Buried waveguides with nearly symmetrical refractive index profile and high homogeneity were obtained by applying the reverse-proton-exchange technique to MgO doped stoichiometric lithium tantalate, a promising nonlinear material due to its low coercive field and high damage threshold. By characterizing several samples fabricated under different experimental conditions, we identified a fabrication procedure in which the annealing and the reverse-exchange processes are performed at the same temperature, and the diffusion of hydrogen ions towards the substrate is negligible during the burial step. These fabrication conditions are simpler than the conventional ones used for lithium niobate. Accurate empirical laws were found, relating the fabrication conditions to the optical parameters.
©2004 Optical Society of America
Waveguides fabricated by reverse-proton-exchange [1–3] (RPE) present a great potential for the realization of all-optical devices for WDM networks based on second order nonlinear interactions [4–5]. In this context a very promising result was recently achieved in periodically-poled lithium niobate (PPLN) RPE waveguides , with a 150%W-1cm-2 efficiency in a second harmonic generation process from a fundamental wavelength within the C-band. Such a result is made possible by the fact that RPE provide homogenous buried waveguides having nearly-symmetrical refractive index and field profiles. This results in a high overlap of the fields interacting through the nonlinear susceptibility. Further advantages of RPE waveguides are the low losses and the very high butt-coupling efficiency with optical fibres. However, the main drawback of PPLN RPE waveguides is the low optical damage threshold of the material, which requires very high operating temperatures in order to avoid photorefractive effects. To overcome this limitation, attention has been devoted to magnesium doped crystals, both in the congruent and in the stoichiometric compositions [7,8]. Among these crystals, a very promizing one is the magnesium-doped stoichiometric lithium tantalate (SLT), characterized by a high χ 33 nonlinear coefficient, a very high optical damage threshold and a low coercive field for ferroelectric domain inversion .
This paper reports on the fabrication and modelling of RPE waveguides in the recently developed 0.5% MgO doped SLT . We made several planar waveguides with different fabrication parameters and characterized them through conventional m-lines spectroscopy. Highly homogeneous waveguides were obtained by performing the reverse-exchange and annealing processes at the same temperature (350°C), thus following a rather simple fabrication procedure. Moreover, under these fabrication conditions the annealing process has a highly nonlinear behaviour, which can be exploited to obtain a fine control on the waveguide optical parameters. Indeed, the refractive index profile of the waveguide changes very rapidly in the first few hours of annealing; in the following hours the diffusion of H+ ions towards the substrate and thus the modification of the index profile is negligible. Thanks to such behaviour, if the reverse-exchange is started when the annealing effect is stabilized, during the burial step the refractive index profile is excavated at the surface, but it remains almost constant on the substrate side.
2. Fabrication and characterization procedures
The waveguides were made in 0.5% MgO doped SLT , which has a high optical damage threshold (>1MW/cm2) and a very low coercive field for ferroelectric domain inversion (~1.7kV/mm). The proton-exchange (PE) was realised in pure benzoic acid at 280°C by means of the sealed ampoule technique . The following steps, annealing and reverse-exchange, were both performed at T=350°C, the annealing in air, the reverse-exchange in an euthectic melt composed by LiNO3, KNO3 and NaNO3, again employing the sealed ampoule technique. The use of the same temperature for the two latter processes gave very good results in terms of waveguide quality and provided a simplification of the modelling due to the fact that the diffusion of H+ ions towards the substrate during the reverse-exchange occurs in the same conditions as during the annealing.
The waveguides were made with different PE durations, as reported in Table I, but with the same annealing and reverse-exchange steps. After a first annealing step of 3h, some samples (specifically #2,#3,#4) were divided into two parts. One of them was merely annealed at 350°C, while the other one was reverse-exchanged at the same temperature and the same time duration. Three subsequent reverse-exchange/annealing steps were performed, respectively equal to 4h, 7h and 16h. The deep part of the refractive index profile, which is mostly due to the annealing process, was retrieved from the characterization of the annealed parts of the samples, whereas the index profile at the surface, which results from the reverse-exchange process, was determined from the characterization of the reverse-exchanged counterparts.
As a characterization technique, we used m-lines spectroscopy at λ=0.633µm for determining the effective indices neff of the guided modes , and the inverse-WKB method for the reconstruction of the index profiles . The substrate refractive indices were assumed equal to those reported for the same material in Ref. .
3. Experimental results and discussion
In this paragraph we report the results we obtained by applying the sequence of proton-exchange (PE), annealing and reverse-exchange processes to 0.5% MgO doped SLT.
