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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 13 — Jun. 18, 2012
  • pp: 13833–13840
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Simultaneous measurement of electro-optical and converse-piezoelectric coefficients of PMN-PT ceramics

Pingping Xiao, Xianping Wang, Jingjing Sun, Meizhen Huang, Xianfeng Chen, and Zhuangqi Cao  »View Author Affiliations


Optics Express, Vol. 20, Issue 13, pp. 13833-13840 (2012)
http://dx.doi.org/10.1364/OE.20.013833


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Abstract

A new scheme is proposed to measure the electro-optical (EO) and converse-piezoelectric (CPE) coefficients of the PMN-PT ceramics simultaneously, in which the PMN-PT ceramics acts as the guiding layer of a symmetrical metal-cladding waveguide. As the applied electric field exerts on the waveguide, the effective refractive index (RI) (or synchronous angle) can be effectively tuned from a selected mode to another adjacent mode owing to the high sensitivity and the small spacing of the ultra-high order modes. Subsequently, a correlation between EO and CPE coefficients is established. With this correlation and the measurement of the effective RI change to the applied voltage, the quadratic EO and CPE coefficients of PMN-PT ceramics are obtained simultaneously. The obtained results are further checked by fitting the variations of effective RI to a quadratic function. Our measurement method can be extended to a wide range of other materials.

© 2012 OSA

1. Introduction

The development of new optical materials with large EO and CPE coefficients is currently of great interest because of the possibility to further minimize device size and reduce operation voltage [1

1. G. H. Haertling, “PLZT electro-optic materials and applications – a review,” Ferroelectrics 75(1), 25–55 (1987). [CrossRef]

8

8. Y.-L. Lu, B. Gaynor, C. Hsu, G. Jin, M. Cronin-Golomb, F. Wang, J. Zhao, S.-Q. Wang, P. Yip, and A. J. Drehman, “Structural and electro-optic properties in lead magnesium niobate titanate thin films,” Appl. Phys. Lett. 74(20), 3038–3040 (1999). [CrossRef]

]. Although the lanthanum-modified lead zirconate titanate (PLZT) [1

1. G. H. Haertling, “PLZT electro-optic materials and applications – a review,” Ferroelectrics 75(1), 25–55 (1987). [CrossRef]

] transparent ceramics exhibits much higher EO and CPE effect than that of LiNbO3 crystal, its significant electric hysteresis [2

2. T. Tamura, K. Matsuura, H. Ashida, K. Kondo, and S. Otani, “Hysteresis variations of (Pb, La)(Zr,Ti)O3 capacitors baked in a hydrogen atmosphere,” Appl. Phys. Lett. 74(22), 3395–3397 (1999). [CrossRef]

] is unsuitable to build the precision apparatuses. Fortunately, the newly presented (1-x)Pb(Mg1/3Nb2/3Nb2/3)O3-xPbTiO3 (PMN-PT) ceramics [3

3. H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, and Y. Wang, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380–394 (2005). [CrossRef]

], which is transparent from 500 to 7000 nm of the light wavelength, effectively resolves the issues of hysteresis and possesses a morphotropic phase boundary (MPB) [4

4. S. W. Choi, T. R. Shrout, S. J. Jang, and A. S. Bhalla, “Morphotropic phase boundary in Pb(Mg1/3Nb2/3)O3-PbTiO3 system,” Mater. Lett. 8(6-7), 253–255 (1989). [CrossRef]

,5

5. R. Zhang, B. Jiang, and W. Cao, “Elastic, piezoelectric, and dielectric properties of multidomain 0.67 Pb(Mg1/3Nb2/3)O3-0.33PbTiO3 single crystals,” J. Appl. Phys. 90(7), 3471–3475 (2001). [CrossRef]

] between the tetragonal and rhombohedral phases. Its anomalously high EO and CPE properties around the MPB are understood as a result of enhanced polarizability arising from the coupling between the two above-mentioned phases [6

