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Because the function of a single crystal of potassium tantalate niobate (KTa1-xNbxO3, KTN) is largely decided by the trapped charge density inside it, it is essential to determine its value. We quantitatively estimate the charge density using two optical analysis methods, namely by investigating KTN’s deflection angle when it is used as a deflector and by investigating KTN’s focal length when it is used as a graded-index (GRIN) lens. A strobe technique is introduced with which to perform the measurement. The charge density values under different temperature conditions are shown. These results suggest that the charge density can be determined with both methods, and is constant in a specific temperature range. The charge density value is around 80 C/m3 in our setup.
© 2014 Optical Society of America
1. Introduction
Potassium tantalate niobate crystal (KTa1-xNbxO3, KTN), is well known for its huge second-order EO (Kerr) effect [1]. After applying a constant or low-frequency electric field, the refractive index of KTN crystal has a specific distribution along the direction of the electric field, and an optical beam is deflected in the crystal [2]. When a high-frequency periodic electric field is supplied, the crystal acts as a high-speed beam scanner, and a scan speed exceeding 100 kHz is available [3]. This characteristic makes KTN crystal attractive for new applications, such as a swept light source for optical coherence tomography (OCT) [4], a fast varifocal lens [5], and a microscope [6].
The ultra-high-speed scanning phenomenon is well explained based on the proposed model with trapped charges inside the crystal [3]. Electrodes are established on the surface of a crystal as shown in Fig. 1. A DC voltage is supplied, and then electrons are injected into the crystal. Miyazu and Sasaki et al. [3, 7] have reported that the refractive index distribution in the crystal is relative to the square of the intensity of the electric field induced by the injected charges:
Consequently the deflection angle θ(x) is calculated bywhere n is the refractive index of the KTN crystal before the electrons are injected, g11 is the EO coefficient, e is the elementary electric charge, N is the electron density, L is the interaction length, x is the position of the cross-sectional direction, d is the thickness of the crystal, V is the applied voltage for beam deflection and ε is the permittivity, which is coherent with temperature [2].On one hand, Eqs. (1) and (2) reveal that the fundamental reason why the deflection angle can be changed is that the refractive index distribution can be altered by controlling the voltage. They also reveal that the deflection angle is sensitive to temperature. On the other hand, Eq. (1) indicates that KTN crystal becomes a graded-index (GRIN) lens [8] when V = 0. A beam passing through the crystal is focused as shown in Fig. 1. The beam profiles in the illustration were obtained with an InGaAs camera. As the gradient constant of a GRIN lens, the focal length of KTN f can be expressed by
It is obvious that the density of charges trapped inside the crystal eN is crucial to the deflection angle and focal length of the KTN crystal, which are the most significant parameters in terms of practical use. However, no quantitative analysis of eN has yet been reported. In this paper, we estimate eN in the KTN crystal by analyzing the deflection angle and focal length using optical analysis.
2. Charge density estimation
2.1 Estimation from deflection angle measurement
Figure 2(a) shows the schematic deflection angle measurement system. The KTN crystal is cut to a size of 1.2 mm × 3 mm × 4 mm (x × y × z), titanium electrodes are fixed to the yOz surface, and a reflection coating and anti-reflection coating are deposited to the xOy surface to form a three-path deflector [7] whose optical path length is three times the length of the crystal in the z-direction. To stabilize the Kerr effect, the crystal is embedded in a jig with a Peltier device to keep the temperature constant.
Fig. 2 (a) Illustration of deflection angle measurement system, DFB, pigtail DFB laser, FG, function generator, OS, oscilloscope, CM, cylinder lens, PH, pinhole, PD, Peltier device, PS, power supplier, CP, current probe, CM, InGaAs camera. (b) Profiles of voltage supplied to KTN crystal (black), and pulse for DFB laser output (red) in this system.
A beam with a Gaussian distribution output from a pigtail distributed feedback (DFB) laser (λ = 1.3 μm) is collimated by a microscope lens. Before the beam is transmitted through the crystal, it is resized with a 0.2 mm pinhole. A multifunction resonance power supplier connected to the electrode of the crystal provides DC ± 400 V for 10 s to inject charges and supply a high frequency AC voltage (Vp-p = 720 V, ν = 200 kHz). The displacement current in the crystal Ic is measured with a current probe (P6021, TEKTRONIX®) to determine the ε value. The camera detector, whose frame rate is no more than several tens of Hz, is placed on a three-axis automatic positioning stage. To measure a deflection angle shift with a response < 5 μs, a strobe technique is used to keep the deflection angle unchanged. With this technique, the AC voltage is monitored by an oscilloscope and drives the oscilloscope to output a square wave as a trigger, the frequency of which is same as the AC voltage, to synchronize a function generator. As the switch of the DFB laser is controlled precisely by the function generator, the laser is synchronized by the AC voltage. Moreover, by adjusting the phase delay supplied to the function generator, the beam output moment can be locked at an arbitrary phase of the AC voltage. These voltage profiles are shown in Fig. 2(b).
