Abstract

KTa1-xNbxO3 is known for its huge Kerr effect, which is a second order electrooptic (EO) effect. By utilizing the large refractive index change Δn of this EO effect, a fast optical beam deflector has been realized. However, anomalous spatial distributions of Δn were observed with this beam deflector. This anomaly is ascribed to distortions caused by the electrostrictive effect that occurs when voltage is applied. We assumed a spheric distortion and used a variational method to deduce an analytic solution for the strains that accompany this distortion. The analytic solution coincides with numerical results obtained with the finite element method. In addition, the solution agrees well with the experimentally obtained Δn distribution.

© 2015 Optical Society of America

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References

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  1. S. Triebwasser, “Study of ferroelectric transitions of solid-solution single crystals of KNbO3- KTaO3,” Phys. Rev. 114(1), 63–70 (1959).
    [Crossref]
  2. F. S. Chen, J. E. Geusic, S. K. Kurtz, J. G. Skinner, and S. H. Wemple, “Light modulation and beam deflection with potassium tantalate niobate crystals,” J. Appl. Phys. 37(1), 388–398 (1966).
    [Crossref]
  3. 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]
  4. S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
    [Crossref]
  5. Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, J. Kobayashi, and M. Ohmi, “High-speed optical coherence tomography system using a 200-kHz swept light source with a KTN deflector,” Opt. Photonics J. 3(2), 190–193 (2013).
    [Crossref]
  6. 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]
  7. T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, S. Kawamura, M. Sasaura, and K. Fujiura, “Fast response varifocal lenses using KTa1-xNbxO3 crystals and a simulation method with electrostrictive calculations,” Appl. Opt. 51(10), 1532–1539 (2012).
    [Crossref] [PubMed]
  8. J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, “Electro-optic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964).
    [Crossref]
  9. T. Imai, S. Toyoda, J. Miyazu, J. Kobayashi, and S. Kojima, “Changes in permittivity of KTa1-xNbxO3 crystals induced by electron injection in relation to nonlinear dielectric response,” Appl. Phys. Express 7(7), 071501 (2014).
    [Crossref]
  10. R. Hofmeister, A. Yariv, and A. Agranat, “Growth and characterization of the perovskite K1-yLiyTa1-xNbxO3: Cu,” J. Cryst. Growth 131(3-4), 486–494 (1993).
    [Crossref]
  11. T. Imai, J. Miyazu, and J. Kobayashi, “Measurement of charge density distributions in KTa1-xNbxO3 optical beam deflectors,” Opt. Mater. Express 4(5), 976–981 (2014).
    [Crossref]
  12. K. Uchino, S. Nomura, and L. E. Cross, “Anomalous temperature dependence of electrostrictive coefficients in K(Ta0.55Nb0.45)O3,” J. Phys. Soc. Jpn. 51, 3242–3244 (1982).
    [Crossref]
  13. L. A. Knauss, X. M. Wang, and J. Toulouse, “Polarization-strain coupling in the mixed ferroelectric KTa1-xNbxO3.,” Phys. Rev. B Condens. Matter 52(18), 13261–13268 (1995).
    [Crossref] [PubMed]
  14. J. Miyazu, S. Kawamura, T. Imai, and J. Kobayashi, “Temperature dependence of photoelastic effect in KTa1-xNbxO3 crystals and investigation of its origin,” Jpn. J. Appl. Phys. 52(9S1), 09KC03 (2013).
    [Crossref]
  15. S. H. Wemple and M. DiDomenico., “Theory of the elasto-optic effect in nonmetallic cystal,” Phys. Rev. B 1(1), 193–202 (1970).
    [Crossref]

2014 (2)

T. Imai, S. Toyoda, J. Miyazu, J. Kobayashi, and S. Kojima, “Changes in permittivity of KTa1-xNbxO3 crystals induced by electron injection in relation to nonlinear dielectric response,” Appl. Phys. Express 7(7), 071501 (2014).
[Crossref]

T. Imai, J. Miyazu, and J. Kobayashi, “Measurement of charge density distributions in KTa1-xNbxO3 optical beam deflectors,” Opt. Mater. Express 4(5), 976–981 (2014).
[Crossref]

2013 (2)

