1. Introduction

Large aperture quasi-phase-matching (QPM) devices are desirable for high energy nonlinear optical applications such as in optical-parametric oscillators (OPOs) and in quantum technologies utilizing QPM crystals as spontaneous parametric down-conversion (SPDC) sources. Examples of the latter are quantum ghost-imaging [1] and quantum imaging using undetected photons [2]. The resolution of these quantum imaging techniques can be further improved by better spatial coherence of photons [3] and stronger momentum correlation by increasing the incident pump beam waist [4]. One way to achieve that is by having a larger aperture of the SPDC source. However, imaging using a larger incident beam size for such nonlinear interaction has yet to be explored since the standard aperture sizes for such QPM periods in KTP isomorphs have only been limited to 1 mm [5].

Despite the appeal of large aperture QPM devices, their use is not widespread, partly because of the expensive raw material and the stringent demand on the crystal’s homogeneity to ensure that the inverted domains propagate uniformly throughout the crystal’s thickness during the poling process. Indeed, periodic poling of large aperture devices has been achieved so far, mainly for above 1 µm-laser pumped OPO QPM periods, which typically lie in the range of 30-40 µm for ferroelectric crystals such as lithium niobate (LiNbO₃, LN) [6,7] and KTP (KTiOPO₄) -isomorphs [8,9]. However, for many applications, especially in quantum technologies, it is desirable to have large aperture devices with an order of magnitude reduced periodicity for 405 nm pump beam. Furthermore, large aperture periodically-poled device is useful for high-energy backward-wave OPO, although in this case an even larger reduction of the poling period is needed [10].

Periodic poling of large aperture crystals requires very high voltages, which poses a challenge, especially for congruent LN, which has high coercive electric field. Although this field can be reduced by doping or changing the crystal’s stoichiometry, the resulting domains can be unstable [11]. Moreover, LN-isomorphs exhibit hexagonal and triangular domain shapes with low domain growth anisotropy [12], which limits the reduction of the lateral domain size. Hence, short QPM periods in LN are typically shallow and large-aperture periodically-poled LN crystals have longer QPM periods [13]. On the other hand, KTP isomorphs have a more moderate ${E_c}$, which facilitates the application of the required external voltage. Coupled with their anisotropic domain growth, fine-pitch periodic poling can be readily achieved in larger aperture crystals. However, the main challenge remains controlling the domain propagation and domain spread throughout the crystal thickness. Even though the forward domain growth along the polar axis is orders of magnitude larger than the sideways domain growth in KTP, domain broadening is still unavoidable due to the transversal fringing fields at the edges of the electrodes.

Recently, a novel poling technique based on creating high-and-low ${E_c}$ regions in the crystal via ion exchange (IE), so-called coercive-field engineering has proven to be promising in fabricating short-period, and even sub-µm domain grating in 1 mm thick, bulk Rb-doped KTP (RKTP) crystals [14–16]. This KTP isomorph contains only 0.3% Rb concentration in the bulk; however, this amount is sufficient to lower its ionic conductivity and improve its resistance to photochromatic damage [17]. IE increases the ${E_c}$ of the exchanged region and decreases its ionic conductivity, whereas the non-IE region has a lower ${E_c}$ compared to IE region. Hence, by selectively ion-exchanging regions of IE on RKTP surface, grating of high-and-low ${E_c}$ can be fabricated, bypassing the need of metal electrodes during electric field poling. During the IE process, the RKTP crystals are immersed in a Rb-rich molten nitrate melt at an elevated temperature. The $R{b^ + }$ from the melt is exchanged with the ${K^ + }$ from the RKTP through a diffusion mechanism starting on the crystal’s z-faces, along the conduction channels. When a ${K^ + }$ ion near the polar surface diffuses out from the crystal, it leaves behind a negatively charged K-vacancy, $V_K^ - $. As a result, a $R{b^ + }$ ion from the melt diffuses into the crystal to counter this charge imbalance. By adding a divalent ion such as $B{a^{2 + }}$, extra vacancies are created, which facilitate the in-diffusion of $R{b^ + }$, thus creating a faster ion-exchange rate and a deeper ion-exchange volume. ${K^ + }$ can be introduced into the melt to slow down the IE process and thus ease the stress created in the crystal lattice when the larger $R{b^ + }$ occupy the K-sites. The exchange process between the dopant cation with charge n in liquid phase, $M_l^{n + }$ and a potassium ion in solid phase, $K_s^ + $ can be represented by Eq. (1) [18]:

Here, ${V_K}$ is the potassium vacancy.