Equation (2) reveals that when the beam propagates through the center of the electrode gap (x = d/2), V is linearly coherent with θ, and so we focus our attention on this beam. And for experimental accuracy, we target the full scanning angle θmax, which can be expressed by:
where Vp-p is the peak-to-peak voltage of the AC voltage. The parameters used here are n = 2.21, g11 = 0.1006 m4/C2 [9], L = 12 mm, and d = 1.2 mm. Therefore, even the deflection angle is decided by the permittivity, eN, which can be calculated from the linear coefficient of the Vp-p-θmax line if we stabilize the working temperature TAC. TAC is defined as the temperature at which the AC voltage is supplied. In this experiment, the temperature TDC is fixed at 27.4 °C when the charges are injected. Because ε varies more than 10% in a 2°C range [2], we set TAC at 26.4, 27.4 and 28.4 °C in three different measurements to clarify whether the charge density is influenced by wide range permittivity change.To ensure that the experiment proceeds steadily, the measurement is started 5 minutes after the charges are injected and an AC voltage is supplied. The camera focuses on the output end of the crystal as the measurement origin z = 0. We sample the beam path by moving the camera on the z-axis from z = 0 to z = 20 mm with intervals of 2 mm (11 points), and we adjust the x-coordinate automatically every movement, according to the beam shift from the center of the detector, to ensure that the center of gravity of the beam remains located in the center of the detector from the beginning of the measurement. The deflected beam path can be acquired via linear fitting, and the slope is the tangent of the deflection angle. The results of linear fitting and a single full scanning angle measurement are shown in Fig. 3.
However, we find that not all the Vp-p-θmax curves are actually linear as shown in Fig. 4(a). This is because, when the AC voltage is applied, the temperature inside the crystal increases owing to the heat generated by dielectric dissipation, which also forces ε to change during the measurement [10]. As a result, ε and V cannot be analyzed separately. Nevertheless, we note that Ic can be expressed by
where S is the electrode surface. Equations (4) and (5) demonstrate that we are able to ignore the diversity of ε by using Ic directly. Consequently, θmax can also be expressed bywhere B is the coefficient calculated from fitting the Ic-θmax line. The angle distribution results are shown in Fig. 4(b). Although the working temperatures are different, the points almost all lie along a line. As a result,and the dielectric constant εr and the results of B and eN measured at different working temperature are shown in Table 1.Fig. 4 Results for deflection angle distribution at different temperatures. (a) Nonlinear relation between deflection angle and AC voltage. (b) Linear distribution by relating displacement current and deflection angle.
Table 1. Results of Charge Density eN from Deflection Angle Measurement
Table 1 demonstrates that although the permittivity alters greatly, the slope of Ic-θmax line B remains almost unchanged, and the charge density in the crystal is also constant. This means that after injection the charge density is completely unaffected by the diversity of the permittivity.
2.2 Estimation from focal length measurement
Because KTN is very thin, all the incident beams can be regarded as near axis beams (h = x- d/2 ; 0). The incident wave is assumed to be a plane wave, and it is distorted into a wave with a curved surface due to the lens effect of KTN. According to the laws of physical optics, the radius of curvature of an external wave front is also the focal length f. In this case, the refractive index is constant in the y-direction, so f is only decided by the wave front shape in the xOz section z = F(h). An analysis of the wave front using analytic geometry is shown in Fig. 5(a). As each point in the wave front moves forward along a normal vector, for example , there is F’(hi) = tan(α(hi)), where F’(hi) is the tangent of the wave front curve at hi, α(hi) is the angle between the beam exiting the ti-position and the z-axis, O is the principal point, P is the tangent point, Q is the center of curvature, and R is the cross point of the tangent and the t-axis. Thus, the length of OQ is the focal length, and we can acquire α(h) by measuring a large number of beams with different tilts and obtain the curve formula by integrating F’(h). Then, f can be expressed by
Fig. 5 Principle of focal length measurement method. (a) Wave front curve analysis by analytic geometry. (b) Experimental method for focal length measurement.