J. Miyazu, S. Kawamura, T. Imai, and J. Kobayashi, “Temperature dependence of photoelastic effect in KTa1-xNbxO3 crystals and investigation of its origin,” Jpn. J. Appl. Phys. 52(9S1), 09KC03 (2013).
[Crossref]

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, J. Kobayashi, and M. Ohmi, “High-speed optical coherence tomography system using a 200-kHz swept light source with a KTN deflector,” Opt. Photonics J. 3(2), 190–193 (2013).
[Crossref]

2012 (2)

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, S. Kawamura, M. Sasaura, and K. Fujiura, “Fast response varifocal lenses using KTa1-xNbxO3 crystals and a simulation method with electrostrictive calculations,” Appl. Opt. 51(10), 1532–1539 (2012).
[Crossref] [PubMed]

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

2011 (1)

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]

2008 (1)

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]

1995 (1)

L. A. Knauss, X. M. Wang, and J. Toulouse, “Polarization-strain coupling in the mixed ferroelectric KTa1-xNbxO3.,” Phys. Rev. B Condens. Matter 52(18), 13261–13268 (1995).
[Crossref] [PubMed]

1993 (1)

R. Hofmeister, A. Yariv, and A. Agranat, “Growth and characterization of the perovskite K1-yLiyTa1-xNbxO3: Cu,” J. Cryst. Growth 131(3-4), 486–494 (1993).
[Crossref]

1982 (1)

K. Uchino, S. Nomura, and L. E. Cross, “Anomalous temperature dependence of electrostrictive coefficients in K(Ta0.55Nb0.45)O3,” J. Phys. Soc. Jpn. 51, 3242–3244 (1982).
[Crossref]

1970 (1)

S. H. Wemple and M. DiDomenico., “Theory of the elasto-optic effect in nonmetallic cystal,” Phys. Rev. B 1(1), 193–202 (1970).
[Crossref]

1966 (1)

F. S. Chen, J. E. Geusic, S. K. Kurtz, J. G. Skinner, and S. H. Wemple, “Light modulation and beam deflection with potassium tantalate niobate crystals,” J. Appl. Phys. 37(1), 388–398 (1966).
[Crossref]

1964 (1)

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, “Electro-optic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964).
[Crossref]

1959 (1)

S. Triebwasser, “Study of ferroelectric transitions of solid-solution single crystals of KNbO3- KTaO3,” Phys. Rev. 114(1), 63–70 (1959).
[Crossref]

Agranat, A.

R. Hofmeister, A. Yariv, and A. Agranat, “Growth and characterization of the perovskite K1-yLiyTa1-xNbxO3: Cu,” J. Cryst. Growth 131(3-4), 486–494 (1993).
[Crossref]

Chen, F. S.

F. S. Chen, J. E. Geusic, S. K. Kurtz, J. G. Skinner, and S. H. Wemple, “Light modulation and beam deflection with potassium tantalate niobate crystals,” J. Appl. Phys. 37(1), 388–398 (1966).
[Crossref]

DiDomenico, M.

S. H. Wemple and M. DiDomenico., “Theory of the elasto-optic effect in nonmetallic cystal,” Phys. Rev. B 1(1), 193–202 (1970).
[Crossref]

E. Cross, L.

K. Uchino, S. Nomura, and L. E. Cross, “Anomalous temperature dependence of electrostrictive coefficients in K(Ta0.55Nb0.45)O3,” J. Phys. Soc. Jpn. 51, 3242–3244 (1982).
[Crossref]

Fujiura, K.

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, S. Kawamura, M. Sasaura, and K. Fujiura, “Fast response varifocal lenses using KTa1-xNbxO3 crystals and a simulation method with electrostrictive calculations,” Appl. Opt. 51(10), 1532–1539 (2012).
[Crossref] [PubMed]

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]

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]

Geusic, J. E.

F. S. Chen, J. E. Geusic, S. K. Kurtz, J. G. Skinner, and S. H. Wemple, “Light modulation and beam deflection with potassium tantalate niobate crystals,” J. Appl. Phys. 37(1), 388–398 (1966).
[Crossref]

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, “Electro-optic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964).
[Crossref]

Haruna, M.

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

Hofmeister, R.

R. Hofmeister, A. Yariv, and A. Agranat, “Growth and characterization of the perovskite K1-yLiyTa1-xNbxO3: Cu,” J. Cryst. Growth 131(3-4), 486–494 (1993).
[Crossref]

Imai, T.