6. B. Noheda, D. E. Cox, G. Shirane, J. Gao, and Z. G. Ye, “Phase diagram of the ferroelectric relaxor (1-x)PbMg1/3Nb2/3O3-xPbTiO3,” Phys. Rev. B 66(5), 054104 (2002). [CrossRef]

,7

7. O. Noblanc, P. Gaucher, and G. Calvarin, “Structural and dielectric studies of Pb(Mg1/3Nb2/3)O3-PbTiO3 ferroelectric solid solutions around the morphotropic boundary,” J. Appl. Phys. 79(8), 4291–4297 (1996). [CrossRef]

]. Moreover, no consideration of the crystalline orientation is required [8

8. Y.-L. Lu, B. Gaynor, C. Hsu, G. Jin, M. Cronin-Golomb, F. Wang, J. Zhao, S.-Q. Wang, P. Yip, and A. J. Drehman, “Structural and electro-optic properties in lead magnesium niobate titanate thin films,” Appl. Phys. Lett. 74(20), 3038–3040 (1999). [CrossRef]

], as PMN-PT is polycrystalline and polarization independent. Consequently, the PMN-PT transparent ceramics offers promise of widespread applications in the optical communication system, such as optical limiter [9

9. Y. L. Lu and C. Gao, “Optical limiting in lead magnesium niobate-lead titanate multilayers,” Appl. Phys. Lett. 92(12), 121109 (2008). [CrossRef]

], polarization controller [10

10. B. C. Lim, P. B. Phua, W. J. Lai, and M. H. Hong, “Fast switchable electro-optic radial polarization retarder,” Opt. Lett. 33(9), 950–952 (2008). [CrossRef] [PubMed]

] and optical switch [11

11. Y. K. Zou, Q. S. Chen, R. Zhang, K. K. Li, and H. Jiang, “Low voltage, high repetition rate electro-optic Q-switch,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper CTuZ5.

,12

12. L. Qiao, Q. Ye, J. L. Gan, H. W. Cai, and R. H. Qu, “Optical characteristics of transparent PMNT ceramic and its application at high speed electro-optic switch,” Opt. Commun. 284(16-17), 3886–3890 (2011). [CrossRef]

], etc.

Despite the continuous fundamental investigations and extensive utilizations, the values of EO and CPE coefficients of PMN-PT have not been completely known. These complete properties could lay the groundwork for the reliable simulation packages which makes the device design process more efficient. EO coefficients can be determined by one-beam-ellipsometric technique [13

13. Y. T. Lin, B. Ren, X. Y. Zhao, D. Zhou, J. Chen, X. B. Li, H. Q. Xu, D. Lin, and H. S. Luo, “Large quadratic electro-optic properties of ferroelectric base 0.92Pb(Mg1/3Nb2/3)O3-0.08PbTiO3 single crystal,” J. Alloy. Comp. 507(2), 425–428 (2010). [CrossRef]

,14

14. C. J. He, W. W. Ge, X. Y. Zhao, H. Q. Xu, H. S. Luo, and Z. X. Zhou, “Wavelength dependence of electro-optic effect in tetragonal lead magnesium niobate lead titanate single crystals,” J. Appl. Phys. 100(11), 113119 (2006). [CrossRef]

] for measuring the induced phase retardation between two orthogonal plane-polarized lights and by two-beam-interferometric arrangements [15

15. C. J. He, Z. X. Zhou, D. J. Liu, X. Y. Zhao, and H. S. Luo, “Photorefractive effect in relaxor ferroelectric 0.62Pb(Mg1/3Nb2/3)O3-0.38PbTiO3 single crystal,” Appl. Phys. Lett. 89(26), 261111 (2006). [CrossRef]

], such as Mach-Zehnder and Michelson interferometers, for measuring the interference between two parallel plane-polarized lights. On the other hand, the CPE coefficients are always determined from the resonance frequencies by the IEEE standard technique [16

16. S. E. Park and T. R. Shrout, “Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals,” J. Appl. Phys. 82(4), 1804–1811 (1997). [CrossRef]

]. Diverse as measurement techniques are, they can be characterized by one common shortage, namely involving only one effect. However, when an electric field is applied to PMN-PT ceramics, the changes in the optical path length consists of both the change in refractive index (RI) due to EO effect and the change in sample thickness resulting from the CPE effect. Therefore, it is highly expected that a simple method is capable of measuring the EO and CPE coefficients of PMN-PT ceramics simultaneously.

