Abstract

We fabricated cylindrical varifocal lenses with fast responses by using the strong Kerr effect of KTa1xNbxO3 (KTN) single crystals. We observed focus shifts of up to 87 mm with the assistance of a 250 mm focal length lens, which corresponds to a focus shift from infinity to 720 mm by the KTN lens itself. The response time was as fast as 1 μs. We also present a simulation method for calculating refractive index distributions in KTN single crystals, which is essential when designing the lens. The method is characterized by the strain contribution, which has not conventionally been typical of electro-optic simulations. We used this method to explain the refractive index modulations that are characteristic of the varifocal lenses.

© 2012 Optical Society of America

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  1. B. Wang, M. Ye, and S. Sato, “Lens of electrically controllable focal length made by a glass lens and liquid-crystal layers,” Appl. Opt. 43, 3420–3425 (2004).
    [CrossRef]
  2. T. Kaneko, Y. Yamagata, T. Idogaki, T. Hattori, and T. Higuchi, “3-Dimensional specific thickness glass diaphragm lens for dynamic focusing,” IEICE Trans. Electron. E78-C, 123–127 (1995).
  3. B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: an application of electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
    [CrossRef]
  4. A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “High-speed varifocal imaging with a tunable acoustic gradient index of refraction lens,” Opt. Lett. 33, 2146–2148 (2008).
    [CrossRef]
  5. T. Shibaguchi and H. Funato, “Lead-lanthanum zirconate-titanate (PLZT) electrooptic variable focal-length lens with stripe electrodes,” Japanese J. Appl. Phys. 31, 3196–3200 (1992).
    [CrossRef]
  6. T. Khayim, M. Yamaguchi, D. S. Kim, and T. Kobayashi, “Femtosecond optical pulse generation from a CW laser using an electrooptic phase modulator featuring lens modulation,” IEEE J. Quantum Electron. 35, 1412–1418 (1999).
    [CrossRef]
  7. T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, M. Sasaura, and K. Fujiura, “Fast response variable focal-length length lenses using KTa1−xNbxO3 crystals,” Appl. Phys. Express 4, 022501 (2011).
    [CrossRef]
  8. 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, 388–398 (1966).
    [CrossRef]
  9. J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, “Electro-optic properties of some ABO3 perovskite in the paraelectric phase,” Appl. Phys. Lett. 4, 141–143 (1964).
    [CrossRef]
  10. W. A. Banner, E. F. Dearborn, and L. G. Van Uitert, “Growth of potassium tantalate niobate single crystals for optical application,” Am. Ceram. Soc. Bull. 44, 9–11 (1965).
  11. 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]
  12. S. H. Wemple and M. DiDomenico, “Oxygen-octahedra ferroelectrics. II. Electro-optical and nonlinear-optical device applications,” J. Appl. Phys. 40, 735–752 (1969).
    [CrossRef]
  13. H. Uwe and T. Sakudo, “Electrostriction and stress-induced ferroelectricity in KTaO3,” J. Phys. Soc. Japan 38, 183–189 (1975).
    [CrossRef]
  14. F. Jona and G. Shirane, Ferroelectric Crystals (Macmillan, 1962).
  15. S. H. Wemple and M. DiDomenico, “Theory of the elasto-optic effect in nonmetallic crystals,” Phys. Rev. B 1, 193–202 (1970).
    [CrossRef]

2011

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, M. Sasaura, and K. Fujiura, “Fast response variable focal-length length lenses using KTa1−xNbxO3 crystals,” Appl. Phys. Express 4, 022501 (2011).
[CrossRef]

2008

2004

2000

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: an application of electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
[CrossRef]

1999

T. Khayim, M. Yamaguchi, D. S. Kim, and T. Kobayashi, “Femtosecond optical pulse generation from a CW laser using an electrooptic phase modulator featuring lens modulation,” IEEE J. Quantum Electron. 35, 1412–1418 (1999).
[CrossRef]

1995

T. Kaneko, Y. Yamagata, T. Idogaki, T. Hattori, and T. Higuchi, “3-Dimensional specific thickness glass diaphragm lens for dynamic focusing,” IEICE Trans. Electron. E78-C, 123–127 (1995).

1992

T. Shibaguchi and H. Funato, “Lead-lanthanum zirconate-titanate (PLZT) electrooptic variable focal-length lens with stripe electrodes,” Japanese J. Appl. Phys. 31, 3196–3200 (1992).
[CrossRef]

1982

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]

1975

H. Uwe and T. Sakudo, “Electrostriction and stress-induced ferroelectricity in KTaO3,” J. Phys. Soc. Japan 38, 183–189 (1975).
[CrossRef]

1970

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

1969

S. H. Wemple and M. DiDomenico, “Oxygen-octahedra ferroelectrics. II. Electro-optical and nonlinear-optical device applications,” J. Appl. Phys. 40, 735–752 (1969).
[CrossRef]

1966

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, 388–398 (1966).
[CrossRef]

1965

W. A. Banner, E. F. Dearborn, and L. G. Van Uitert, “Growth of potassium tantalate niobate single crystals for optical application,” Am. Ceram. Soc. Bull. 44, 9–11 (1965).

1964

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

Arnold, C. B.

Banner, W. A.

W. A. Banner, E. F. Dearborn, and L. G. Van Uitert, “Growth of potassium tantalate niobate single crystals for optical application,” Am. Ceram. Soc. Bull. 44, 9–11 (1965).

Berge, B.

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: an application of electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
[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, 388–398 (1966).
[CrossRef]

Cross, L. E.

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]

Dearborn, E. F.