Coercive field engineering was previously used to periodically pole 1-mm thick RKTP crystals using IE recipe with molten salt ratio of 73 mol%$RbN{O_3}$, 20 mol%$KN{O_3}$ and 7 mol% $Ba{({N{O_3}} )_2}$ at 375 °C for 4 hours, reporting a $\Delta {E_c}$ of 1.7 kV/mm [14]. The reproducibility and scalability of this method was demonstrated again using the exact molten salt ratio but at a lower temperature, which provided a sufficiently large contrast in ${E_c}$ to ensure fabrication of uniform domain grating with sub-µm periods in 1-mm thick PPRKTP [15]. So far, implementation of coercive field grating method has only been demonstrated in 1-mm thick crystals.

However, extending this technique to larger aperture crystals is not as straight-forward as it might seem at the first glance. Let’s first consider how the technique works: the change in coercive field does not occur throughout the crystal bulk, but rather only in the IE regions very near the crystal’s polar surface, which possess a much larger ${E_c}$ than the non-IE regions. This larger ${E_c}$ prevents domain nucleation from occurring locally in the IE regions. Below the IE depth, i.e., in the bulk, nucleation is too energetically costly to occur since nucleation happens preferentially at the crystal’s surfaces. Thus, domain nucleation and growth occur at a much lower electric field in the non-IE regions than in the IE regions, making it possible for the newly nucleated domain tips to grow towards the opposite polar face. However, for thicker crystals, the voltage required to reverse the polarization of the crystal scales with the sample thickness whereas the introduced $\Delta {E_c}$ remains the same. Moreover, for 1-mm thick crystal with sub-µm periods, we have recently observed that there is a critical depth (corresponding to a critical $R{b^ + }$ concentration) beyond which domain broadening can occur into the IE regions [19]. Taking into account that the applied voltage needed to reverse the polarization of a crystal will scale with the sample thickness whereas the $\Delta {E_c}$ will not, it is not obvious whether this critical depth will suffice to prevent domain broadening into the bulk in large-aperture crystals. Therefore, to extend this technique for large-aperture crystals, it is of paramount importance to understand how the IE conditions should be modified to achieve a $\Delta {E_c}$ that is suitable for thick crystals. In turn, the role of parameters like depth of IE, surface concentration of $R{b^ + }$ or the total amount of $R{b^ + }$ in the crystal affecting the $\Delta {E_c}$ should be clarified.

In this work, we present a comparison of the impact of depth, d and $R{b^ + }$ surface concentration, ${C_s}$ on the $\Delta {E_c}$. We demonstrate that it is the depth of IE that plays the major role in increasing the $\Delta {E_c}$. We show that periodic IE, followed by annealing can be effectively used to periodically pole a period of 3.43 µm over a 3-mm thick RKTP crystal with excellent uniformity throughout the crystal aperture. We also test the resilience of the ${E_c}$-grating over multiple polarization-switching cycles and demonstrate that polarization-cycling can be used to minimize the refractive-index change induced by IE, along the polar direction.