Recently, it is well established that the ultrahigh-order modes excited in the symmetrical metal-cladding waveguide (SMCW) [17

17. H. G. Li, Z. Q. Cao, H. F. Lu, and Q. S. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83(14), 2757–2759 (2003). [CrossRef]

20

20. F. Chen, Z. Q. Cao, Q. S. Shen, X. X. Deng, B. M. Duan, W. Yuan, M. H. Sang, and S. Q. Wang, “Picometer displacement sensing using the ultrahigh-order modes in a submillimeter scale optical waveguide,” Opt. Express 13(25), 10061–10065 (2005). [CrossRef] [PubMed]

] are highly sensitive to the changes of RI and thickness within the guiding layer. That is because the light field confined in the guiding layer is not in the form of evanescent wave but oscillating wave. The SMCW-based oscillating wave sensor has been achieved experimentally, yielding a detection limitation of 8.8×108in RI units [18

18. H. F. Lu, Z. Q. Cao, H. G. Li, and Q. S. Shen, “Study of ultrahigh-order modes in a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 85(20), 4579–4581 (2004). [CrossRef]

] and 3.3 pm in thickness [19

19. J. H. Gu, G. Chen, Z. Q. Cao, and Q. S. Shen, “An intensity measurement refractometer based on a symmetric metal-clad waveguide structure,” J. Phys. D Appl. Phys. 41(18), 185105 (2008). [CrossRef]

]. In this paper, we take advantage of the high sensitivity of the ultra-high order modes in response to the change of the guiding layer parameters and the small separation between two adjacent ultra-high order modes to establish a correlation between EO and CPE coefficients of PMN-PT ceramics. With this correlation and the measurement of the effective RI change to the applied voltage, the quadratic EO and CPE coefficients of PMN-PT ceramics are obtained simultaneously.

2. Structure and principle

The schematic layout of the SMCW for simultaneously measuring EO and CPE coefficients of PMN-PT ceramics (provided by Boston Applied Technology Inc.) is illustrated in Fig. 1
Fig. 1 Structure of SMCW. The PMN-PT ceramics is sandwiched by two sliver films which act as the cladding and the electrodes to supply electric field.
. A thin sliver film and a relative thick sliver film are deposited on the top and bottom side of the PMN-PT ceramics by the thermal evaporation technology, and functioned as the coupling layer and substrate, respectively. Moreover, these two sliver films are also employed as electrodes to supply electrical field and thus the optical properties of the guiding layer can be electrically controlled. From top to bottom, the refractive index (dielectric coefficient) and thickness of the SMCW structure are denoted by nj (εj), hj (j=1,2,3), respectively. Because of symmetrical metal cladding, the effective index of guided modes can be in the range of [0, 1], it is uniquely capable to couple light directly from free space into SMCW [17

17. H. G. Li, Z. Q. Cao, H. F. Lu, and Q. S. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83(14), 2757–2759 (2003). [CrossRef]

]. Furthermore, owing to the millimeter scale thickness of the guiding layer, the waveguide can accommodate tens of thousand modes. Dispersion equation of the mth ultra-high order mode (m>1000) can then be simply approximated as [18

18. H. F. Lu, Z. Q. Cao, H. G. Li, and Q. S. Shen, “Study of ultrahigh-order modes in a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 85(20), 4579–4581 (2004). [CrossRef]

