1. Introduction

The ability to engineer ferroelectric domain structures with an accurate periodicity plays a key role for the quasi-phase matching (QPM) technique, opening the path to realize any second-order nonlinear interaction within the transparency range of the material in a noncritical and efficient way. Since its first demonstration in 1993 [1], electric-field (E-field) poling of ferroelectric oxide crystals has been established as the most advanced and reliable method for QPM implementation. However, it requires precise control over the structure uniformity and duty-cycle, especially for short periods required for frequency conversion into the blue and ultraviolet spectral range [2, 3], as well as for nonlinear interactions involving counter-propagating waves [4]. Constant improvement of the domain engineering techniques has allowed for pushing the limits of the achievable domain aspect-ratio, both for thick crystals [5, 6], and short periods [7], allowing a broader range of possible nonlinear interactions and use of higher energies. For this development to be able to continue, a deeper understanding of the domain dynamics during electric field poling is desired.

Several studies have been previously conducted in order to investigate the domain dynamics in situ for LiNbO₃ (LN) [8], LiTaO₃ (LT) [9], and KTiOPO₄ (KTP) [10]. Most of those studies are based on direct visualization of the growing domains using digital cameras employing the electro-optic effect. Unfortunately, they all have a time resolution of a few milliseconds, at best, which limits their use for investigating fast domain dynamics in the short-pulse periodic poling (PP) regime.

In this work we study the dynamics of the domain-grating formation by monitoring in situ the QPM second harmonic (SH) signal temporal evolution during the periodic poling process with a resolution below one microsecond. In our experiments, we have chosen to work with bulk Rb-doped KTP (RKTP). This, relatively new, commercially available KTP isomorph has similar transmission and nonlinear properties as flux-grown KTP, however its orders of magnitude lower ionic conductivity reduces the domain broadening, making the material very attractive for fine-pitch periodic poling [7]. Here, we demonstrate that the SH signal temporal evolution during periodic poling reflects the dynamics of the QPM grating formation in the crystal. It is shown that poling with single, short pulses can result in a sub-millisecond domain nucleation and domain growth in RKTP. Poling with square-shaped and triangular-shaped E-field pulses are compared and it is shown that periodic poling with a single short symmetric triangular E-field pulse is superior in terms of the resulting QPM grating quality for RKTP.

Although the results presented here refer only to RKTP, our technique is equally applicable to other ferroelectric materials used for QPM applications.

2. Experiments

For our experiments we used four flux-grown, c-cut RKTP wafers, cut into a total of 40 samples with dimensions of 12 × 7 × 1 mm³ along the a (x), b (y) and c (z) crystallographic (dielectric tensor) axes, respectively. Note that only samples from the same boule with similar ionic conductivity were investigated for the single-pulse and multiple-pulse parts of he experiment respectively. The c^- faces of the crystals were patterned with a metal-photoresist grating with 4 μm period and electrode duty-cycle of 0.47 using standard photolithography, while the c⁺ faces of the crystals were left unpatterned. The poling area had the dimensions of 8 × 3 mm² along the a and b axes, respectively. The period was chosen to achieve first order QPM SH generation at 421 nm at room temperature. The crystals were contacted to the poling circuit using liquid KCl-electrodes.

The domain dynamics in RKTP crystals were studied by observing the temporal evolution of the SH signal during periodic poling. It should be noted that while the E-field is applied to the crystal, the electro-optic effect induces a refractive index change which shifts the phase-matching wavelength by 0.11 nmkV⁻¹mm, resulting in a maximum shift of 0.55 nm for the peak applied E-field of 5 kVmm⁻¹. Since the wavelength acceptance bandwidth of our PPRKTP crystals was 0.2 nm, it was difficult to ensure consistent phase matching during the whole periodic poling process using a CW pump laser with a narrow linewidth. Therefore, a mode-locked Ti:sapphire laser was employed as a fundamental wavelength source (see Fig. 1). The laser emitted 170 fs pulses at 76 MHz repetition rate with a central wavelength of 842 nm and a full width at half maximum (FWHM) bandwidth of 6 nm. The z-polarized laser beam was collimated to 30 μm radius (1/e² intensity), launched along the a axis of the crystal, and kept at 0.5 mm from the patterned face along the polar direction. The generated SH signal was filtered out from the pump and monitored with a detector with 14 ns resolution (Thorlabs, DET 36 A). In order to avoid saturation of the photodetector, the incident fundamental power was kept at the relatively low value of 27 mW. The poling voltage, the fundamental and the SH power were recorded simultaneously with an oscilloscope. After poling, the crystals were selectively etched in order to examine the resulting domain structure.