2. Periodic poling of 3-mm thick RKTP using coercive field grating

First, we compared the change in ${E_c}$, surface concentration of $R{b^ + }$ (${C_s}$) and $R{b^ + }$ depth profiles, after IE using two different melt compositions: (i) high $B{a^{2 + }}$ (HB), containing 73 mol% $RbN{O_3}$, 18 mol%$KN{O_3}$ and 9 mol%$Ba{({N{O_3}} )_2}$ and (ii) low $B{a^{2 + }}$ (LB), with composition of 73 mol%$RbN{O_3}$, 20 mol%$KN{O_3}$ and 7 mol%$Ba{({N{O_3}} )_2}$. The two melts were also compared at two different temperatures (330 °C and 360 °C). For all the IE recipes, the exchange time was kept constant at 8 hours, since it was previously observed that the change in coercive field saturates after 8 hours of IE [14]. Here, it was expected that higher concentration of $B{a^{2 + }}$ and higher temperature should increase the penetration depth of $R{b^ + }$ into the RKTP crystal, creating a deeper IE layer. Furthermore, previously it has been shown that additional step of annealing post-exchange increases the depth of doping ions, without affecting the total amount of exchanged ions [20,21]. Therefore, a post-exchange annealing step was added in our comparison for HB recipe, the modified recipe is therefore called HB + A. For this purpose, several z-cut 1 mm-thick RKTP crystals of similar ionic conductivity were used for planar IE. The IE was performed through the ${z^ - }$ face, since domain-nucleation in RKTP predominantly occurs on that surface [22]. An IE stop-layer was created on the ${z^ + }$ surface via oxygen plasma etching, similar to the method reported in [14]. We believe that exposure to oxygen plasma damages the crystalline structure at the surface, preventing in-and out-diffusion of ions. Each crystal was then treated with different IE conditions, as summarized in Table 1. After the exchange process, the crystals were removed from the melt and left to cool down to room temperature. For HB + A recipe, the crystal was later annealed in air at 300 °C for 24 hours. The ${E_c}$ after IE was measured by applying an electrical pulse with ramp rate of 0.70 kV/ms to completely reverse the spontaneous polarization in our RKTP samples while monitoring the current, similar to the method reported in [22]. The peak of the polarization switching current during the voltage ramp is defined as the ${E_c}$. The $R{b^ + }$ depth profile (d) and surface concentration of $R{b^ + } ({C_s})$ in atomic mass percentage were characterized using energy-dispersive X-ray spectroscopy (EDX) on the crystals’ y-faces. Taking into consideration that typically in-diffusion of $R{b^ + }$ in polar axis of KTP follows an error function distribution, the depth of the exchange can be estimated by using Eq. (2) [23]:

Table 1. Comparison of the effect of different melt compositions and temperatures of IE on the change in ${\textrm R}{{\textrm b}^ + }$ concentration on the surface, depth of ${\textrm R}{{\textrm b}^ + }$ and change in coercive field, $\Delta {{\textrm E}_{\textrm c}}$.

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At temperature of 330 °C, the higher amount of $B{a^{2 + }}$ in the melt does lead to a deeper ion-exchange, and results in the largest ${C_s}$. However, at a higher temperature of 360 °C, larger $B{a^{2 + }}$ concentration in the melt does not lead to an increase of ${C_s}$, but rather increases the penetration depth of $R{b^ + }$. Post-annealing the sample results in a lower ${C_s}$, but increases the depth of exchange, as expected. The most prominent trend is the dependence of $\Delta {E_c}$ on d, as shown in Fig. 1(a), a larger d leads to a larger $\Delta {E_c}$. Indeed, this trend is also confirmed by the annealed-IE RKTP, which has a larger d, exhibiting larger $\Delta {E_c}$ than its non-annealed counterpart, which was subjected to the same IE condition (HB). The EDX curves comparing the depth of $R{b^ + }$ in the non-annealed and annealed samples are shown in Fig. 1(b). Note that annealing just re-distributes the $R{b^ + }$ already present in the crystal after IE. With this data, it becomes evident that the penetration depth is the key parameter to obtain a large coercive field contrast between the exchanged and the non-exchanged regions.

 

Fig. 1. (a) $\Delta {E_c}$ versus d. (b) The depth of $R{b^ + }$ diffusion before (black) and after annealing (red). The points on the scatter plot represent the real data and the full lines represent the complementary error function fits.

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Next, we verified the above observations by periodically poling thick RKTP samples. All the samples used for periodic poling were 3 mm thick and had dimensions of 6.5 × 4.0 × 3.0 mm³ (along the crystallographic x-, y- and z-axes respectively). First, they were photolithographically patterned with 3.43 µm period on their z- faces. An IE stop-layer was created in the photoresist openings with a 20% duty-cycle and a planar IE stop-layer on the opposite polar face. The duty-cycle value was chosen to reach 50% duty-cycle in the bulk, taking into account of the broadening that we expect below the IE layer [19]. After removing the photoresist layer, the crystals were ion-exchanged using the recipe HB + A. Prior to poling, the IE stop-layers were etched away in a $KOH:KN{O_3}$ solution. For comparison, some crystals were exchanged using LB and HB recipes. A few samples were not exchanged and instead were patterned with conventional metal electrodes. All the crystals were periodically poled by applying triangular electric field pulses of 5-10 ms duration and magnitude of 4.5–5.8 kV/mm, depending on the specific ionic conductivity of each crystal.

