1. Introduction

Recently, KTa_1−xNb_xO₃ (KTN) crystals have drawn much attention for their excellent electro-optic (EO) effects near phase transition temperature, which play important roles in many applications such as beam scanning [1–3], scale-free optics [4–6], enhanced EO modulators [7], and refractive light needles [8]. By cooling an copper-doped KTN:Li crystal, DelRe et al. have observed an interesting phenomenon of diffractionless wave propagation, which may lead to new applications for high-resolution imaging and microscopy [9]. Unique optical nonlinearity based on intrinsic negative mass was also observed in a slab waveguide of KTN under a supercooling process [10]. In addition, giant electro-optic effect and large recoverable piezoelectric effect were obtained by using various KTN crystals [11, 12]. All these novel optical effects and applications were implemented by controlling the KTN phase transition near para-ferroelectric boundary where polar nanostructures emerge inside the crystals [13–19].

Previous investigations on KTN crystals exploit Peltier or thermostat devices to adjust temperature for controlling the phase transition process. However, these conventional methods are inefficient and imprecise due to slow thermal transfer between the object and the source. Temperature gradient within the crystal can also be generated when the temperature of a Peltier module is much different from the surroundings [6, 13]. In this work, we demonstrate a fast and highly efficient ferro-paraelectric phase transition control in KTN crystals by using AC electric fields. In addition, we use a laser scattering method to monitor in real time the crystal phase transitions which are associated with the dynamic development of KTN polar nanostructures. Based on the dielectric property, thermal effect can be directly produced inside the KTN crystal without using extra thermal sources or complicate thermostat system. As compared to using the Peltier module, the resultant thermal distribution is much uniform with less temperature gradient or fluctuation. The study will be significant for designing various photonic functional devices based on novel electro-optic and ferroelectric effects for a wide range of photonic applications.

2. KTN polar nanostructures and optical scattering

KTa_1−xNb_xO₃ is the solid solution of KTaO₃ and KNbO₃ and can be in its cubic, tetragonal or orthogonal phase at room temperature depending on the value of x, thus it is highly adaptable for different kinds of device applications. With temperature decreases across T_c, Nb ions displace off from their original center sites, forming mesoscopic polarization domains of dipoles [20–26]. Further decreasing the temperature strengthens the polarization formation due to the increased displacement of Nb ions. Meanwhile, the polarization domains grow to larger nanostructured clusters, which are called polar nano-regions (PNRs), polar nano-domains (PNDs) or ferroelectric domains based on their sizes [27].

It is well known that dielectric loss (DL) exists in ferroelectric materials, originating from the inelastic polarization rotation of dipoles under electric fields. The process of dipole reorientation consumes energy and thus produces heat. When an AC electric field is applied, the DL is much significant due to the repeated alignment of dipoles [28–31]. The heat is directly produced inside the crystal and thus no additional thermal sources as well as thermal transfer are required. As such, we may control the crystalline phases by electric fields with this internal thermal effect, which is highly efficient and fast. On the other hand, since the fast DL-induced thermal effect occurs internally, it is difficult to detect the temperature by using conventional thermistors to monitor the KTN phase transition. Infrared thermal camera can be used to detect internal temperature of the crystal, but its spatial resolution is too low to precisely detect the phase change of our KTN chip with very small size. In our experiments, we use a method of light scattering to detect the change of KTN polar nanostructures which concurs with the phase transition process.

Figure 1 shows the schematic of our experimental setup that uses a laser beam to probe dynamic crystalline phase transition induced by AC electric fields. A 532 nm laser is incident to a sample chip of Cu:KTN after passing through a polarizer and a lens, respectively. The Cu:KTN single crystal with high optical quality has been grown using the top-seeded solution growth method [32]. The crystal is cut into a cuboid with size 1.61(x) × 3.39(y) × 5.11(z) mm³ with its x axis along the crystallographic (100) direction. All of the six faces are polished with two large surfaces (y × z planes) coated with silver electrodes. The transmitted light is detected by a photodetector for intensity measurements and a CCD for imaging evaluation. An AC electric field is applied on the sample along x direction through the two electrodes to induce the phase transition of the Cu:KTN crystal. It should be noted that a Peltier is also used in the experiments but only for presetting an initial temperature of the sample.

