length as the sample is rotated. The poled sample does not exhibit these fringes as the total thickness of the non-linear region is less than the coherence length, which is:
With multi-layer structures, unlike the case of bulk silica, the ion mobility varies along the sample length. In the doped regions of the structures, the mobility was assumed to be zero relative to the mobility in the undoped regions. The varying mobility, with a peak magnitude of $\mu = 1.5 \times {10^{ - 17}}{m^2}{V^{ - 1}}{s^{ - 1}}$, was simulated with a rounded square profile as shown in Fig. 5 for the 1000nm-200 nm undoped-doped structure. The charge density is again set to ${p_{init}} = 9.5 \times {10^{22}}ions/{m^3}$.
Fig. 5. Mobility of charges in an 8-layer structure. In our simulation undoped regions have a higher mobility than the doped regions, which was set to zero.
The charge distribution for 4-layers of an 8-layer structure (sample A) subjected to a field of 6 MV/m for 30 seconds is shown in Fig. 6(a). We see that the charges build up where the mobility drops to zero. This process happens at each layer, resulting several internal electric fields. This process is very similar to what would be expected for capacitors in series as there will be a combined voltage drop across all the layers that counters the applied field. Within each layer, charges will migrate until the voltage drop across the layer of high mobility is zero at equilibrium. Once equilibrium is reached at each layer, charge migration is arrested. In the case where the charge density is not high enough to cancel the applied field, equilibrium will still be reached as charges are trapped in each layer. The magnitude of the non-linearity that results from this sample is shown in Fig. 6(b).
Fig. 6. (a) Charge density profile in the multi-layer structure sample A. The charge is free to move in the high mobility region but builds up where the mobility drops to zero. The voltage across the mobile region eventually flattens as the system reaches equilibrium. (b) The non-linearity that forms from the resulting induced electric field.
In the simulations below we have assumed a positive charge carrier with a charge density of to ${p_ + } = 9.5 \times {10^{22}}ions/{m^3}$. The mobility is varied to match the timescales observed in the lab.
4. Experimental results and discussion
4.1 Variation of duty-cycle
We begin by investigating the induced SON in multi-layer samples where the duty cycle of the doped regions has been varied. In Fig. 7 we see the Maker Fringes from an 8-layer 1 µm(un-doped)/200 nm(doped) (Sample A from Fig. 1) multilayer structure after 5 minutes of poling. For comparison, we see the Fringes from an 8-layer 200 nm(un-doped)/1µm(doped) (Sample B from Fig. 1). The observed second harmonic radiation, which is proportional to the square of the induced non-linearity, is a factor of 5 higher in Sample A than in B.
Fig. 7. – Comparison of SHG from sample A and B from Fig. 1. The second harmonic generated from sample A is approximately 5 times higher than in sample B.
To help us understand the origin of this discrepancy, and to verify if this phenomenon can be explained by charge migration, we look at predicted non-linearity from the theoretical model. In this case we set the charge density to ${p_{init}} = 9.5 \times {10^{22}}ions/{m^3}$ and varied the mobility to achieve saturation within 5 minutes. A mobility of $\mu = 1 \times {10^{ - 17}}{m^2}{V^{ - 1}}{s^{ - 1}}$ was required for sample A to begin to saturate. The model suggests that sample B should reach equilibrium at earlier times although this was not tested in our experiment. In Fig. 8 (a) we see the modeled charge distribution and voltage (in the presence of the applied external electric field), as well as the mobility profile, as it approaches equilibrium for four layers of sample A. We see that, according to the model, the charge density is not high enough to completely counter the applied electric field, otherwise the voltage would be constant across the high mobility region. The migration of charges is arrested as they cannot break through the low mobility barrier. If we use a high enough charge density in the model, it is possible to achieve equilibrium by completely countering the applied electric field. The resulting non-linearity for sample A is shown in Fig. 8 (b). For comparison, Fig. 8 (c) shows the charge distribution and voltage for a 4-layers in sample B. Charges in sample B migrate to oppose the voltage drop across the 200 nm undoped layer. In Fig. 8 (d) we see that the induced non-linearity is lower in sample B. From Fig. 8 (b) and (d) the calculated non-linearity that forms in sample A is approximately 3.2 times greater than in sample B.
Fig. 8. a) Modeled charge density, voltage and mobility in sample A after 5 minutes. b) The SON generated in sample A compared to the mobility. c) and d) are the same in sample B. It is clear that the non-linearity generated in sample A is larger.
The predicted Maker fringe profile for these calculated non-linearities is shown in Fig. 9. The sign of the non-linearity which are opposite in sample A and B, does not impact the modeled SHG. In Fig. 9 the magnitude is normalized to the SON generated in A. The model suggests that, under the conditions, the SHG from sample A should be as much as 30 times higher than that of sample B. The charge migration mechanism does explain a discrepancy in observed SHG, although it is likely that there is some charge migration between layers. Charge breakthrough likely occurs in the thin doped regions in sample A, although we do not know the extend, and could explain the lower observed discrepancy in the SHG between the samples.