The proton-exchange gives rise to a step-like refractive index profile with an index-change Δnp (p standing for proton-exchanged) slightly higher than that achievable under the same fabrication conditions in the congruent lithium tantalate. It ranges from 0.0190 to 0.0200 depending mainly on the aging of the exchanged layer, which takes a few days to stabilize after PE. In Fig. 1 we report the depth dp of the profiles as a function of the proton-exchange duration tp. The experimental values follow the typical Arrhenius law
with a diffusion coefficient Dp=0.41µm2/h at T=280°C, which is about 1.2 times lower than that reported for the congruent crystal .
The annealing process, as it is well known, forces the hydrogen ions provided by PE to diffuse towards the substrate. Such diffusion determines the change of the index profile shape, which increases but remains flat at the surface, and decays exponentially towards the substrate. The overall profile can thus be described by three parameters, namely the index change of the flat part Δna, its depth dstep, and the 1/e depth of the exponential part dexp. It is worth noting that in all samples, when comparing the index profile before and after the annealing, the area subtended by the profile increases abruptly during the first annealing step while it remains constant during the subsequent steps. Indeed, the area of the annealed profiles is equal Δna·da, with da=dstep+dexp, giving 3.05 (±5%) times the area of the starting step-profile of PE. In Fig. 2 we report as an example the index profiles that were obtained from sample #2. After the first 3h of annealing Δna was ~1.5 Δnp and da was ~2de, which gives a threefold increase in the area. In the following 27h of annealing the area does not change appreciably, and only a slight increase in da and a monotonic reduction of the ratio dstep/dexp occur. The first effect is illustrated in Fig. 3, which reports for each sample the experimental depth values da as a function of the annealing times ta, together with the corresponding fitting curves. All the curves satisfy the following empirical law:
with Da=2.059µm/h and δ=10.345µm. The standard deviation is 0.13µm, corresponding to a 2% average spread of the experimental results. In Eq. (2) the saturation effect of the depth with the annealing time is parameterised by the exponent dp/δ, which ranges from 0.16 to 0.28 depending on the sample. To complete the study of the annealing process we determined an empirical law fitting the monotonic reduction of the ratio dstep/dexp as a function of ta. Such reduction is lower for deeper PE layers, according to the formula:
with α=-0.823µm/h and β=3.279µm, valid for ta>3h. Eq. (3) gives a normalized standard deviation of the order of 20%, which is a rather high value. However, good predictions of the optical properties of a waveguide can still be achieved by employing Eq. (3) since the effective indices of the modes do not depend critically on the ratio dstep/dexp, but mainly on the profile area and on the total depth da. Thus, by combining Eq. (3) with Eq. (2), and by taking into account the constant area, one obtains a powerful tool for designing the modal structure of an annealed SLT waveguide.
The analysis of the annealing process clearly shows that after a first, very rapid phase where the annealing strongly modifies the structural and thus the optical properties of the guiding layer, a second phase occurs, with very smooth changes even if the annealing is performed for many hours. Such a high nonlinear behaviour is very well suited for the realization of buried waveguides through reverse-proton-exchange. Indeed, by starting the reverse-exchange after the first annealing step, one obtains at the same time a fast diffusion of Li+ ions at the surface and a slow diffusion of H+ ions towards the substrate. Under these conditions a very fine control on the optical properties of the buried waveguide can be easily achieved, since the deepest part of the index profile is determined essentially by the annealing step, and the surface part by the subsequent reverse-exchange step. Actually, in our case, starting with PE waveguides having depth from 1.69µm to 2.87µm, 3h of annealing were sufficient as a first annealing step. Thus, after such step, three of the samples reported in Table I were divided into two parts, one part being only annealed and the other one also reverse-exchanged in the subsequent treatments at T=350°C.
Figure 4 reports the overall refractive index profiles of the three reverse-exchanged samples, after 4 (a), 11 (b) and 27h (c) of reverse-exchange tr (note that tr=ta-3h). The profiles, as represented in Fig.5, result from the combination of the step-exponential profile due to the annealing, with a second profile due to the reverse-exchange. The mathematical expression that describes this latter profile was found to be a Gaussian function with complete recovery of the substrate index at the surface:
where x is the depth spatial coordinate, nes is the extraordinary substrate index , Δnm is the maximum index change that we determined on annealed samples, equal to 0.03, and dr is the 1/e depth of the Gaussian curve, as calculated for each sample by least square fitting the measured neff. It is worth pointing out that Eq. (4) best predicts the modal structure of the samples reverse-exchanged for longer times (11h and 27h). Indeed, these waveguides are the most useful for the applications since they have a burial depth higher than the PE depth, and thus unspoiled nonlinear coefficients and low scattering losses.