 

Fig. 1 Schematic of experimental setup for studying the phase transition of Cu:KTN crystal induced by electric fields.

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Figure 2(a) shows the experimental ε_r-T curve of the Cu:KTN sample, indicating T_c is located at 42 °C. During the phase transition of the crystal, polarizations of nanostructured clusters are formed and scatter the incident laser beam. The light transmission depends on the state of microstructures, which is corresponding to the stage of the phase transition process. In experiments, we observe that the optical transmission of the sample varies with the temperature. As expected, the transmission changes from 0 to 100% with increasing the temperature across T_c (the red lines), and vice versa (the blue line), as shown in Fig. 2(b).

 

Fig. 2 (a) ε_r-T curve of Cu:KTN used in our experiment. (b) Transmitted light intensity of Cu:KTN when temperature was changed across T_c. The total 100% transmitted light intensity corresponds to 100 μW optical power when no scattering happens.

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3. Dynamic phase transition by AC electric fields

For fast and efficient temperature control of Cu:KTN based on the DL mechanism, we use an sinusoidal AC electric field with amplitude of E₀ = 200 V and frequency of f = 400 kHz. We first set an initial temperature to 36 °C by using the Peltier. At this temperature, no light is transmitted due to the strong scattering of polarization domains. To avoid optical damage in Cu:KTN crystals due to photorefractive effect [33], we utilize an incident laser with low power of only 100 μW.

When we apply the electric field, we observe light transmission quickly increases to nearly 100% within about 0.332 s as shown in Fig. 3(a). Since the transmission variation reflects the development of polar nanostructured clusters which are directly associated with stages of the crystalline phase transition, we can determine that the crystal temperature at 0.332 s corresponds to the Curie temperature T_c = 42 °C. Therefore, the temperature of KTN sample is changed from 36 °C to 42 °C in about 0.332 s, much faster and more efficient than the Peltier devices which need at least 6s for the same change in the measurement. Also, the temperature distribution should be identical within the crystal of high quality with less temperature gradient or fluctuation, because the electric field is uniform between two close silver coatings of electrodes. Figure 3(b) shows the infrared thermal images of the sample taken by an infrared imager (FLIR, TG167, 9 Hz) before and after the AC field is applied. We first preset the temperature to 36 °C by using the Peltier. Then, we turn on the AC fields. The thermal images show the temperature increases extremely fast with a uniform distribution. This is a direct evidence that the light scattering accompanied with the ferro-paraelectric phase transition is induced by a fast and efficient thermal effect due to the DL, rather than a slow process such as photorefractive effect in Cu:KTN [33]. Figure 3(c) shows the transmitted laser beam which keeps collimated with Gaussian profile over different stages of phase transition. As such, nonlinear effects are negligible and it is relatively precise to monitor crystal phase transition by evaluating beam transmission.

 

Fig. 3 (a) Transmitted light intensity versus time after the AC electric fields being applied. (b) Infrared thermal images of the sample area without (the left one) and 0.333 s after the AC fields (the right one). (c) Direct imaging of transmitted light spots shot by CCD