The same system and method of beam measurement mentioned in Section 2.1 are used in this experiment. From Eq. (3), f should be incoherent with permittivity, nevertheless, to provide a contrast with the results acquired from deflection angle measurement, f and eN are also measured at different temperatures. Moreover, as shown by the schematic of the measurement in Fig. 5(b), to realize an incident beam from a different height, a two-axis automatic positioning stage is added to the crystal jig. The output moments of the beams are locked to phase 0, when V is an instantaneous 0 V, to ensure that the crystal acts as a GRIN lens. The incident heights are set at t = 0 mm, ± 0.15 mm, and ± 0.3 mm. The beam measurement results obtained at TAC = 27.4°C are shown in Fig. 6(a) as an example. The figure shows that beams incident on the KTN block at different heights have different tilts α(h) and cross over each other at a specific location, which is the focal point.
Fig. 6 Approach for focal length of crystal. (a) Output beams from different incident heights (TAC = 27.4°C). (b) Cubic polynomial fitting of tilt of beams from different heights.
α(h) is fitted by a linear function as
where ai (i = 0, 1) is the coefficient of the linear function, and all the results are shown in Fig. 6(b). By deduction from Eqs. (8) and (9), we find that the focal length is available as follows:Then by resolving Eq. (3), the results of eN estimation can be obtained.The results are shown in Table 2. They confirm that f is independent of permittivity as we expected and the fact that the injected charge density has no effect on permittivity is again proven.
Table 2. Results of Charge Density eN from Focal Length Measurement
3. Conclusion
The trapped charge density in a KTN crystal was successfully quantitatively estimated by two methods: the measurement of the maximum deflection angle and the measurement of the focal lens as a GRIN lens, where TDC = 27.4 °C. Both methods provided results of around 80 C/m3. Moreover, as the results show, the charge density is very stable despite changes in temperature even in a 2 °C range, which means that the permittivity of the crystal was greatly changed. However, a comparison of Tables 1 and 2 shows that there is an approximately 10% difference between the two charge density results, while we expected them to be the same. We consider that the charge density distribution in the crystal, which is assumed to be constant, is in fact not completely homogeneous, and this is why the difference exists. Especially, the beam deviation during the focal length measurement as seen in Fig. 6(a) suggests the nonuniformity of the charge density distribution. The direction of this beam deviation depends on the last state of the DC voltage and its sign applied to KTN crystal. This result implies the improvement of uniformity by choosing the appropriate DC voltage.
Since charge density is proven be essential to the function of KTN crystal, its value should be known when designing a device. Also, these results suggest that KTN crystal works sufficiently steadily under the control of a Peltier device in practical use. Finally, the estimation of the charge density described in this work could be helpful for clarifying the origin of the electron trap.
References and links
1. J. van Raalte, “Linear electro-optic effect in Ferroelectric KTN,” J. Opt. Soc. Am. 57(5), 671–674 (1967). [CrossRef]
2. K. Nakamura, J. Miyazu, Y. Sasaki, T. Imai, M. Sasaura, and K. Fujiura, “Space-charge-controlled electro-optic effect: Optical beam deflection by electro-optic effect and space-charge-controlled electrical conduction,” J. Appl. Phys. 104(1), 013105 (2008). [CrossRef]
3. J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, and K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011). [CrossRef]
4. Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, and M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012). [CrossRef]
5. T. Imai, Y. Takayama, J. Miyazu, and J. Kobayashi, “Performance of varifocal lenses using KTa1-xNbxO3 crystals with response times faster than 2 μs,” Electron. Lett. 49(23), 1470–1471 (2013). [CrossRef]
6. K. Isobe, H. Kawano, A. Kumagai, A. Miyawaki, and K. Midorikawa, “Implementation of spatial overlap modulation nonlinear optical microscopy using an electro-optic deflector,” Biomed. Opt. Express 4(10), 1937–1945 (2013). [CrossRef] [PubMed]
7. Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, and K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013). [CrossRef]
8. J. Arai, F. Okano, H. Hoshino, and I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. 37(11), 2034–2045 (1998). [CrossRef] [PubMed]
9. J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, “Electrooptic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964). [CrossRef]
10. S. Toyoda, M. Ueno, S. Yagi, and J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013). [CrossRef]
