1. Introduction

Periodically poled KTiOPO₄ (PPKTP) is an excellent nonlinear optical (NLO) material and has become a material of choice for spontaneous-parametric down-conversion (SPDC) processes [1], especially for those pumped with short wavelengths, thanks to its resistance to photochromatic damage and absence of photorefraction [2]. Due to the highly anisotropic properties of the KTiOPO₄ (KTP) crystal family, it is especially favorable for implementing fine-pitch domain gratings for quasi-phase matching (QPM) down to the sub-micrometer regime. These ultra short-period devices allow counterpropagating nonlinear wave interactions which have unique spectral properties [3]. Indeed, spontaneous parametric down conversion with counterpropagating photons can be used to generate spectrally tailored, heralded single photons, which are extremely important for quantum networking [4,5] and quantum information processing [6,7]. Integration of these sub-µm period QPM devices in a waveguide format would allow high conversion efficiency with low pumping power. However, this requires a means to independently engineer the waveguides and domain structure, so that one process does not interfere with the other.

The process of poling KTP for QPM is complex due to the ionic conductivity, which can result in domain broadening and even lead to dielectric breakdown. This is substantially improved when the crystal is grown with a small amount of Rb to create a bulk doped material of the form Rb_0.003K_0.997TiOPO₄ (RKTP), as this lowers the conductivity by two orders of magnitude compared to KTP. Thus, RKTP has since become the preferred material for short-period bulk poling. However, there are still challenges to overcome when pushing the limits into sub-µm poling periods. At these dimensions, conventional poling techniques with metal electrodes, with the accompanying fringing fields, lead to unwanted sideways growth of domains. This results in broadening and merging of domains, with poor or non-existent pattern fidelity. Therefore, it is of paramount importance to develop methods to accurately control the domain growth. So far, the only reliable method for achieving this is using periodic Rb-exchange at the polar surface to create a coercive field (E_c) grating for electric-field poling, so called coercive field engineering. The ion-exchange creates a diffusion gradient up to 100 µm into the crystal [8], where 0.02-65% of K⁺ ions may be replaced with Rb⁺ at the polar surface [9], depending on the exchange recipe. The E_c field is higher in the exchanged regions and inhibits domain nucleation, while the depth of the exchange limits sideways domain growth. The mechanism behind the increased coercive field in Rb-exchanged KTP has been attributed to a reduced ionic conductivity, and the distortion of the lattice by the larger Rb-ion [10]. Liljestrand et al. [11] reported an increase in the coercive field by 30% (1.7 kV/mm) for an exchange containing 73 mol% RbNO₃ + 20 mol% KNO₃ + 7 mol% Ba(NO₃)₂, while also reducing the ionic conductivity by 50%. Exchanges using combinations of Rb-, K-, and Ba-nitrates have since been used to pole bulk periods down to 317 nm [12]. It is well-known that the addition of Rb ⁺-ions in the KTP lattice increases the refractive index of the crystal. This has been used to make waveguides [13] and periodically poled waveguides [10,14] at the polar surfaces. However, the use of Rb⁺ ion-exchange leads to simultaneous coercive field and refractive index changes, which limits the possibilities of creating advanced waveguiding structures, as the two purposes demand different exchange characteristics. The coercive field grating, which is periodic along the optical axis, thus creates a periodic refractive index change that introduces losses for waveguiding structures along the optical axis. Another downside of the Rb-exchange coercive field engineering is that it introduces a gradient shift of the phase matched wavelength along the polar axis of the crystal [11]. This gradient may be detrimental for bulk applications requiring a narrow linewidth output throughout the whole aperture. Furthermore, the introduced stress in the Rb-exchanged areas makes further processing challenging as the crystals become prone to chipping or breaking. Therefore, it is highly desirable to investigate new coercive field engineering methods that make it possible to control the coercive field without modifying the refractive index. This would allow engineering of the domain pattern and the waveguide structure independently.

In KTP, ion exchange in a molten salt happens through diffusion and can be expressed as:

The aim of this paper is to investigate the switching characteristics resulting from ion-exchange in a melt containing 7 mol% Ba(NO₃)₂ and 93 mol% KNO₃, from now on referred to as the Ba/K melt. Furthermore, we aim to determine its usefulness for making periodically poled waveguides and bulk PPRKTP. We show that this mixture leads to an increase in switching time of more than an order of magnitude, without substantial changes in the bulk ionic conductivity. We demonstrate that the poled domain structures are stable at high temperatures, which may be beneficial for subsequent fabrication of channel waveguides. In addition, this method does not introduce a refractive index change, and thus should avoid optical losses attributed to interference with waveguiding structures.