]
κ2mh2=mπ,m=0,1,2,
(1)
where κ2m=k02n22βm2 is the vertical propagation constant,k0=2π/λ is the wavenumber with light wavelengthλ in free space, and βm=k0Nm is the transverse propagation constant with the effective index Nm of the guided modes. The resonance excitation of the guided mode occurs at
βm=k0nairsinθm,
(2)
where nair represents the RI of the air, θm is the incident angle, and m is the mode order. Two typical ultrahigh-order modes (their mode orders are denoted by m+1 and m) with small N are shown in Fig. 2
Fig. 2 (Color online) Theoretical variation of synchronous angles in response to the applied voltage.
. The used calculating parameters are as follows: nair=1.0, n2=2.620, ε1=ε3=18.6+0.5i, h1=39nm, h2=3.0mm, h3=300nm and λ=632.8nm. The RI of PMN-PT ceramics was obtained from the material supplier (provided by Boston Applied Technology Inc.). The thickness and the complex dielectric permittivity of the top silver film are determined by the double-wavelength method [21

21. W. P. Chen and J. M. Chen, “Use of surface plasma waves for determination of the thickness and optical constants of thin metallic films,” J. Opt. Soc. Am. 71(2), 189–191 (1981). [CrossRef]

]. When an electric field is applied, the RI and thickness of PMN-PT ceramics is altered by the EO and CPE effect, and then the synchronous angles (θm+1,θm) of the two ultrahigh-order modes are shifted to a new position (θm+1,θm).

According to differential principle and Eq. (1), one can obtain the variation of the effective RI as
ΔN=n2NΔn2+n22N2Nh2Δh2,
(3)
where Δn2 and Δh2 are the electric field-induced changes in the RI and thickness of PMN-PT ceramics, respectively. It is seen that the effective RI of the ultrahigh-order modes, which are excited at very small incident angles, i.e. N0, shows a high sensitivity to Δn2 and Δh2.

The birefringence Δn2 of an electro-optic material in the presence of an electric field can be described by the equation
Δn2=Δn20n232[γ(Vh2)+S(Vh2)2],
(4)
where Δn20 is the birefringence of the material in the absence of an electric field, γ and S is the linear Pockels EO coefficient and the quadratic Kerr EO coefficient, respectively, and Vis the applied voltage. Since PMN-PT is optical isotropic in the absence of an electric field [10

10. B. C. Lim, P. B. Phua, W. J. Lai, and M. H. Hong, “Fast switchable electro-optic radial polarization retarder,” Opt. Lett. 33(9), 950–952 (2008). [CrossRef] [PubMed]

,22

22. K. K. Li, Y. Lu, and Q. Wang, “Electro-optic ceramic material and device,” U.S. patent 6, 890, 874B1 (2005).

], Δn20 and γ are essentially zero. If the incident light is TE polarized, the RI change of the PMN-PT ceramics can be simplified from Eq. (4)
Δn2=12n23S33(Vh2)2,
(5)
where S33 is a component of the quadratic EO coefficient. For the case of the linear electro-optical ceramics, the similar analysis process can be easily obtained.

The thickness change of the PMN-PT ceramics is expressed as
Δh2=d33h2(Vh2),
(6)
where d33 is a component of CPE coefficient. By combining Eq. (5) and Eq. (6), the variation of effective RI in Eq. (3) can be rewritten as
ΔN=AV2+BV,
(7)
where
{A=12n24Nh22S33B=n22N2Nh2d33
(8)
In Eq. (7), n2 and h2 are the known quantities, Vis the applied electric voltage, effective RI N=nairsinθ and ΔN can be detected in the experiment. S33 and d33 are quantities to be determined. It is clear that Eq. (7) can be solved only if there is a correlation between S33 and d33.