 

Fig. 1 Experimental setup.

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It is known that periodic poling with short, millisecond-range, E-field pulses is advantageous for KTP isomorphs since it effectively mitigates the domain broadening [7, 11]. Therefore the pulse length was kept fixed at 5 ms, we compared the SH signal temporal evolution when periodic poling was performed with two basic pulse shapes; square and symmetric triangular pulses. In addition, we also studied the effect of poling with multiple E-field pulses on the QPM grating quality. In this case the pulse peak magnitude was kept constant, while the number of applied pulses was varied and the SH signal evolution was recorded during each pulse.

For each pulse shape we distinguished between three different poling outcomes: underpoling – when the domain-grating did not form completely; overpoling – resulting in partial or total domain merging underneath the insulating photoresist; and grating-poling – resulting in a periodic domain structure throughout the crystal thickness of 1 mm. Figure 2 shows the SH time evolution (red curves) and applied E-field (black curves), of representative examples for Fig. 2(a) underpoling, 2(b) grating- poling and 2(c) overpoling, using square pulses; and 2(d) underpoling, 2(e) grating- poling, and 2(f) overpoling, using triangular pulses.

 

Fig. 2 Applied E-field (black curves) and second harmonic traces (red curves) for the cases of (a) underpoling, (b) grating poling, and (c) overpoling, using square pulses, and (d) underpoling, (e) grating poling, and (f) overpoling, using triangular pulses.

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As can be seen in Fig. 2, there are several features in the SH traces that are common to all the poling events studied here. First, there is a certain “incubation time”, (t_i), where the SH signal stays at the noise level. We define t_i as the time from the start of the voltage pulse until the SH signal reaches 5% of its peak value. The SH signal growth is represented by the “rise time” (t_r) and is defined in our experiments as the time it takes for SH signal to rise from 5% to 90% of its peak value. For the overpoling cases, two additional features can be observed: a “dwell time” (t_d) – here defined as the time, while the SH signal stays above 95% of its peak value, followed by the “fall time” (t_f), defined as the time it takes for SH signal to fall down to 5% of its peak value.

Table 1 summarizes representative values obtained in underpoled, grating-poled and overpoled crystals using single, 5 ms-long square or triangular E-field pulses corresponding to Fig. 2(a)-2(f).

Table 1. Typical periodic poling results, obtained with square and triangular pulses in the case of underpoling, grating- poling, and overpoling.

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As can be seen from Table 1, all poling cases studied here display incubation times in the range of a few ms. The rise times obtained with triangular pulses are within a few hundred µs, and are considerably shorter than those obtained with square pulses. The dwell times on the order of one ms with sub-ms fall times are observed in overpoled samples both for square and triangular pulses.

As we will show next, the different features observed in the SH traces reflect different stages of the poling process.

In order to understand the physical meaning of the incubation time and its apparent weak dependence on the electric pulse shape, we performed the following experiment; several crystals were poled with E-field pulses shorter than the expected incubation time. This was done for both square and triangular pulses, using pulse lengths of up to 90% of the expected incubation times. The voltage was turned off rapidly at the end of each pulse. For all cases, a rectifying diode was added to the poling circuit in order to prevent possible domain back-switching. Finally, the crystals were selectively etched.

A widely accepted model of polarization switching in ferroelectrics involves the following stages: domain nucleation, followed by domain growth in the polar direction, lateral expansion of the domains, and domain coalescence [12]. No domain nucleation on the polar surfaces of the etched crystals could be observed for any of the investigated crystals. Therefore, we conclude that the incubation time can be attributed to the time needed to form critical domain nuclei, which will then stabilize and grow only if the field continues to be applied. The existence of an incubation time has been previously reported for several other materials such as triglycine sulfate [13], LT [8] and KTP [14], and was similarly attributed to critical-nuclei formation and stabilization time.