2. Results and discussion

First, we studied the impact of Ba/K ion-exchange on the switching dynamics. Five virgin c-cut RKTP crystals, with dimensions 6*6*1 mm³ (along a*b*c crystallographic axes), were immersed in the Ba/K melt. The crystals were kept in this melt for different exchange durations ranging between 10 min to 4 h, while the melt temperature was kept constant at 375 °C. After the exchange, the crystals were characterized and compared with a virgin crystal. Direct measurement of the coercive field for ferroelectrics with ionic conductivity can be challenging, as it requires the switching current to be distinguishable from the ionic current. This sets a lower boundary on the E-field ramping rate. At the same time, a too high ramp rate requires high peak electrical fields which might cause dielectric breakdown. Here we have instead compared the polarization-switching time, t_s, between exchanged and non-exchanged crystals. For KTP, the switching time dependence on the external electric field magnitude, E, has been found to be $1/{t_s} \propto exp ({\alpha E} )$, for the low field regime; and $1/{t_s} \propto \beta E$ for the high field regime, where α and β are constants [18]. Thus, for a fixed value of the external field, an increase in E_c will translate in an increase in the switching time.

To measure t_s, we use the linear electro-optic (Pockels) effect. A He-Ne laser is launched along­ the crystal’s c-axis, followed by a polarization filter. The changes in internal E-fields cause the polarization of the light to change during polarization-switching [19]. This causes modulation of the transmitted signal, which is recorded by a photodetector. The switching time is taken as the time needed to complete polarization-switching as observed from the electro-optic effect. For each crystal, the electric field magnitude was kept constant at 5 kV/mm, and several 20 ms-long square electrical pulses were applied until polarization-switching was completed. The ionic conductivity of each sample was measured in the following way: after completing polarization switching, another electric pulse of the same magnitude and length was applied to the crystal, and the current was measured at 10 ms. The conductivity of each sample was divided by that of the virgin crystal to be able to compare the different samples.

Figure 1 displays the switching time and the normalized ionic conductivity, t_s, for all the exchanged samples as well as a virgin crystal. For the virgin crystal t_s is 3.5 ms. Note that already after 10 min exchange, there is an order of magnitude increase in t_s. The switching time increases by a further 50% after 30 min exchange, and by 100% after 2.5 h exchange. The 4 h exchange time does not seem to give a further significant rise in switching time. Furthermore, there is no indication that the ion-exchange gives substantial changes in the bulk ionic conductivity.

 

Fig. 1. Measured switching times (●) and conductivity, with error bars showing standard deviation, (▴) depending on Ba/K-exchange time. The dashed lines show the general trends.

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To understand the effects of the exchange we need to consider the interplay between coercive field and ionic conductivity. In RKTP, the potassium ions are the main carriers of the ionic conductivity. The conductivity is highly anisotropic, with preferred motion of the K ⁺-ions in chiral pathways along the polar axis [20]. An increased amount of potassium vacancies and defects in the crystal lattice increases the ionic conductivity and coercive field. The increased conductivity is ascribed to the vacancies and defects becoming pathways for K⁺/V_K^- mobility, while the coercive field increase is a consequence of the increased charge screening arising from the conductivity increase [16]. As mentioned above, this agrees with the previous studies by Canalias et al. [17], where they showed that by immersing flux grown KTP in a KNO₃ melt one can reduce the number of vacancies in the crystal through K ⁺-ion indiffusion, which leads to a reduction of the coercive field by 0.5 kV/mm. On the other hand, Liljestrand et al. [11] measured a large increase of conductivity and E_c, when ion-exchange was performed in a K⁺ rich melt that also contained Rb⁺ and the same concentration of Ba²⁺ as the one studied here. When they performed the exchange in a Rb-rich melt, the increase in coercive field was 35%. In the present case, however, no increase in conductivity is observed. On the other hand, the large increase in switching time should correspond to ΔE_c of more than 60% [17], giving a substantially larger E_c contrast than what is obtained with a pure K⁺ exchange or in a mixture of K⁺ and Rb ⁺. A plausible explanation for these results is that the concentration of vacancies increases at the exchange layer, creating local charge screening that prevents nucleation and thus increases the coercive field. At the same time, the local increase of vacancies may not be enough to have a significant impact on the bulk conductivity. It is assumed that a large diffusion depth will start to influence the bulk conductivity. Indeed, it has previously been observed by Roelofs et al. [9] that the addition of divalent ions in KTP causes a significant increase in conductivity only after long exchange durations (at least 15 h exchange), which are much longer than what we have investigated here. Another notable difference between our and previous methods is that with our method the Ba/K-exchange is performed on both polar faces, whereas with Rb-exchange is done on one polar face. The results obtained here together with those reported previously point to the complex interplay between exchange ions, ionic conductivity and polarization switching. It should be noted that it is difficult to measure the exact ratio of Ba/V_k/K in the exchanged regions, as these ions are light and difficult to quantify at these concentrations via broadly available techniques such as energy-dispersive x-ray spectroscopy. Therefore, we are currently performing further studies to properly quantify and clarify the effects of Ba/K-exchange on RKTP and its use in the development of the method. Those results will be published elsewhere.

