1. Introduction

The terahertz (THz) frequency window, which has become extensively exploited during the past two decades, extends from about 0.1 to 10 THz, thus covering the far-infrared (FIR) and lower part of the mid-infrared (MIR) spectral region. Nowadays THz technology is of enormous interest for scientific and technical applications as it overlaps with many fundamental elementary excitations of physical systems, for instance, molecular vibrations, phonons, quasi-free electrons, excitons, and magnons [1,2]. To enable active control of the propagation of THz radiation, the investigation of tuning properties of various materials and structures plays an important role in the development of THz functional devices.

Potassium tantalate (KTaO₃, KTO) is a cubic incipient ferroelectric with interesting potential for technical application, in which the quantum fluctuations at low temperatures prevent a displacive ferroelectric phase transition to occur. The low-frequency dielectric behavior of the compound is fully determined by the soft mode dynamics. Recently, research on properties of KTO in the terahertz spectral range has drawn the attention of many researchers [3–9]. Yuki Ichikawa et al. observed the soft-mode dispersion in the incipient ferroelectric KTO, and concluded that the origin of the extremely large static permittivity in KTO is almost fully attributed to the TO1 mode dispersion [3]. Then they reported the influence of lattice polarizability on interacting Li-induced dipoles distributed in incipient ferroelectric KTO [4]. Sebastjan Glinsĕk et al. investigated the lattice dynamics and broad-band dielectric properties of KTO ceramics, and found that the soft mode frequency agrees well with the values that in single crystal, which indicated a negligible influence of the grain boundaries on the dielectric response in KTO unlike in other ferroelectric or incipient ferroelectric perovskite ceramics [5]. V. Skoromets et al. reported an evidence of ferroelectric phase transition in polycrystalline KTO thin film revealed by terahertz spectroscopy [6].

In view of the above reports, the dielectric properties about the soft-mode behavior under the optical field in bulk KTO obtained by THz spectroscopy have rarely been reported. Besides, only few observation of the tunability of KTO single crystal at room temperature has been reported up to now. For practical applications, it is necessary for the permittivity to be modulated over as wide a range as possible around room temperature. In this letter, we report on a study of dielectric properties and optical-field-induced tunability of bulk KTO at room temperature.

2. Experiment

The KTO crystals are manufactured by MTI Corporation. The dimensions of the crystals are 10 × 10 × 0.53 mm³, and the crystal orientation is <100>.

As can be seen in Fig. 1, we used a terahertz time domain spectroscopy (THz-TDS) [10] to measure the transmittance waveform at room temperature. In this THz-TDS system, a fiber femtosecond laser beam (center wavelength 780 nm, repetition rate 50 MHz, pulse width 90 fs) is divided into pump beam and probe beam. The pump beam is focused on GaAs emitter to generate THz radiation. And the transmitted THz wave is focused on ZnTe crystal and detected by the balanced detector [11]. The frequency resolution is 10 GHz, and the THz spot diameter at the focus is 3 mm. A 532nm continuous-wave (cw) laser was obliquely incident on the surface of the samples, the incidence angle is 45° and the spot diameter is 5 mm. Using a temperature control system, the temperature of the system was maintained at 24°C throughout the measurement. As the optical axis is along <100>, the THz beam is ordinary polarized.

 

Fig. 1 A sketch of the experimental facility.

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3. Results and discussion

Figure 2(a) shows the transmittance waveforms under different green laser power, and the reference waveform is also shown in Fig. 2(b). When there is no laser, the time lag between the reference and transmittance waveforms is around 26.3 ps. And that time lag decreases with the increasing green laser power. As can be seen in Fig. 2(a), when the laser power is 600 mW, the transmittance waveform shifts about 0.55 ps, compared to that without laser.

 

Fig. 2 (a) Time domain transmittance waveforms of KTO crystal under different green laser power. (b) The reference waveform.

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Through a Fourier transform, we acquired the complex transmittances of KTO in frequency domain. Using an iterative program, the complex refractive index N(f) and permittivity ε(f) were calculated correspondingly. Figure 3 shows examples of complex dielectric spectra of the samples under different green laser power. The detectable frequency range is 0.1-0.8 THz (3.3-26.6 cm⁻¹), since even the thinnest bulk KTO samples are, similarly to SrTiO₃, completely opaque above ~1THz [12]. And the oscillation in the low frequency is supposed to be caused by noises. It is found that both real and imaginary parts of the permittivity decrease with increasing laser power. As can be seen in Fig. 3(a), when the laser power is 600 mW, the real part ε’(f) could be tunable by up to 3.5%. Figure 3(b) demonstrates that the imaginary part of dielectric constant also decreases a little, under the appearance of green laser.

 

Fig. 3 Frequency dependence of (a) real part and (b) imaginary part of complex dielectric constant of KTO with different green laser power at room temperature. The data points are our measured values, and the solid lines are the fit by Eq. (1).