Although we do not have enough statistical data to determine the exact dependence of the incubation time on the E-field, it is obvious that the incubation time decreases when increasing the E-field magnitude, being as short as 1.46 ms for a square pulse of 4.2 kVmm⁻¹. For triangular pulses, we also see a sharp decrease in incubation time when we increase the ramp rate. For instance, ramping up the voltage at 1.52 kVmm⁻¹ms⁻¹ resulted in 2.62 ms incubation time; when the ramp rate was increased to 2.0 kVmm⁻¹ ms⁻¹ the incubation time decreased to 2.41 ms. In both cases, it can be attributed to an increase in nucleation probability at larger E-fields. Nevertheless, it is worth noting that the incubation time per se seems to have little influence on the quality of the QPM structure.

The detection of SH signal during poling begins when a sufficient amount of reversed domains crosses the probe beam path in the crystal, and reaches maximum when the QPM grating has the optimal duty-cycle. The following observations can be made: (1) Both for square and triangular pulses, the rise time decreases when the E-field magnitude is increased (see Table 1); (2) For grating poling, the rise times for triangular pulses are in the sub-ms regime and an order of magnitude shorter than for square pulses: The rise time for square pulses ranges between 1.12 ms and 2.87 ms (the variation in rise time is 1.75 ms) when the E-field varies from 5 kVmm⁻¹ to 3.6 kVmm⁻¹, whereas for triangular pulses the rise time changes from 0.22 ms to 0.40 ms (0.18 ms variation) when the ramping rate changes from 2.08 kVmm⁻¹ms⁻¹ to 1.76 kVmm⁻¹ms⁻¹. (3) Poling with triangular pulses gives QPM gratings of higher quality than poling with square pulses, as can be seen in Fig. 3, which shows in Fig. 3(a) and 3(b) the etched domain patterns corresponding to the poling events in Fig. 2(b), and 2(e), respectively.

 

Fig. 3 Chemically etched domain structures representing grating poling on the former c⁺ crystal faces; (a) poled with a square pulse (corresponding to Fig. 2b) and (b) poled with a triangular pulse (corresponding to Fig. 2e). The insets show the c^- faces of the crystal in the same scale.

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Moreover, this fact is also confirmed by the significantly higher normalized conversion efficiencies obtained in PPRKTP crystals poled with triangular pulses, compared to those obtained in the crystals poled with square pulses, (see Table 1), and in good agreement with previous reports [2].

All these observations can be interpreted in the following way: Since no domain formation occurs during the incubation time, the rise time should account for most of the polarization–switching process; domain nucleation, propagation in the polar direction and coalescence under the metal electrodes. The SH signal increases when there is growth of new periodic domains in the sampled volume. Thus, a long rise time indicates that the formation of individual domains is more spread out in time, i.e., some domains are still in the nucleation stage, while others have already been formed and propagated through the sample. On the other hand, a short rise time suggests a more uniform formation of the QPM structure; i.e., most domains nucleate and grow at the same pace.

It is well accepted that the switching process is nucleation-limited in the low field regime (i.e., E-fields below the coercive field), while at high fields (i.e., higher than the coercive field), the nucleation is not a limiting factor any more, and the switching is governed by the domain wall motion [15]. For triangular pulses, the majority of domain nucleation takes place at the vicinity of the peak of the pulse (high-field regime), where the nucleation rate is the highest, followed by growth of these simultaneously nucleated domains. In addition, the non-constant field ensures nucleation in the regions of the crystals that, due to deviation from stoichiometry and/or defects might have slightly larger coercive field. Moreover, since sideways domain expansion occurs via nucleation and growth of step-like domains adjacent to already existing domain walls [16], domain broadening is only likely to occur within the short time near the peak of the E-field pulse. Consequently, a more uniform QPM grating is formed, which is well-reflected by a relatively short SH rise time. On the other hand, for square pulses, constant E-field throughout the duration of the pulse provides constant nucleation probability; however, regions within the crystal with slightly different coercive field will have different nucleation rates. Thus, nucleation of individual domains is spread in time during the pulse, resulting in overall less homogeneous QPM grating, which is reflected by an order of magnitude longer rise time, compared to triangular pulses.