In order to study the speed of the reverse-exchange process we refer to Fig. 6, which reports the burial depths dr as a function of the exchange times tr for the different samples. After 4h and 11h the dr values are the same for all the samples, at least within the experimental errors, and the dependence of dr on tr follows with a reasonable approximation a law (more precisely, with Dr=0.257µm2/h). However, for tr=27h the dr values are different from one another and far from the law. Indeed, in all the samples the reverse-exchange was performed when the crystallographic phase was already completely stabilized after the first annealing step (as discussed with reference to Fig. 3). In such conditions no difference arises from sample to sample as long as the flat parts of the annealed index profiles are excavated, and a diffusion-like behaviour is found. However, once the reverse-exchange process reaches the exponential part of the profile, an acceleration of the process occurs, which is the higher the lower is the depth of the waveguide, i.e. the fewer are the protons to be substituted. This is the reason why the burial depths of the samples for tr=27h are inversely ordered with respect to their PE depths. Actually, the most interesting waveguides are those obtained with reverse-exchange times around 11h, which can be easily modelled with the law. In fact, they exhibit at the same time high optical quality, as a result of a burial depth being higher than the PE depth, and tight field confinement, which is essential for maximizing the overlap integral between the interacting modes in nonlinear processes.
We verified the waveguide uniformity, which is essential to get high interaction lengths in the nonlinear processes, by simply measuring the neff at λ=0.633µm in different points of the waveguide: we found them to be homogenous within 0.0002 over a 2cm length, thus quite promising for high conversion efficiency in nonlinear processes. Moreover, we defined fabrication parameters giving rise to a single-mode waveguide at λ=1.55µm with good fiber mode-matching and at the same time. The sample that best satisfies this requirement is #4: indeed, we verified that after 11h of reverse-exchange the waveguide is single-mode at the telecom wavelengths. The near field profile of the mode, as determined on a 8µm wide channel waveguide fabricated with the same parameters as #4, is reported in Fig. 7(a). It presents an ellipticity factor of ~1.25, a high symmetry in the x direction by virtue of the buried refractive index profile, and a very good matching in the y direction with the field profile of a telecom fibre, reported as a sake of comparison in Fig. 7(b). The calculated butt-coupling efficiency, by neglecting Fresnel losses, is 94%. This value was used for estimating the waveguide losses: we coupled the ASE of an optical amplifier into the waveguide and compared the waveguide output power with the input power. Due to the temporal incoherence of the ASE, no Fabry-Perot effect arises in the waveguide, and the relationship between the input and output power depends only on the Fresnel reflectivities (that are known), on the overlap integral between fiber and waveguide field profiles (equal to 0.94 in the best coupling conditions) and on the waveguide attenuation, which is the parameter to be determined. In this way we obtained an attenuation ≤0.57 dB/cm, which is comparable to the best values reported in the literature for the conventional annealed proton-exchanged waveguides in lithium niobate . These results attest the potentials of RPE SLT waveguides for the realization of highly efficient nonlinear devices with low insertion and propagation losses.
Since the actual realization of devices is based on a single reverse-exchange step, we reproduced waveguide #4 (fabricated with two reverse-exchange steps, 4h and 7h) in a single reverse-exchange step lasting 11h (sample #5), and compared the optical parameters of the two waveguides. In this way we could verify the reliability of the model when performing the reverse-exchange process without any interruption. The neff at λ=0.633µm of the two samples are reported in Table 2. In sample #5 we observed an average reduction of the neff of about 0.0003, which however does not give rise to appreciable changes either in the mode field-profiles or in the phase-matching conditions if the waveguide is exploited for nonlinear quasi-phase-matched interactions. These facts prove the reliability of the above empirical laws for assessing the best design parameters for the fabrication of buried nonlinear devices.
The reverse-exchange process (RPE) has been successfully applied for the first time to the fabrication of optical-grade waveguides in stoichiometric lithium tantalate (SLT) with a 0.5% MgO doping. A detailed investigation has been performed of the optical properties of the waveguides after proton-exchange, annealing and reverse-exchange. For each of these processes we have determined the resulting refractive index-profile and simple empirical laws relating the optical parameters of the profile to the fabrication conditions. Altogether, these laws provide a powerful modelling tool for the design of SLT RPE waveguides with optimal properties. We have also verified that highly homogenous waveguides with a near symmetrical mode field profile can be fabricated. On the basis of these features and of the very high optical damage threshold and low coercive field of SLT, we believe SLT RPE waveguides to be a most promising dielectric structure for the realization of telecom all-optical devices exploiting nonlinear processes in the quasi-phase-matched regime and operating at room temperature.
This study was financially supported by the FIRB project “Miniaturized Systems for Electronics and Photonics”.
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