T. Imai, J. Miyazu, and J. Kobayashi, “Measurement of charge density distributions in KTa1-xNbxO3 optical beam deflectors,” Opt. Mater. Express 4(5), 976–981 (2014).
[Crossref]

T. Imai, S. Toyoda, J. Miyazu, J. Kobayashi, and S. Kojima, “Changes in permittivity of KTa1-xNbxO3 crystals induced by electron injection in relation to nonlinear dielectric response,” Appl. Phys. Express 7(7), 071501 (2014).
[Crossref]

J. Miyazu, S. Kawamura, T. Imai, and J. Kobayashi, “Temperature dependence of photoelastic effect in KTa1-xNbxO3 crystals and investigation of its origin,” Jpn. J. Appl. Phys. 52(9S1), 09KC03 (2013).
[Crossref]

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, S. Kawamura, M. Sasaura, and K. Fujiura, “Fast response varifocal lenses using KTa1-xNbxO3 crystals and a simulation method with electrostrictive calculations,” Appl. Opt. 51(10), 1532–1539 (2012).
[Crossref] [PubMed]

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]

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]

Kato, K.

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

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]

Kawamura, S.

J. Miyazu, S. Kawamura, T. Imai, and J. Kobayashi, “Temperature dependence of photoelastic effect in KTa1-xNbxO3 crystals and investigation of its origin,” Jpn. J. Appl. Phys. 52(9S1), 09KC03 (2013).
[Crossref]

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, S. Kawamura, M. Sasaura, and K. Fujiura, “Fast response varifocal lenses using KTa1-xNbxO3 crystals and a simulation method with electrostrictive calculations,” Appl. Opt. 51(10), 1532–1539 (2012).
[Crossref] [PubMed]

Knauss, L. A.

L. A. Knauss, X. M. Wang, and J. Toulouse, “Polarization-strain coupling in the mixed ferroelectric KTa1-xNbxO3.,” Phys. Rev. B Condens. Matter 52(18), 13261–13268 (1995).
[Crossref] [PubMed]

Kobayashi, J.

T. Imai, S. Toyoda, J. Miyazu, J. Kobayashi, and S. Kojima, “Changes in permittivity of KTa1-xNbxO3 crystals induced by electron injection in relation to nonlinear dielectric response,” Appl. Phys. Express 7(7), 071501 (2014).
[Crossref]

T. Imai, J. Miyazu, and J. Kobayashi, “Measurement of charge density distributions in KTa1-xNbxO3 optical beam deflectors,” Opt. Mater. Express 4(5), 976–981 (2014).
[Crossref]

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, J. Kobayashi, and M. Ohmi, “High-speed optical coherence tomography system using a 200-kHz swept light source with a KTN deflector,” Opt. Photonics J. 3(2), 190–193 (2013).
[Crossref]

J. Miyazu, S. Kawamura, T. Imai, and J. Kobayashi, “Temperature dependence of photoelastic effect in KTa1-xNbxO3 crystals and investigation of its origin,” Jpn. J. Appl. Phys. 52(9S1), 09KC03 (2013).
[Crossref]

Kojima, S.

T. Imai, S. Toyoda, J. Miyazu, J. Kobayashi, and S. Kojima, “Changes in permittivity of KTa1-xNbxO3 crystals induced by electron injection in relation to nonlinear dielectric response,” Appl. Phys. Express 7(7), 071501 (2014).
[Crossref]

Kurtz, S. K.

F. S. Chen, J. E. Geusic, S. K. Kurtz, J. G. Skinner, and S. H. Wemple, “Light modulation and beam deflection with potassium tantalate niobate crystals,” J. Appl. Phys. 37(1), 388–398 (1966).
[Crossref]

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, “Electro-optic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964).
[Crossref]

Miyazu, J.