The quality of each PPRKTP sample was evaluated by characterizing its second harmonic generation (SHG) output. As a fundamental beam, we launched a continuous-wave Ti:Sapphire laser (Spectra-Physics Model 3900S) emitting at 810 nm into the crystal along its x-direction, focused to a beam size of 30 µm at the centre of the crystal and polarization parallel to the crystal’s polar axis. The SHG output at 405 nm was separated by a band-pass filter (Newport BG40) from the IR-beam and measured using a power meter (Thorlabs S120VC). Figure 2 illustrate the direction of the QPM grating vector relative to the crystals’ axes and the face of IE. All the crystals were scanned in room temperature, along their polar axis, at the same y-position (centre of the crystal’s y-axis) to evaluate their uniformity along the depth of the crystal. Figure 3 shows the normalized SHG output of the PPRKTP poled using metal electrodes, as well as different IE conditions (LB, HB, HB + A) along the crystals’ polar axes starting from z = 0.1 mm, located 0.1 mm below the patterned polar surface (z = 0) to avoid the IE layer. The SHG output is normalized to the maximum SHG power obtained for each crystal and is defined in Eq. (3).

All the samples show good conversion efficiencies near the surface of the crystals. However, deeper into the bulk, the crystal poled with metal electrodes exhibit the worst performance as its conversion efficiency starts to decay rapidly to zero after the first 1.5 mm depth. This is followed by sample treated with LB recipe that is usually used for 1-mm thick samples, with a slower decay throughout the crystal’s aperture. The crystal with higher $B{a^{2 + }}$ (HB) shows a steadier conversion efficiency that is maintained down to 1 mm below the IE surface but starts to decay further down into the crystal. Only crystal treated with HB + A condition shows uniform conversion efficiency throughout the entire crystal thickness.

 

Fig. 2. Sketch of (a) the RKTP crystal after IE. (b) The SHG measurement of the PPRKTP.

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Fig. 3. Comparisons of the normalized SHG outputs of several 3-mm thick PPRKTP, poled using different methods.

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To complement the conversion efficiency data, all the aforementioned PPRKTP crystals were selectively etched to reveal domain structures on their polar surfaces. For all the IE-PPRKTP, the patterned face exhibits a periodic domain structure, reproducing the patterned duty-cycle, in good agreement to our previous results for 1-mm thick samples, whereas for the PPRKTP poled with conventional metal electrodes, the duty cycle had already increased to roughly 50%. Nevertheless, on the former ${z^ + }$ faces, substantial differences can be observed on the resulting domain structures for different IE conditions. Figure 4 shows the micrographs of the non-patterned faces of representative PPRKTP samples.

 

Fig. 4. The inverted domain structures on the ${z^ + }$ face of PPRKTP poled with (a) metal electrode (b) IE with low $B{a^{2 + }}$ (LB) (c) IE with high $B{a^{2 + }}$ without annealing (HB) and (d) IE with high $B{a^{2 + }}$ and annealing (HB + A).

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The micrographs reflect well the results presented in Fig. 3. As expected, the sample poled using metal electrodes shows no pattern fidelity on the non-patterned face and has the most uneven domain duty cycle among all these samples. This is not surprising, as it is already well-established that even for 1-mm thick crystals, the fringing fields at the edges of the metal electrodes and the associated domain broadening, make it challenging to pole dense domain structures. However, while the IE process improves the domain structure, the low $B{a^{2 + }}$ recipe was not sufficient to propagate the domain grating with the correct duty-cycle throughout the entire crystal thickness. Increasing the $B{a^{2 + }}$ content improved the propagation depth of the inverted domains, but it was not enough to grant a uniform structure throughout the entire thickness. The additional step of annealing, post- IE, which increased the $R{b^ + }$ penetration depth, improved the homogeneity of the domain reversal, leading to high pattern-fidelity throughout the entire crystal thickness. This points out the importance of having a deeper IE when a higher voltage is required to switch the polarization.

The 6.5 mm long, 3 mm thick HB + A crystal generated 2.1 mW of 405 nm when pumped with 0.48 W of 810 nm with a FWHM beam waist of 30 µm, which corresponds to a normalized conversion efficiency of 1.4%/Wcm, using Eq. (4).