As previously mentioned, in the case of the overpoling, for both square and triangular pulses there exists a “dwell time”: the SH signal stays at its maximum for nearly a millisecond, indicating the absence of domain broadening during this time, at least in the sampled volume. The dwell time can be attributed to the time needed to nucleate new domains under the photoresist, which will naturally be slower due to the limited charge injection under the insulating photoresist layer. If the applied field is not switched off after the SH reached its peak value, domain nucleation, growth and merging under the insulating photoresist layer eventually occurs, causing deviations from the ideal duty cycle in the QPM grating, with the corresponding decline of SH signal. The SH fall time indicates how fast the transition from a periodic domain structure to an almost single domain state occurs.

Finally, we also studied the switching behavior when poling was performed using multiple pulses. Figure 4(a) shows the results of using multiple square pulses with the peak magnitude of 3.4 kVmm⁻¹ (low-field regime). The waiting time between pulses was 1 min. The first applied pulse resulted in an incubation time of 3.32 ms, while the SH signal was rising instantly with the beginning of the subsequent pulse. The maximum SH output power reached 263 μW in this case. It should be noted that crystals from a different boule, with a higher coercive field, were used for this part of the experiment.

 

Fig. 4 Second harmonic signal evolution (red) and applied E-field (black) during periodic poling with multiple square (a) and triangular (b) pulses.

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An example of the SH signal evolution when using multiple triangular pulses is shown in Fig. 4(b). The peak of each pulse was set to 3.8 kVmm⁻¹, with 1 min waiting time between pulses. Although there is always some incubation time in the beginning of each applied pulse, the field at which the SH signal begins to change, decreases with each subsequent pulse. In this case, the maximum SH output power reached 48 μW, before decreasing to approximately half. While the examples shown in Fig. 4 are achieved with three pulses, experiments with lower E-field magnitude and more pulses lead to qualitatively the same results.

In terms of QPM grating quality and conversion efficiency, these results indicate that there is essentially no difference between poling with single and multiple square pulses. The fact that the incubation time can be observed only during the first applied square pulse suggests that the polarization switching within a subsequent applied pulse resumes from the state it has reached when the previous pulse has ended. This is in good agreement with previous studies on KTP [14] and differs substantially from the behavior of LT; where there is always certain incubation time, needed to unpin the existing domain walls [17].

In contrast, periodic poling with multiple triangular pulses results in less homogeneous domain structures and lower conversion efficiency, compared to poling with a single triangular pulse. In this case, the polarization switching takes place in the low-field nucleation-limited regime. In addition, even though the domain nucleation rate is still highest at the peak of the triangular E-field pulse, now the domain formation is divided between multiple triangular pulses, promoting new domain nucleation in unwanted regions and leading to domain broadening, and therefore, the benefit of using the triangular pulse shape is lost.

3. Conclusions

We show that the temporal evolution of the SH signal during periodic poling reflects the formation of the ferroelectric domain grating and exhibits characteristic features, which are related to the resulting QPM grating quality. We investigated the influence of the E-field pulse shape, the pulse magnitude and the number of pulses on the QPM grating quality in RKTP in the short-pulse poling regime. We showed that periodic poling with a single triangular E-field pulse is the preferred choice for obtaining high quality QPM gratings in RKTP crystals. Periodic poling with multiple triangular E-field pulses proved to have a detrimental effect on the QPM grating quality. In contrast, periodic poling with multiple square E-field pulses shows no negative effect on the resulting domain structure and may be even beneficial due to provided additional flexibility. Our method is non-destructive, flexible in terms of material choice, and can serve as an accurate periodic poling monitoring technique. While RKTP was identified as the most interesting candidate for our investigation, this method can be equally well applied to other ferroelectric materials used for QPM applications.