T. Imai, S. Toyoda, J. Miyazu, J. Kobayashi, and S. Kojima, “Changes in permittivity of KTa1-xNbxO3 crystals induced by electron injection in relation to nonlinear dielectric response,” Appl. Phys. Express 7(7), 071501 (2014).
[Crossref]

T. Imai, J. Miyazu, and J. Kobayashi, “Measurement of charge density distributions in KTa1-xNbxO3 optical beam deflectors,” Opt. Mater. Express 4(5), 976–981 (2014).
[Crossref]

J. Miyazu, S. Kawamura, T. Imai, and J. Kobayashi, “Temperature dependence of photoelastic effect in KTa1-xNbxO3 crystals and investigation of its origin,” Jpn. J. Appl. Phys. 52(9S1), 09KC03 (2013).
[Crossref]

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, S. Kawamura, M. Sasaura, and K. Fujiura, “Fast response varifocal lenses using KTa1-xNbxO3 crystals and a simulation method with electrostrictive calculations,” Appl. Opt. 51(10), 1532–1539 (2012).
[Crossref] [PubMed]

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]

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]

Naganuma, K.

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, S. Kawamura, M. Sasaura, and K. Fujiura, “Fast response varifocal lenses using KTa1-xNbxO3 crystals and a simulation method with electrostrictive calculations,” Appl. Opt. 51(10), 1532–1539 (2012).
[Crossref] [PubMed]

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

Nakamura, K.

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]

Nomura, S.

K. Uchino, S. Nomura, and L. E. Cross, “Anomalous temperature dependence of electrostrictive coefficients in K(Ta0.55Nb0.45)O3,” J. Phys. Soc. Jpn. 51, 3242–3244 (1982).
[Crossref]

Ohmi, M.

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, J. Kobayashi, and M. Ohmi, “High-speed optical coherence tomography system using a 200-kHz swept light source with a KTN deflector,” Opt. Photonics J. 3(2), 190–193 (2013).
[Crossref]

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

Okabe, Y.

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, J. Kobayashi, and M. Ohmi, “High-speed optical coherence tomography system using a 200-kHz swept light source with a KTN deflector,” Opt. Photonics J. 3(2), 190–193 (2013).
[Crossref]

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

Sakamoto, T.

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, J. Kobayashi, and M. Ohmi, “High-speed optical coherence tomography system using a 200-kHz swept light source with a KTN deflector,” Opt. Photonics J. 3(2), 190–193 (2013).
[Crossref]

Sasaki, Y.

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, J. Kobayashi, and M. Ohmi, “High-speed optical coherence tomography system using a 200-kHz swept light source with a KTN deflector,” Opt. Photonics J. 3(2), 190–193 (2013).
[Crossref]

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

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]

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]

Sasaura, M.

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, S. Kawamura, M. Sasaura, and K. Fujiura, “Fast response varifocal lenses using KTa1-xNbxO3 crystals and a simulation method with electrostrictive calculations,” Appl. Opt. 51(10), 1532–1539 (2012).
[Crossref] [PubMed]

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

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]

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]

Shibata, Y.

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

Skinner, J. G.

F. S. Chen, J. E. Geusic, S. K. Kurtz, J. G. Skinner, and S. H. Wemple, “Light modulation and beam deflection with potassium tantalate niobate crystals,” J. Appl. Phys. 37(1), 388–398 (1966).
[Crossref]

Toulouse, J.

L. A. Knauss, X. M. Wang, and J. Toulouse, “Polarization-strain coupling in the mixed ferroelectric KTa1-xNbxO3.,” Phys. Rev. B Condens. Matter 52(18), 13261–13268 (1995).
[Crossref] [PubMed]

Toyoda, S.

T. Imai, S. Toyoda, J. Miyazu, J. Kobayashi, and S. Kojima, “Changes in permittivity of KTa1-xNbxO3 crystals induced by electron injection in relation to nonlinear dielectric response,” Appl. Phys. Express 7(7), 071501 (2014).
[Crossref]

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, J. Kobayashi, and M. Ohmi, “High-speed optical coherence tomography system using a 200-kHz swept light source with a KTN deflector,” Opt. Photonics J. 3(2), 190–193 (2013).
[Crossref]

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, S. Kawamura, M. Sasaura, and K. Fujiura, “Fast response varifocal lenses using KTa1-xNbxO3 crystals and a simulation method with electrostrictive calculations,” Appl. Opt. 51(10), 1532–1539 (2012).
[Crossref] [PubMed]

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]

Triebwasser, S.

S. Triebwasser, “Study of ferroelectric transitions of solid-solution single crystals of KNbO3- KTaO3,” Phys. Rev. 114(1), 63–70 (1959).
[Crossref]

Uchino, K.