Because of the high sensitivity with N0 of the ultra-high order modes and small separation between two adjacent modes, it is possible that exerting a certain critical voltage Vc to shift the synchronous angle of the (m+1)th mode fromθm+1 to θm which is just that of mth mode in the case of zero applied electric field. The new dispersion equation of the (m+1)th mode under the critical voltage is then expressed by
κ2m+1(h2+Δh2)=(m+1)π,
(9)
where κ2m+1=k02(n2+Δn2)2βm+12. On subtracting Eq. (1) from Eq. (9), we obtain
(κ2m+1κ2m)h2+κ2m+1Δh2=π,
(10)
Since βm+1=βm due to θm+1=θm, and the numerical simulation verifies that Δn2 and Δh2h2 are less than 104 order of magnitude as θm+1 shifted to θm. In this case, after neglecting the higher-order small quantities one yields
κ2m+1κ2m=n2k02Δn2κ2,
(11)
By combining Eqs. (5)-(6) and Eqs. (10)-(11), a new correlation between quadratic EO and CPE coefficients can be cast in the form
k022κ2n24h2(Vch2)2S33+κ2h2(Vch2)d33=π,
(12)
where Δn2=12n23S33(Vch2)2and Δh2=d33h2(Vch2) are the corresponding changes in the RI and thickness of the PMN-PT ceramics with applied critical voltage Vc.

Substituting Eq. (12) into Eq. (7) and using Eq. (8), the quadratic EO and CPE coefficients can be determined with the detection values of A and B. In order to assure the reliability of the scheme, the obtained results are further checked by fitting the experiment data to the quadratic function Eq. (7).

3. Experiment and discussion

The optical arrangement for simultaneously measuring the EO and CPE coefficients of PMN-PT ceramics based on the SMCW structure is shown in Fig. 3
Fig. 3 Experiment arrangement for simultaneously measuring the EO and CPE coefficients of PMN-PT ceramics. PD: photodiode.
. A polarizer and two apertures with diameters of 1 mm are subsequently placed about 0.5 m apart. An incident light from a He-Ne laser passes through them to be TE polarized and further collimated. We used a PMN-PT ceramics with dimensions of 5.62mm×4.20mm×3.00mm(length×width×thickness), which is deposited with two sliver films and firmly mounted on a θ/2θ goniometer, and the intensity of the reflected light is detected by a photodiode (PD). A home-made software allows personal computer to control the goniometer and record a series of resonance dips corresponding to the excited guide modes.

In the experiment, the angle of incidence is set around one selected ultrahigh-order mode (θ=4.537o), because the guide mode excited at small angle can offer a higher sensitivity [18

18. H. F. Lu, Z. Q. Cao, H. G. Li, and Q. S. Shen, “Study of ultrahigh-order modes in a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 85(20), 4579–4581 (2004). [CrossRef]

]. The measured resonance dip as a function of the angle of incidence for various applied voltages is shown Fig. 4
Fig. 4 (Color online) Measured resonance dips as a function of the angle of incidence for various applied voltages.
. Because of Δn2>0 and Δh2<0 at any exerted voltage, variation of the resonance peak induced by EO and CPE effects partially compensates one another. Under low voltages, the resonance dip shifts to the left side because the contribution of the CPE effect is greater than that of EO effect (i.e. ΔN<0). As the applied voltages are larger than 400V, the resonance dip shifts to the right side since the contribution of the EO effect in this case is predominated (i.e. ΔN>0)because the EO effect is a quadraticfunction of voltage. The critical voltage Vcfor the resonance dip of the (m+1)th mode tends to that of the adjacent (mth)mode (under zero-field) is about 900V. By using Eqs. (7)-(8) and Eq. (12), and using Eq. (8), we obtain the quadratic EO coefficient S33=2.24×1016m2/V2 and the CPE coefficient d33=96pm/Vof PMN-PT ceramics. In Fig. 4 it is found that the minimum reflectance and the FWHM of the resonance dips gradually increase with the increasing applied voltages, it is perhaps in virtue of an electro-absorptive effect in PMN-PT ceramics [23

23. M. Cuniot-Ponsard, J. M. Desvignes, A. Bellemain, and F. Bridou, “Simulatneous characterization of the electro-optic, converse-piezoelectirc, and electroabsorptive effects in epitaxial (Sr, Ba)Nb2O6 thin films,” J. Appl. Phys. 109(1), 014107 (2011). [CrossRef]

]. That is because the radiative damping and intrinsic damping of the waveguide structure, which are two factors to determine the minimum reflectance and the FWHM of the resonance dips [24

24. K. Kurihara and K. Suzuki, “Theoretical understanding of an absorption-based surface plasmon resonance sensor based on Kretchmann’s theory,” Anal. Chem. 74(3), 696–701 (2002). [CrossRef] [PubMed]

], are functions of the extinction coefficient κ of PMN-PT ceramics that can altered by the electro-absorptive effect.