After characterizing the Ba-exchange, we used it to implement E_c gratings and obtain PPRKTP samples. Several c-cut flux-grown RKTP crystals of the size 6*5*1 mm (a*b*c crystallographic axes) were lithographically patterned with a grating of 2.92 µm period on their c- faces. A diffusion stop-layer was created on the patterned surface through O₂-plasma etching, and the crystals were immersed in the Ba/K melt, where they were kept at 375 °C for 4 hours. We chose 4 h exchange time because although 2.5 h should give similar E_c difference, it has been reported that the depth of the dopants is a key f actor for maintaining the QPM structure along the polar axis when E_c-gratings are created by a Rb-rich melt [21]. The ion-indiffusion creates a coercive field grating in the crystal at the patterned c^- face and a planar exchange layer at the non-patterned c⁺ face. Periodic poling was performed using planar liquid electrodes on the polar faces. Multiple 5 ms-long triangular electric field pulses with a maximum magnitude of 6-7 kV/mm were applied over the crystal. The poling was monitored by measuring the SHG by launching a continuous-wave Ti-sapphire laser along the crystal’s a-axis, with polarization parallel to the polar axis and a beam waist radius of 30 µm. The wavelength was fixed at 779 nm, which gives first order SHG through type 0 QPM.

The SHG power obtained after each poling pulse is shown in figure 2. No SHG is obtained after the first pulse. This is true for a broad range of external field magnitudes, indicating that domain incubation might be occurring at this point. Then, SHG increases with the subsequently applied pulses and reaches a maximum after the 3^rd pulse. The number of pulses needed to reach the maximum SHG varies depending on the external field magnitude. At this point, applying further pulses leads to a decrease in SHG, as seen in the figure, indicating that the domains broaden and finally merge. Interestingly, Lindgren et al. [22] had reported that multiple triangular pulses are detrimental for conventional, metal electrode, periodic poling of RKTP. This is not the case here and, once again, it points to a fundamental change in switching dynamics when ion-exchange is used to create E_c gratings.

 

Fig. 2. SHG power measured after subsequent poling pulses on a periodically Ba-exchanged RKTP crystal.

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Furthermore, by measuring the SHG efficiency between each pulse, the number of applied pulses can be selected to maximize the poling quality and produce PPRKTP crystals with high conversion efficiency. With this method, we poled a 4 mm long PPRKTP with a 2.92 µm period and pumped it with 370 mW of 779 nm to get 1.06 mW of first order SHG. This corresponds to a normalized conversion efficiency of 2%/Wcm. From this we calculate an estimate of the effective nonlinear coefficient, d_eff = 10 pm/V, which is very close to the value calculated from the d₃₃ coefficient for RKTP [23] and our beam parameters. Moreover, the conversion efficiency was homogeneous throughout the crystal aperture of 3 × 1 mm². This was confirmed by scanning the pump beam and measuring the output over the crystal aperture, taking values every 150 µm.

Next, we studied the domain morphology of a sample with the period 2.92 µm, similar to the one mentioned above. The crystal was poled with pulses of 7 kV/mm until a high SHG efficiency was reached. It was cut in the center of the poled area along the b-plane, and piezo force microscopy (PFM) was used to image the domain structure. Figure 3 shows PFM scans of the domains, right below the patterned c- face (a), in the center of the crystal (b) and towards the planar exchanged c + face (c). The domains switch in the non-exchanged regions at the c- face, at first maintaining the duty-cycle of the photolithographic pattern, which in this case had a 40%/60% ratio of non-exchanged to ion-exchanged widths. In the first 20 µm below the patterned surface, we observed an average domain width broadening of 37 nm. From that depth, an average of 16 nm broadening is observed in the domains, which terminate in dagger-like domains above the c⁺ face. This has little to no impact on the conversion efficiency and is in agreement with previous measurements on sub-µm period Rb-exchanged PPRKTP, with a similar level of broadening in the crystal bulk [24]. Nevertheless, at 30 µm from the c⁺ surface the domains start tapering and end around 20 µm above the c⁺ surface. This suggests that it is related to the ion-exchange and that the depth of the exchange is similar on both polar faces. The tapering shape is commonly seen in domains that do not propagate throughout the bulk [25]. Note that this region has been subjected to planar ion exchange and should have a large concentration of mobile charges due to the increased concentration of vacancies. As mentioned above, these contribute to screening the electric field that propagates the forward-growing domains, slowing and stopping them. The screening charges then redistribute along the domain walls, pinning them in the bulk, and creating the “dagger” shape of the charged domain walls. Furthermore, the switching time shows a higher increase with the K/Ba exchange on c⁺ as compared to only exchanging on c^-. This is beneficial for the poling method, allowing the use of multiple pulses to reach the optimal SHG efficiency.