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For the KTO samples, the nonlinear response in the THz range can be described by a generalized 4 parameter oscillator model with the factorized form of the complex permittivity, where the soft-mode frequency ω_TO1 is tunable by the external optical field:

Here ω_TOj and ω_LOj are transverse and longitudinal frequencies of the jth polar phonon, respectively, while γ_TOj and γ_LOj are their respective damping constants. ε_∞ is a cumulative contribution to the permittivity caused by higher-frequency excitations such as hard phonons and electrons.

In KTO there are three IR-active F_1u transverse optical (TO) phonon modes (with increasing frequency TO1, TO2 and TO4), called Slater, Last and Axe modes, respectively (the F_2u TO3 mode is silent). Compared to that of ω_TO1, the optical-field-induced variation of ω_TO2 and ω_TO4 are very tiny, so they can be considered as constants. In principle, the damping constants γ_TOj and γ_LOj can be weakly optical field dependent. However, the field dependence of the damping coefficients has not been found in KTO, so they are recognized as constants in our fit. In addition, the longitudinal frequencies ω_LOj and the high-frequency permittivity ε_∞ do not change with optical field. As a result, the permittivity value in the THz range then crucially depends on the soft-mode frequency ω_TO1.

In Fig. 3 the lines represent fits of the experimental data by Eq. (1). The temperature independent value of 4.3 is taken for ε_∞ [13], and the parameters in Eq. (1) are shown in Table 1, which are in good agreement with those in [5].Yuki Ichikawa et al. [3] investigated a single crystal KTO using time domain THz spectroscopy, and reported slightly lower values of ω_TO1 and γ_TO1 at 300K compared to Glinšek et al.’s results [5]. The value of ω_TO1 obtained from our fit is in good accordance with Glinšek’s results, but the value of γ_TO1 is a little lower than Glinšek’s. We believe that within the accuracy of experiments their results agree well with our data on bulk KTO.

Table 1. Parameters (cm⁻¹) in Eq. (1).

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The fitted results of ω_TO1(I) are shown in Table 2.When the green laser power varies from 0 to 600 mW, the value of ω_TO1(I) shifts from 79.02 cm⁻¹ to 80.33 cm⁻¹, which indicates the soft-mode hardening due to the anharmonic character of its potential. When the light power is 600 mW, the largest change in the soft mode frequency amounts to 1.31 cm⁻¹, which represents ~1.66% of the soft mode frequency.

Table 2. Values of ω_TO1(I) (cm⁻¹) under different light power (mW) from the fit in Eq. (1).

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For the purpose of analyzing the photo-ferroelectric properties of KTO, it is worthy to study the variation of its refractive index |Δn|, under the appearance of green laser. Figure 3 shows |Δn| and its linear fit. It is found that |Δn| is linearly proportional to the power of green laser. This property could be illustrated by the following relationship [14],

Here, the micro mechanisms behind the observed effect are discussed as follows. Generally there are only Ta⁵⁺ ions in KTO single crystals; the local defects could also result in the presence of Ta⁴⁺ ions in the samples [15,16], and thermal excitations are negligible here. When applying the 532nm cw laser, there could be an exchange of electrons between Ta⁴⁺ and Ta⁵⁺ ions, and many free electrons are generated during this process. In the illuminated area, the electrons in Ta⁴⁺ ions can hop to the conduction band, they migrate to the dark area, and then are captured by the trap level of Ta⁵⁺ there. The dominant charge driving force is supposed to be the photovoltaic effect. Drift and diffusion could also have contribution to the movement of the electrons. The migration process would lead to a redistribution of carriers. The space displacement of carriers leads to an internal space charge field shielding the external field. The internal space charge field changes the refractive index of the samples through linear electro-optic effect [14], as shown in Fig. 4.

 

Fig. 4 Laser power dependence of variation of refractive index at 0.4 THz and 0.5 THz for KTO samples. The data points are experimental data, and the solid lines are the fit by Eq. (2).

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It should be mentioned that the local defects could also result in the presence of Ta³⁺ ions in the crystals [17]. The oxidation of Ta³⁺ to Ta⁵⁺ ions could have the same effect, which does an additional contribution to the corresponding variation of refractive index. Such a variation in the dielectric response could be used in phase modulator in the terahertz range.

4. Conclusion

In summary, we have investigated the 532nm cw laser induced modulation of the dielectric properties of bulk potassium tantalate single crystals at room temperature, using terahertz time-domain spectroscopy. The variation of the dielectric properties is interpreted as the hardening of the soft mode under the appearance of 532nm cw laser. An appreciable variation of refractive index in KTO is also demonstrated with different levels of laser power. This property comes from the photovoltaic effect induced by photo-induced electrons apart from their shielding effect which leads to an internal space charge field. Thus it is presumed that these two mechanisms would complement each other, resulting in the observed photo-ferroelectric behaviors of KTO. The results of this paper provide a reference point for further development of tunable structures (such as photonic crystals and/or metamaterials), which could be controlled by an external field.