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We further study the dependence of DL on the amplitude and frequency of AC electric field. The Cu:KTN crystal can be considered as a non-ideal capacitor with the power loss $P=E_0{}^{2}2\pi fC\tan \delta$, where C is capacitance, regarded as constant around phase transition temperature [34]; δ is the DL factor (discussed below); E₀ and f are the amplitude and frequency of applied AC electric field. Before conducting each experiment, we preset the temperature to 36 °C by using the Peltier. Figure 4(a) shows the optical transmission with increasing f. We found that the trend of optical transmission change with f is exactly the same as that with increasing temperature (Fig. 2(b)). In other words, for a given amplitude of the AC electric field, we are able to control the phase transition of Cu:KTN crystal by the AC frequency which corresponds to a certain temperature. As shown in Fig. 4(b), the time response of the phase transition becomes fast with the increasing f and can be much less than 1 second for a given f with over 100 kHz. In addition, we have also conducted experiments regarding the dependence of the DL on the amplitude, as shown in Fig. 4(c). Similarly, for a given f = 400 kHz, we observe that the transmission quickly increases to nearly 100% and the time response of the phase transition decreases to less than 1 second with increasing the AC amplitude to over 120 V as shown in Fig. 4(d). Therefore, for a given electric field amplitude, we can also control the crystalline phase transition by only tuning the amplitude of the AC electric field. According to previous work involving the dielectric property of Cu:KTN [34], δ and P increase with f (below 10⁵ Hz). However, δ decreases with f for 10⁵-10⁶ Hz. Thus, P can either increases or decreases with f. Our results in Fig. 4(a) show the increase of transmission below 50 kHz indicating P increases with the frequency. For f > 50 kHz, the crystal become completely transparent indicating the temperature of the sample is above Tc, but the frequency dependence of P is also uncertain (>50 kHz).

 

Fig. 4 Maximum transmission after the electric fields of varied (a) f or (c) E₀ being turned on; Response time for transmitted light intensity reaching maximum after the electric fields of varied (b) f or (d) E₀ being turned on

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4. In situ phase transition observed by a microscope and X-ray diffractometer

Since the transmission of incident laser beam in our experiment is associated with the polar nanostructured clusters in the KTN sample, it is necessary to investigate the dynamic process of phase transition induced by AC electric fields under a microscope. Figure 5 shows a series of microscopic video clips with an AC electric field applied. At the time t = 0 s corresponding to 24 °C, the sample shows obviously the 90° domain walls in its ferroelectric phase [12]. When we turn on the electric field, we observe the domain walls break down quickly with time. At 2.66 s, we can barely see domain walls due to much small size of polar nanostructured clusters (i.e., PNDs) [27]. At 3 s with temperature near T_c, although the nanostructure (PNRs) size [6, 25] is invisible under the microscope, we can still observe light scattering in the experiments. At 3.33 s where the temperature is over T_c, the crystal become completely transparent.

 

Fig. 5 Selected images of microstructure in KTN with AC electric field (E₀ = 150V, f = 100 KHz) implemented on the sample at room temperature (24 °C). The electric field was turned on at 0 s.

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X-ray diffraction (XRD) is one of powerful techniques for characterization of crystalline structures. To observe the phase transition in the sample, we carry out an in situ X-ray diffraction experiment. Due to the small size of our sample chip, we use a Micro X-ray Diffraction (µXRD) method in the experiments. We observe the change of diffraction peaks due to the phase transition induced by the AC electric field as shown in Fig. 6. In the experiments, both [002] and [200] peaks appear around 2θ = 45° when the sample is set at 24 °C and no electric field is applied, which indicates the crystal is in its tetragonal phase with ferroelectric domains. However, after we turn on the electric field for about 10 s, the µXRD results show only a single peak [200], indicating its cubic phase. In other words, the AC field induces the KTN crystal to undergo a ferro-paraelectric phase transition. Our results are consistent with previous study on X-ray diffraction characterization of KTN [35].

 

Fig. 6 In situ X-ray diffraction spectrum of Cu:KTN at different conditions. Red line: obtained without an AC electric field at room temperature, 24 °C. Blue line: obtained about 10 s after the AC electric field (E₀ = 150 V, f = 100 kHz) turned on.

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5. Conclusions

In conclusion, we have demonstrated an efficient phase transition in a KTN crystals by using AC electric fields with different amplitudes and frequencies. The temperature rising speed is as fast as 18 °C/s under an AC electric field with an amplitude of 200 V and a frequency of 400 kHz limited by our power source. Since the thermal effect is generated directly inside the crystal, the phase transition process is much fast with very low power consumption with respect to conventional methods. In addition, we use a laser beam to probe in real time the dynamic process of crystalline phase transition. Both the amplitude and frequency of the AC electric field can be easily and precisely tuned, thus the technique is very simple and efficient to control the phase transition process of the crystal, which is important for developing novel electro-optic and ferroelectric devices for many potential applications in lasers, imaging and display as well as optical communications.