4. Conclusion

In conclusion, a simple method to measure the EO and CPE coefficients of PMN-PT ceramics simultaneously has been described. This method is based on the high sensitivity to the RI and the thickness of the guiding layer of the ultra-high order modes and the small separation between two adjacent ultra-high order modes. By exerting a critical voltage on the PMN-PT ceramics, a resonance dip can reach the position of the adjacent mode. In this way, we established a correlation between EO and CPE coefficients. Measurement has been performed for a PMN-PT ceramics, and the results are in good agreements with the data obtained by other methods.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 61168002), and opening foundation of the State Key Laboratory of Advanced Optical Communication Systems and Networks (Grant No. 2011GZKF031105).

References and links

1.

G. H. Haertling, “PLZT electro-optic materials and applications – a review,” Ferroelectrics 75(1), 25–55 (1987). [CrossRef]

2.

T. Tamura, K. Matsuura, H. Ashida, K. Kondo, and S. Otani, “Hysteresis variations of (Pb, La)(Zr,Ti)O3 capacitors baked in a hydrogen atmosphere,” Appl. Phys. Lett. 74(22), 3395–3397 (1999). [CrossRef]

3.

H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, and Y. Wang, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380–394 (2005). [CrossRef]

4.

S. W. Choi, T. R. Shrout, S. J. Jang, and A. S. Bhalla, “Morphotropic phase boundary in Pb(Mg1/3Nb2/3)O3-PbTiO3 system,” Mater. Lett. 8(6-7), 253–255 (1989). [CrossRef]

5.

R. Zhang, B. Jiang, and W. Cao, “Elastic, piezoelectric, and dielectric properties of multidomain 0.67 Pb(Mg1/3Nb2/3)O3-0.33PbTiO3 single crystals,” J. Appl. Phys. 90(7), 3471–3475 (2001). [CrossRef]

6.

B. Noheda, D. E. Cox, G. Shirane, J. Gao, and Z. G. Ye, “Phase diagram of the ferroelectric relaxor (1-x)PbMg1/3Nb2/3O3-xPbTiO3,” Phys. Rev. B 66(5), 054104 (2002). [CrossRef]

7.

O. Noblanc, P. Gaucher, and G. Calvarin, “Structural and dielectric studies of Pb(Mg1/3Nb2/3)O3-PbTiO3 ferroelectric solid solutions around the morphotropic boundary,” J. Appl. Phys. 79(8), 4291–4297 (1996). [CrossRef]

8.

Y.-L. Lu, B. Gaynor, C. Hsu, G. Jin, M. Cronin-Golomb, F. Wang, J. Zhao, S.-Q. Wang, P. Yip, and A. J. Drehman, “Structural and electro-optic properties in lead magnesium niobate titanate thin films,” Appl. Phys. Lett. 74(20), 3038–3040 (1999). [CrossRef]

9.

Y. L. Lu and C. Gao, “Optical limiting in lead magnesium niobate-lead titanate multilayers,” Appl. Phys. Lett. 92(12), 121109 (2008). [CrossRef]

10.

B. C. Lim, P. B. Phua, W. J. Lai, and M. H. Hong, “Fast switchable electro-optic radial polarization retarder,” Opt. Lett. 33(9), 950–952 (2008). [CrossRef] [PubMed]

11.

Y. K. Zou, Q. S. Chen, R. Zhang, K. K. Li, and H. Jiang, “Low voltage, high repetition rate electro-optic Q-switch,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper CTuZ5.

12.

L. Qiao, Q. Ye, J. L. Gan, H. W. Cai, and R. H. Qu, “Optical characteristics of transparent PMNT ceramic and its application at high speed electro-optic switch,” Opt. Commun. 284(16-17), 3886–3890 (2011). [CrossRef]

13.

