## Trapped charge density analysis of KTN crystal by beam path measurement |

Optics Express, Vol. 22, Issue 7, pp. 7783-7789 (2014)

http://dx.doi.org/10.1364/OE.22.007783

Acrobat PDF (960 KB)

### Abstract

Because the function of a single crystal of potassium tantalate niobate (KTa_{1-}* _{x}*Nb

*O*

_{x}_{3}, 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/m

^{3}in our setup.

© 2014 Optical Society of America

## 1. Introduction

_{1-}

*Nb*

_{x}*O*

_{x}_{3}, KTN), is well known for its huge second-order EO (Kerr) effect [1

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 KTa_{1-x}Nb_{x}O_{3} 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 KTa_{1-x}Nb_{x}O_{3} 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]

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 KTa_{1-x}Nb_{x}O_{3} crystals,” Appl. Phys. Express **4**(11), 111501 (2011). [CrossRef]

*et al.*[3

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 KTa_{1-x}Nb_{x}O_{3} crystals,” Appl. Phys. Express **4**(11), 111501 (2011). [CrossRef]

7. Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, and K. Naganuma, “Resolution enhancement of KTa_{1-x}Nb_{x}O_{3} electro-optic deflector by optical beam shaping,” Appl. Phys. Express **6**(10), 102201 (2013). [CrossRef]

*θ*(

*x*) is calculated bywhere

*n*is the refractive index of the KTN crystal before the electrons are injected,

*g*

_{11}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

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]

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]

*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

*f*can be expressed by

*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

*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

7. Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, and K. Naganuma, “Resolution enhancement of KTa_{1-x}Nb_{x}O_{3} electro-optic deflector by optical beam shaping,” Appl. Phys. Express **6**(10), 102201 (2013). [CrossRef]

*z*-direction. To stabilize the Kerr effect, the crystal is embedded in a jig with a Peltier device to keep the temperature constant.

*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 (

*V*= 720 V,

_{p-p}*ν =*200 kHz). The displacement current in the crystal

*I*is measured with a current probe (P6021, TEKTRONIX

_{c}^{®}) 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).

*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

*θ*, which can be expressed by:where

_{max}*V*is the peak-to-peak voltage of the AC voltage. The parameters used here are

_{p-p}*n*= 2.21,

*g*= 0.1006 m

_{11}^{4}/C

^{2}[9

9. J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, “Electrooptic properties of some ABO_{3} perovskites in the paraelectric phase,” Appl. Phys. Lett. **4**(8), 141–143 (1964). [CrossRef]

*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

*V*line if we stabilize the working temperature

_{p-p}-θ_{max}*T*.

_{AC}*T*is defined as the temperature at which the AC voltage is supplied. In this experiment, the temperature

_{AC}*T*is fixed at 27.4 °C when the charges are injected. Because

_{DC}*ε*varies more than 10% in a 2°C range [2

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]

*T*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.

_{AC}*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.

*V*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

_{p-p}-θ_{max}*ε*to change during the measurement [10

10. S. Toyoda, M. Ueno, S. Yagi, and J. Kobayashi, “First estimation of power consumption of KTa_{x}Nb_{1-x}O_{3} crystal upon application of high voltage under high frequency,” Appl. Phys. Express **6**(12), 122601 (2013). [CrossRef]

*ε*and

*V*cannot be analyzed separately. Nevertheless, we note that

*I*can be expressed bywhere

_{c}*S*is the electrode surface. Equations (4) and (5) demonstrate that we are able to ignore the diversity of

*ε*by using

*I*directly. Consequently,

_{c}*θ*can also be expressed bywhere

_{max}*B*is the coefficient calculated from fitting the

*I*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

_{c}-θ_{max}*ε*and the results of

_{r}*B*and

*eN*measured at different working temperature are shown in Table 1.

*I*line

_{c}-θ_{max}*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

*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

*F’*(

*h*) = tan(

_{i}*α*(

*h*)), where

_{i}*F’*(

*h*) is the tangent of the wave front curve at

_{i}*h*,

_{i}*α*(

*h*) is the angle between the beam exiting the

_{i}*t*-position and the

_{i}*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

*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

*T*= 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

_{AC}*α*(

*h*) and cross over each other at a specific location, which is the focal point.

*α*(

*h*) is fitted by a linear function aswhere

*a*(

_{i}*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.

*f*is independent of permittivity as we expected and the fact that the injected charge density has no effect on permittivity is again proven.

## 3. Conclusion

*T*= 27.4 °C. Both methods provided results of around 80 C/m

_{DC}^{3}. 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.

## References and links

1. | J. van Raalte, “Linear electro-optic effect in Ferroelectric KTN,” J. Opt. Soc. Am. |

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. |

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 KTa |

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. |

5. | T. Imai, Y. Takayama, J. Miyazu, and J. Kobayashi, “Performance of varifocal lenses using KTa |

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 |

7. | Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, and K. Naganuma, “Resolution enhancement of KTa |

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. |

9. | J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, “Electrooptic properties of some ABO |

10. | S. Toyoda, M. Ueno, S. Yagi, and J. Kobayashi, “First estimation of power consumption of KTa |

**OCIS Codes**

(230.2090) Optical devices : Electro-optical devices

(260.1180) Physical optics : Crystal optics

**ToC Category:**

Electrooptics

**History**

Original Manuscript: December 26, 2013

Revised Manuscript: January 30, 2014

Manuscript Accepted: January 30, 2014

Published: March 27, 2014

**Citation**

Chenhui Huang, Yuzo Sasaki, Jun Miyazu, Seiji Toyoda, Tadayuki Imai, and Junya Kobayashi, "Trapped charge density analysis of KTN crystal by beam path measurement," Opt. Express **22**, 7783-7789 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-7783

Sort: Year | Journal | Reset

### References

- J. van Raalte, “Linear electro-optic effect in Ferroelectric KTN,” J. Opt. Soc. Am. 57(5), 671–674 (1967). [CrossRef]
- K. Nakamura, J. Miyazu, Y. Sasaki, T. Imai, M. Sasaura, 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]
- J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011). [CrossRef]
- Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012). [CrossRef]
- T. Imai, Y. Takayama, J. Miyazu, 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]
- K. Isobe, H. Kawano, A. Kumagai, A. Miyawaki, 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]
- Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013). [CrossRef]
- J. Arai, F. Okano, H. Hoshino, 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]
- J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, S. H. Wemple, “Electrooptic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964). [CrossRef]
- S. Toyoda, M. Ueno, S. Yagi, 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]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.