The uniformity of the HB + A crystal is illustrated in Fig. 5, which shows the normalized conversion efficiency map of the PPRKTP poled after IE using HB + A. The SHG map of the PPRKTP aperture was obtained by scanning the fundamental beam in steps of 100 µm in the z-direction and steps of 200 µm in the y-direction. As it can be seen, the conversion efficiency is uniform along the PPRKTP z- and y-axes.

 

Fig. 5. The normalized conversion efficiency of SHG over the entire 3 mm x 3 mm aperture of the PPRKTP using IE pattern with HB + A recipe.

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3. Resilience of the coercive field grating

In conventional metal-electrode poling of KTP isomorphs, the photoresist-metal electrodes can be used for a limited number of applied electrical pulses before degradation of the electrodes occurs, making it challenging to achieve a periodic domain structure if the polarization has been cycled a few times. For coercive field grating, the pattern is embedded within the crystal sub-surface, providing a more solid structural integrity. Therefore, we investigated whether the coercive field grating properties are maintained by cycling the crystal’s spontaneous polarization multiple times. This could potentially be very useful to increase the overall yield for periodic poling; for instance, when the incorrect properties of electric field pulse are chosen at the first attempt [24]. To investigate this matter, a 3-mm RKTP crystal with coercive field grating fabricated via HB + A condition, was polarization-cycled several times in the following manner: first, a positive electric field pulse relative to the ground was supplied with the aim to invert the domains in a periodical fashion in the as-patterned sample. Then, two positive pulses of larger magnitude were applied to invert completely the original polarization of the crystal into one single polarization state. We will refer to pulses applied in this direction as forward poling. Afterwards, we applied negative electric field pulse relative to the ground to again seek a periodic domain structure. This pulse was then followed by two negative pulses of larger electric field to return the polarization to its original spontaneous polarization state. These pulses will be named as reverse poling. The conversion efficiency was monitored at the same spot at the center of the crystal’s aperture after each applied electric field pulse via SHG at 810 nm using the Ti:Sapphire laser, as described previously. Figure 6 shows the normalized conversion efficiency of a representative cycle. Note that the expected conversion efficiency is achieved when the first forward poling pulse is applied and then it goes to almost zero after the consecutive forward pulses are applied. The first reverse poling pulse results in a very low, but non-zero conversion efficiency, that goes again to zero after the second and third reverse pulses. This cycle was repeated more than 25 times. Interestingly, we have not been able to obtain a good periodic structure with reverse poling pulses. This can be understood by considering that domain nucleation starts on the ${z^ - }$ face, which for forward poling corresponds to the IE face. For reverse poling, now the nucleation starts from the “new ${z^ - }$ face” i.e., the face where no IE grating is present, and therefore, there are no means to selectively suppress domain growth. The small, non-zero conversion efficiency is ascribed to a few domain walls being pinned in the position they had during forward poling.

 

Fig. 6. The cycle of one polarization-switching event: first forward pulse to switch the polarization, second and third forward pulses to deliberately overpole the crystal (i.e. the entire crystal has the same polarization). The fourth pulse was applied in the opposite direction (reverse poling) to attempt to pole the crystal periodically but yielded very low conversion efficiency. Another two more reverse pulses were applied to switch completely the entire crystal into one single polarization, its original polarization state. Top of the figure illustrates how the polarizations in the RKTP changes at each electrical pulse.

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Figure 7 shows the conversion efficiency normalized to 1, obtained in the first forward electrical pulse versus number of polarization cycles. The magnitude of the first forward electrical pulse was varied between 4.70-4.90 kV/mm for the first five cycles; to identify the best electric poling pulse. Electrical pulse that is too low will lead to underpoling and on the other hand, pulse that is too high will lead to overpoling. Nonetheless, both scenarios will result in very low conversion efficiency whereas high conversion efficiency will be obtained when the correct electrical poling pulse is applied. Once the best poling pulse value was identified at 4.76 kV/mm, which occurred on the 5^th polarization-switching cycle, a high-quality domain structure can be obtained after each first forward pulse with excellent conversion efficiency. The poling pulse was kept constant at 4.76 kV/mm until the 25^th polarization-switching cycle. The SHG output was monitored at the same position at the center of the crystal, 1.5 mm below the crystal z-face. The fluctuations in SHG output are most probably due to small variations in the pump power, which we could not monitor in the poling set up, and therefore presented as normalized to the maximum measured SHG power. This result indicates that no degradation of the coercive field grating occurs even after 25 cycles, and that if there is any further $R{b^ + }$ diffusion into the crystal due to the applied electric field, the effect is negligible, preserving the IE grating stability and characteristics. Here it is also worth noting that no scattering or degradation of the SHG beam was observed after multiple cycling, indicating that no substantial stress or defects were accumulated at the domain walls.