K. Uchino, S. Nomura, and L. E. Cross, “Anomalous temperature dependence of electrostrictive coefficients in K(Ta0.55Nb0.45)O3,” J. Phys. Soc. Jpn. 51, 3242–3244 (1982).
[Crossref]

Ueno, M.

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, J. Kobayashi, and M. Ohmi, “High-speed optical coherence tomography system using a 200-kHz swept light source with a KTN deflector,” Opt. Photonics J. 3(2), 190–193 (2013).
[Crossref]

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

Van Uitert, L. G.

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, “Electro-optic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964).
[Crossref]

Wang, X. M.

L. A. Knauss, X. M. Wang, and J. Toulouse, “Polarization-strain coupling in the mixed ferroelectric KTa1-xNbxO3.,” Phys. Rev. B Condens. Matter 52(18), 13261–13268 (1995).
[Crossref] [PubMed]

Wemple, S. H.

S. H. Wemple and M. DiDomenico., “Theory of the elasto-optic effect in nonmetallic cystal,” Phys. Rev. B 1(1), 193–202 (1970).
[Crossref]

F. S. Chen, J. E. Geusic, S. K. Kurtz, J. G. Skinner, and S. H. Wemple, “Light modulation and beam deflection with potassium tantalate niobate crystals,” J. Appl. Phys. 37(1), 388–398 (1966).
[Crossref]

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, “Electro-optic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964).
[Crossref]

Yagi, S.

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, S. Kawamura, M. Sasaura, and K. Fujiura, “Fast response varifocal lenses using KTa1-xNbxO3 crystals and a simulation method with electrostrictive calculations,” Appl. Opt. 51(10), 1532–1539 (2012).
[Crossref] [PubMed]

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

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]

Yariv, A.

R. Hofmeister, A. Yariv, and A. Agranat, “Growth and characterization of the perovskite K1-yLiyTa1-xNbxO3: Cu,” J. Cryst. Growth 131(3-4), 486–494 (1993).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Express (2)

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]

T. Imai, S. Toyoda, J. Miyazu, J. Kobayashi, and S. Kojima, “Changes in permittivity of KTa1-xNbxO3 crystals induced by electron injection in relation to nonlinear dielectric response,” Appl. Phys. Express 7(7), 071501 (2014).
[Crossref]

Appl. Phys. Lett. (1)

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, “Electro-optic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964).
[Crossref]

J. Appl. Phys. (2)

F. S. Chen, J. E. Geusic, S. K. Kurtz, J. G. Skinner, and S. H. Wemple, “Light modulation and beam deflection with potassium tantalate niobate crystals,” J. Appl. Phys. 37(1), 388–398 (1966).
[Crossref]

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]

J. Cryst. Growth (1)

R. Hofmeister, A. Yariv, and A. Agranat, “Growth and characterization of the perovskite K1-yLiyTa1-xNbxO3: Cu,” J. Cryst. Growth 131(3-4), 486–494 (1993).
[Crossref]

J. Phys. Soc. Jpn. (1)

K. Uchino, S. Nomura, and L. E. Cross, “Anomalous temperature dependence of electrostrictive coefficients in K(Ta0.55Nb0.45)O3,” J. Phys. Soc. Jpn. 51, 3242–3244 (1982).
[Crossref]

Jpn. J. Appl. Phys. (1)

J. Miyazu, S. Kawamura, T. Imai, and J. Kobayashi, “Temperature dependence of photoelastic effect in KTa1-xNbxO3 crystals and investigation of its origin,” Jpn. J. Appl. Phys. 52(9S1), 09KC03 (2013).
[Crossref]

Opt. Mater. Express (1)

Opt. Photonics J. (1)

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, J. Kobayashi, and M. Ohmi, “High-speed optical coherence tomography system using a 200-kHz swept light source with a KTN deflector,” Opt. Photonics J. 3(2), 190–193 (2013).
[Crossref]

Phys. Rev. (1)

S. Triebwasser, “Study of ferroelectric transitions of solid-solution single crystals of KNbO3- KTaO3,” Phys. Rev. 114(1), 63–70 (1959).
[Crossref]

Phys. Rev. B (1)

S. H. Wemple and M. DiDomenico., “Theory of the elasto-optic effect in nonmetallic cystal,” Phys. Rev. B 1(1), 193–202 (1970).
[Crossref]