 

Fig. 3. PFM images of the b-face of a poled RKTP crystal at different positions along the c-axis. Image a) shows the area just below the c- polar surface, which has been periodically exchanged with Ba/K. Image b) shows the same domains at the center of the crystal. Image c) shows the same domains and the tapering behavior above the c + polar surface, which was exposed to planar Ba/K-exchange.

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One concern for PPKTP with short periods (<4 µm) is the grating stability issues caused by charged domain walls. Charged domain walls are created when the domain walls are not aligned with the polar axis and can result in backswitching or merging of domains [26]. This has been identified as a detrimental factor for implementing waveguides after periodic poling [27]. Since our domain gratings do present charged walls close to the c⁺ surface, it is important to establish the domain stability of the crystals. For this purpose, a poled crystal was annealed at 330 °C for 24 h. The conversion efficiency was measured before and after the annealing process and was found to be unchanged, thus suggesting that the domain structure is stable. A plausible explanation for the stability is that the dagger-shaped domain tips are pinned in the planar exchanged region, thanks to an increased number of mobile ions.

It has been previously reported that E_c-gratings with Rb-rich ion exchange induce a gradient shift of the phase-matching wavelength throughout the crystal thickness, even if the exchanged layer is not thicker than tens of µm [11]. To investigate if this effect is present here as well, the phase-matching temperature curve was measured at two distant points along the polar (c) axis in a 1 mm thick Ba/K-exchanged PPRKTP crystal with a poled period of 2.92 µm. The fundamental wavelength was kept fixed at 779 nm, while the temperature of the crystal was tuned and the SHG output at different set temperatures was recorded. The normalized tuning curves are shown in figure 4. Blue and red curves correspond to measurements made at two different depths of 200 and 800 µm below the patterned surface, respectively.

 

Fig. 4. Phase matching temperature curves measured with a fundamental wavelength of 779 nm close to the c- and c + surface, respectively.

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Note that there is no visible change in the phase-matching temperature between these two locations in the crystal. In comparison, for a Rb-rich ion-exchange a phase matching temperature shift of ΔT = 2.3 °C was reported for a spatial separation of 500 µm in a crystal with a period of 3.16 µm [11]. This has been attributed to a stress induced by the exchange layer that propagates throughout the crystal. In the present case, the introduced Ba-ions are smaller than the replaced K ⁺-ions and the concentration is low, therefore the macroscopic effect of the Ba/K-exchange is very small to non-existent. Although further investigation is required, the results presented here indicate an important difference between the two ion-exchange recipes that has a significant macroscopic effect. The fact that the Ba/K-exchange does not create a gradient shift in the phase matching wavelength is useful for generating a narrow linewidth signal in crystals poled with this method.

Furthermore, since the method does not induce any refractive index change and provides high stability for the QPM structures, it is highly promising for future QPM waveguide development.

3. Conclusions

We have investigated K/Ba ion-exchange in RKTP for coercive field engineering, using a recipe of 7% mol. Ba(NO₃)₂ and 93% mol. KNO₃. We have shown that this exchange produces an order of magnitude increase in polarization switching time, t_s. Using this ion-exchange method for periodic poling of a 1 mm thick RKTP crystal with a period of 2.92 µm, we demonstrated SHG at 779 nm with a conversion efficiency of 2%/Wcm. As the domain grating is shown to be stable after heat treatment at 330 °C and the refractive index of the crystal is unaffected by the exchange, this method is promising to independently control domain formation with short or ultra-short periods, and subsequent addition of waveguides. Another feature with this exchange is that it does not introduce a phase-matching wavelength gradient along the polar axis. The crystal stoichiometry, dopants and ratio of monovalent- to divalent-ions in the exchange melt all play a role in the switching dynamics and optical characteristics of the RKTP crystals. The intricate interplay between these has been touched upon in this article, however it will be explored further in coming studies.