 

Fig. 7. The normalized conversion efficiency was monitored at each cycle of polarization-switching. The PPRKTP undergone 25 polarization-switching cycles with no signs of degradation.

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4. Polarization-cycling and refractive index change

We have previously observed that for 1-mm PPRKTP crystals, the IE led to a small refractive index gradient along the crystal’s polar axis [14]. This gradient was tentatively attributed to stress due to the difference in the lattice between the exchanged and the non-exchanged regions that extends far beyond the IE layer. Although this might be attractive for some applications which can take advantage of such fine-tuning of refractive index, it is also important to understand its origin and develop the means to control this behavior. In principle, cycling the spontaneous polarization many times might help to relax the stress caused by IE as the ${K^ + }$ (and the $R{b^ + }$) changes oxygen coordination during polarization switching [25] therefore, we compared a HB + A crystal that had been periodically poled with a single pulse to another HB + A crystal that had been polarization-cycled multiple times prior periodic poling, as described in Section 3. To characterize the change of refractive index along the polar axis, we tracked the SHG phase-matching temperature curves of the PPRKTP crystals at a fixed y-position but at different z-positions (0.2, 0.5, 1.5, 2.5 mm) below the IE region, shown in Fig. 8. The pump wavelength was fixed at 811.0 nm throughout the entire measurement and using the SHG set-up described before, the output SHG power was measured while the temperature of the crystal was slowly varied in steps of 0.2 °C using a Peltier element. It was not possible to track the change of SHG wavelengths along the crystal’s polar axis since the wavelength change is smaller than 0.05 nm which is the resolution limit of the optical spectrum analyzer (ANDO, AQ-6315A).

 

Fig. 8. SHG phase-matching temperature curves of the PPRKTP crystals poled with single pulse and 10 polarization cycles, measured at depths of 0.2, 0.5, 1.5 and 2.5 mm below IE surface.

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The single-pulse poled PPRKTP has an overall larger temperature shift, $\Delta T$ of 1.0 °C, meanwhile this shift was reduced to 0.4 °C when the RKTP was subjected to multiple polarization-cycles, which corresponds to a change of refractive index, $\Delta n$ of $1.66 \times {10^{ - 5}}$ and $0.66 \times {10^{ - 5}}$ respectively using Weichmann’s refractive index temperature derivatives for KTP [26]. Note that for the single-pulse poled crystal, the change in refractive index, $\Delta n$ is more gradual throughout the crystal thickness, whereas for the multiple polarization-cycled sample, $\Delta n$ is more pronounced close to the IE region, and becomes negligible from a depth of 1.5 mm and onwards. This indicates that poling with multiple polarization-cycles minimizes $\Delta n$ of PPRKTP, at least in the lower half of the crystal. A plausible explanation is that cycling the polarizations reduces the lattice disorder, also observed by [27], whereby electrical annealing was used to obtain a KTP with a higher degree of crystallinity.

5. Conclusions

Grating with high-and-low coercive fields were engineered via IE to periodically-pole 3 mm x 3 mm aperture RKTP crystals with QPM period of 3.43 µm and SHG normalized conversion efficiency of 1.4%/Wcm at 405 nm. The coercive field contrast can be increased by increasing the depth of IE layer, which was accomplished by adding more $B{a^{2 + }}$, increasing the temperature and adding an additional step of annealing post IE. We have also demonstrated that the properties of the coercive field grating were preserved even after multiple polarization-switching cycles. This can be utilised to increase the yield of high-quality PPRKTP and to manage the change of refractive index created after IE, in the bulk along the polar axis. Finally, these findings pave the way for domain reversal in much thicker crystals towards realization of large aperture sub-µm PPRKTP, which will allow us to demonstrate high-energy BWOPO, pushing the boundaries of periodically poled QPM devices.