Phys. Rev. B Condens. Matter (1)

L. A. Knauss, X. M. Wang, and J. Toulouse, “Polarization-strain coupling in the mixed ferroelectric KTa1-xNbxO3.,” Phys. Rev. B Condens. Matter 52(18), 13261–13268 (1995).
[Crossref] [PubMed]

Proc. SPIE (1)

S. Yagi, K. Naganuma, T. Imai, Y. Shibata, J. Miyazu, M. Ueno, Y. Okabe, Y. Sasaki, K. Fujiura, M. Sasaura, K. Kato, M. Ohmi, and M. Haruna, “Improvement of coherence length in a 200-kHz swept light source equipped with a KTN deflector,” Proc. SPIE 8213, 821333 (2012).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Structure of KTN optical beam deflector.
Fig. 2
Fig. 2 Spatial distribution of retardation in KTN deflector showing a Δn anomaly near the cathode. The right end is the midpoint between the electrodes. The anode is located at + 0.6 mm and is not shown in this figure.
Fig. 3
Fig. 3 Illustration of spherical distortion model. The distortion is caused by the horizontal shrinkage of the crystal near the cathode. Oo is the center of the sphere.
Fig. 4
Fig. 4 Spatial distributions of strain components. The solid lines show our analytical solutions and the plots show numerical values by the finite element method.
Fig. 5
Fig. 5 Spatial distributions of retardation. The solid line shows our analytical solution and the plots show experimental data shown in Fig. 1.

Equations (20)

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Δ n x = 1 2 n 0 3 g 11 ε 2 E x 2 , Δ n y = 1 2 n 0 3 g 12 ε 2 E x 2
Δ n x = 1 2 n 0 3 g 11 P x 2 , Δ n y = 1 2 n 0 3 g 12 P x 2
R=( Δ n x Δ n y )L= 1 2 n 0 3 ( g 11 g 12 )L P x 2
P x ( x )ε E x ( x )=ρ( x+ d 2 )+ P 0
[ e ]=[ Q ][ PP ]
[ e ]=[ e xx e yy e zz e yz e zx e xy ], [ Q ]=[ Q 11 Q 12 Q 12 0 0 0 Q 12 Q 11 Q 12 0 0 0 Q 12 Q 12 Q 11 0 0 0 0 0 0 Q 44 0 0 0 0 0 0 Q 44 0 0 0 0 0 0 Q 44 ], [ PP ]=[ P x P x P y P y P z P z P y P z P z P x P x P y ]
[ Δβ( P ) ][ β( P ) ][ β( 0 ) ]=[ p ][ e ]
Δ n x = 1 2 n 0 3 ( p 11 e xx + p 12 e yy + p 12 e zz ), Δ n y = 1 2 n 0 3 ( p 12 e xx + p 11 e yy + p 12 e zz )
e xx = Q 11 P x ( x ) 2 , e yy = e zz = Q 12 P x ( x ) 2 , e yz = e zx = e xy =0
e yy = e zz = 1 r a ( r 0 x r a )
f= 1 2 [ e ][ c ][ e ][ e ][ c ][ Q ][ PP ]
F= block fdV =S d/2 d/2 fdx
d dx ( f y ) f y =0
e xx =( Q 11 +2 c 12 c 11 Q 12 ) P x 2 ( x )2 c 12 c 11 e yy =( Q 11 +2 c 12 c 11 Q 12 ) P x 2 ( x )2 c 12 c 11 1 r a ( r 0 x r a )
r 0 = d 3 12H ( 1+ G d ), r a = d 3 12H
G d/2 d/2 Q 12 P x ( x ) 2 dx , H d/2 d/2 x Q 12 P x ( x ) 2 dx
r a = d 2 Q 12 ρεV , r 0 = d 2 Q 12 ρεV + ρ d 3 24εV + εV 2ρd
Δ n x = 1 2 n 0 3 { g 11 e ( ρx g 11 s g 11 e εV d ) 2 ( g 11 s g 11 e )( g 11 s g 11 e ε 2 V 2 d 2 ρ 2 d 2 12 ) }
g 11 e p 11 Q 11 +2 p 11 Q 12 c 12 c 11 , g 11 s p 11 Q 11 +2 p 12 Q 12
g 11 s g 11 e ε 2 V 2 d 2 > ρ 2 d 2 12

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