Fig. 9. Comparison of the modeled SHG sample A and sample B. The calculated SHG from sample A is approximately 30 times higher than sample B.
4.2 Bulk vs. multi-layer structures
SHG from a Maker Fringe experiment using a bulk sample with varying poling times, using the poling conditions outlined in section 2, is shown in Fig. 10. We see that the induced non-linearity in the sample continues to grow over the course of 60 minutes until it saturates. The absence of fringes in the pattern indicates that the induced non-linearity occupies a narrow region of the sample.
Fig. 10. (a) the Maker fringe pattern for poled bulk silica. The observed non-linearity saturates over the course of 1 hr. (b) The Maker fringe pattern from an 8-layer multi-layer structure (Sample A in Fig. 1). We see that the observed non-linearity is equivalent to the bulk value with 5 minutes.
For comparison, Maker Fringes from an 8-layer P-doped multi-layer structure is shown in Fig. 10(b). We see that, under the same conditions the multi-layer structure poles at a much faster rate than the bulk sample. Again, the total extent of the non-linear region cannot be larger than the coherence length as there are no fringes present.
To understand why the poling rate is much higher in multi-layer structures than in bulk samples we turn to our theoretical model to look at how long is required for the charge migration in the sample to reach equilibrium.
In Fig. 11 we compare the simulated SHG generated in the bulk and multi-layer samples. The charge density is again set at ${p_{init}} = 9.5 \times {10^{22}}ions/{m^3}$, as with the duty cycle comparison. In our bulk simulation the charge migration was arrested in an hour with a charge mobility of ${\mu _{bulk}} = 5 \times {10^{ - 16}}{m^2}{V^{ - 1}}{s^{ - 1}}$, a factor of 4 less than in the study above [30]. As the precise composition of the JGS2 substrate is unknown, and the mobility depends on temperature, a discrepancy between our results and the previous study in Infrasil is reasonable. In the multi-layer simulation, the charge migration was again arrested after 5 minutes for a mobility of ${\mu _{m - layer}} = 1 \times {10^{ - 17}}{m^2}{V^{ - 1}}{s^{ - 1}}$. The multi-layer structure poles faster even though the mobility used for the bulk sample is much higher. As can be seen in Fig. 11 the simulated SHG magnitude was much lower in the multi-layer structure, however, the charge density of carriers in the multi-layer structure is unknown and was arbitrarily set to be the same as the bulk. Increasing the charge density will increase the simulated SHG. This model suggests, even with a much smaller mobility, that the rapid increase in non-linearity in the multi-layer samples can be attributed to the simultaneous poling of each layer, requiring the charges to travel the much shorter distance of 1 $\mu m,$ compared to 3.6 $\mu m$ in the bulk sample, before reaching equilibrium. Increasing the charge density in the multi-layer structure would only serve to cause the SHG to saturate at a faster rate.
Fig. 11. Simulated Maker fringe profile for bulk sample (a) and multi-layer sample (b). We see that, even with a smaller charge mobility, the multi-layer structure reaches saturation faster than the bulk sample.
As it is likely that the mobile charges in the bulk sample and the PECVD layers are different, it is possible that the reduction in poling time could simply be a consequence of a higher charge mobility in the multi-layer structure. While it is true that the multi-layer structure could contain more mobile charges, the model suggests that the multi-layer structure would only serve to further increase the poling rate. It is interesting to note that the ratio of mobilities in our model is roughly the same as Na+ and hydrogen [30], suggesting that slower moving hydrogen could be the charge carrier in the multi-layer structures.
5. Conclusion
In this study we investigated the poling characteristics of multi-layer doped silica structures. We observed that the duty cycle of the doping in the sample played a significant role in the overall non-linearity that could be achieved through thermal poling. Multi-layer structures with thick undoped regions (sample A) formed larger non-linearities than structures with thin undoped regions (sample B). Using a theoretical model, we were able to show that this behavior was consistent with charge migration. The model suggested that the larger electric field, and resulting non-linearity, in sample A was a consequence of the increased overall charge in its thicker undoped region. The modeled discrepancy in non-linearity was larger than was observed experimentally, although it is likely that there is some migration of charges through the doped layers, which would reduce the induced electric field.
We also investigated the relative poling duration of bulk silica compared to a multi-layer structure. We found that the multi-layer structures poled much more rapidly than the bulk sample. Our theoretical model suggested that this could be explained by each 1 $\mu m$ layer poling simultaneously, while the charge is required to travel 3.6 $\mu m$ in the bulk sample. This was true even when the mobility used in the simulation for the multi-layer structure was 50 times smaller than the bulk sample. It is unknown what charges are mobile in our structures, but it is interesting to note that this discrepancy in mobility is comparable to the difference in mobility of Na+ and hydrogen.
Funding
Natural Sciences and Engineering Research Council of Canada (STPGP 463044).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this manuscript is described in figures but the underlying data may be obtained from the authors upon reasonable request.
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