Y. T. Lin, B. Ren, X. Y. Zhao, D. Zhou, J. Chen, X. B. Li, H. Q. Xu, D. Lin, and H. S. Luo, “Large quadratic electro-optic properties of ferroelectric base 0.92Pb(Mg1/3Nb2/3)O3-0.08PbTiO3 single crystal,” J. Alloy. Comp. 507(2), 425–428 (2010). [CrossRef]

14.

C. J. He, W. W. Ge, X. Y. Zhao, H. Q. Xu, H. S. Luo, and Z. X. Zhou, “Wavelength dependence of electro-optic effect in tetragonal lead magnesium niobate lead titanate single crystals,” J. Appl. Phys. 100(11), 113119 (2006). [CrossRef]

15.

C. J. He, Z. X. Zhou, D. J. Liu, X. Y. Zhao, and H. S. Luo, “Photorefractive effect in relaxor ferroelectric 0.62Pb(Mg1/3Nb2/3)O3-0.38PbTiO3 single crystal,” Appl. Phys. Lett. 89(26), 261111 (2006). [CrossRef]

16.

S. E. Park and T. R. Shrout, “Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals,” J. Appl. Phys. 82(4), 1804–1811 (1997). [CrossRef]

17.

H. G. Li, Z. Q. Cao, H. F. Lu, and Q. S. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83(14), 2757–2759 (2003). [CrossRef]

18.

H. F. Lu, Z. Q. Cao, H. G. Li, and Q. S. Shen, “Study of ultrahigh-order modes in a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 85(20), 4579–4581 (2004). [CrossRef]

19.

J. H. Gu, G. Chen, Z. Q. Cao, and Q. S. Shen, “An intensity measurement refractometer based on a symmetric metal-clad waveguide structure,” J. Phys. D Appl. Phys. 41(18), 185105 (2008). [CrossRef]

20.

F. Chen, Z. Q. Cao, Q. S. Shen, X. X. Deng, B. M. Duan, W. Yuan, M. H. Sang, and S. Q. Wang, “Picometer displacement sensing using the ultrahigh-order modes in a submillimeter scale optical waveguide,” Opt. Express 13(25), 10061–10065 (2005). [CrossRef] [PubMed]

21.

W. P. Chen and J. M. Chen, “Use of surface plasma waves for determination of the thickness and optical constants of thin metallic films,” J. Opt. Soc. Am. 71(2), 189–191 (1981). [CrossRef]

22.

K. K. Li, Y. Lu, and Q. Wang, “Electro-optic ceramic material and device,” U.S. patent 6, 890, 874B1 (2005).

23.

M. Cuniot-Ponsard, J. M. Desvignes, A. Bellemain, and F. Bridou, “Simulatneous characterization of the electro-optic, converse-piezoelectirc, and electroabsorptive effects in epitaxial (Sr, Ba)Nb2O6 thin films,” J. Appl. Phys. 109(1), 014107 (2011). [CrossRef]

24.

K. Kurihara and K. Suzuki, “Theoretical understanding of an absorption-based surface plasmon resonance sensor based on Kretchmann’s theory,” Anal. Chem. 74(3), 696–701 (2002). [CrossRef] [PubMed]

OCIS Codes
(120.4530) Instrumentation, measurement, and metrology : Optical constants
(160.2100) Materials : Electro-optical materials
(130.2755) Integrated optics : Glass waveguides

ToC Category:
Materials

History
Original Manuscript: April 11, 2012
Revised Manuscript: May 9, 2012
Manuscript Accepted: May 14, 2012
Published: June 6, 2012

Citation
Pingping Xiao, Xianping Wang, Jingjing Sun, Meizhen Huang, Xianfeng Chen, and Zhuangqi Cao, "Simultaneous measurement of electro-optical and converse-piezoelectric coefficients of PMN-PT ceramics," Opt. Express 20, 13833-13840 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-13833


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References

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