W. A. Banner, E. F. Dearborn, and L. G. Van Uitert, “Growth of potassium tantalate niobate single crystals for optical application,” Am. Ceram. Soc. Bull. 44, 9–11 (1965).

DiDomenico, M.

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

S. H. Wemple and M. DiDomenico, “Oxygen-octahedra ferroelectrics. II. Electro-optical and nonlinear-optical device applications,” J. Appl. Phys. 40, 735–752 (1969).
[CrossRef]

Fujiura, K.

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, M. Sasaura, and K. Fujiura, “Fast response variable focal-length length lenses using KTa1−xNbxO3 crystals,” Appl. Phys. Express 4, 022501 (2011).
[CrossRef]

Funato, H.

T. Shibaguchi and H. Funato, “Lead-lanthanum zirconate-titanate (PLZT) electrooptic variable focal-length lens with stripe electrodes,” Japanese J. Appl. Phys. 31, 3196–3200 (1992).
[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, 388–398 (1966).
[CrossRef]

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

Hattori, T.

T. Kaneko, Y. Yamagata, T. Idogaki, T. Hattori, and T. Higuchi, “3-Dimensional specific thickness glass diaphragm lens for dynamic focusing,” IEICE Trans. Electron. E78-C, 123–127 (1995).

Higuchi, T.

T. Kaneko, Y. Yamagata, T. Idogaki, T. Hattori, and T. Higuchi, “3-Dimensional specific thickness glass diaphragm lens for dynamic focusing,” IEICE Trans. Electron. E78-C, 123–127 (1995).

Idogaki, T.

T. Kaneko, Y. Yamagata, T. Idogaki, T. Hattori, and T. Higuchi, “3-Dimensional specific thickness glass diaphragm lens for dynamic focusing,” IEICE Trans. Electron. E78-C, 123–127 (1995).

Imai, T.

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, M. Sasaura, and K. Fujiura, “Fast response variable focal-length length lenses using KTa1−xNbxO3 crystals,” Appl. Phys. Express 4, 022501 (2011).
[CrossRef]

Jona, F.

F. Jona and G. Shirane, Ferroelectric Crystals (Macmillan, 1962).

Kaneko, T.

T. Kaneko, Y. Yamagata, T. Idogaki, T. Hattori, and T. Higuchi, “3-Dimensional specific thickness glass diaphragm lens for dynamic focusing,” IEICE Trans. Electron. E78-C, 123–127 (1995).

Khayim, T.

T. Khayim, M. Yamaguchi, D. S. Kim, and T. Kobayashi, “Femtosecond optical pulse generation from a CW laser using an electrooptic phase modulator featuring lens modulation,” IEEE J. Quantum Electron. 35, 1412–1418 (1999).
[CrossRef]

Kim, D. S.

T. Khayim, M. Yamaguchi, D. S. Kim, and T. Kobayashi, “Femtosecond optical pulse generation from a CW laser using an electrooptic phase modulator featuring lens modulation,” IEEE J. Quantum Electron. 35, 1412–1418 (1999).
[CrossRef]

Kobayashi, T.

T. Khayim, M. Yamaguchi, D. S. Kim, and T. Kobayashi, “Femtosecond optical pulse generation from a CW laser using an electrooptic phase modulator featuring lens modulation,” IEEE J. Quantum Electron. 35, 1412–1418 (1999).
[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, 388–398 (1966).
[CrossRef]

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

McLeod, E.

Mermillod-Blondin, A.

Miyazu, J.

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, M. Sasaura, and K. Fujiura, “Fast response variable focal-length length lenses using KTa1−xNbxO3 crystals,” Appl. Phys. Express 4, 022501 (2011).
[CrossRef]

Naganuma, K.

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, M. Sasaura, and K. Fujiura, “Fast response variable focal-length length lenses using KTa1−xNbxO3 crystals,” Appl. Phys. Express 4, 022501 (2011).
[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]

Peseux, J.

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: an application of electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
[CrossRef]

Sakudo, T.

H. Uwe and T. Sakudo, “Electrostriction and stress-induced ferroelectricity in KTaO3,” J. Phys. Soc. Japan 38, 183–189 (1975).
[CrossRef]

Sasaura, M.

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, M. Sasaura, and K. Fujiura, “Fast response variable focal-length length lenses using KTa1−xNbxO3 crystals,” Appl. Phys. Express 4, 022501 (2011).
[CrossRef]

Sato, S.

Shibaguchi, T.

T. Shibaguchi and H. Funato, “Lead-lanthanum zirconate-titanate (PLZT) electrooptic variable focal-length lens with stripe electrodes,” Japanese J. Appl. Phys. 31, 3196–3200 (1992).
[CrossRef]

Shirane, G.

F. Jona and G. Shirane, Ferroelectric Crystals (Macmillan, 1962).

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, 388–398 (1966).
[CrossRef]

Toyoda, S.

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, M. Sasaura, and K. Fujiura, “Fast response variable focal-length length lenses using KTa1−xNbxO3 crystals,” Appl. Phys. Express 4, 022501 (2011).
[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]

Uwe, H.

H. Uwe and T. Sakudo, “Electrostriction and stress-induced ferroelectricity in KTaO3,” J. Phys. Soc. Japan 38, 183–189 (1975).
[CrossRef]

Van Uitert, L. G.

W. A. Banner, E. F. Dearborn, and L. G. Van Uitert, “Growth of potassium tantalate niobate single crystals for optical application,” Am. Ceram. Soc. Bull. 44, 9–11 (1965).

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

Wang, B.

Wemple, S. H.

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

S. H. Wemple and M. DiDomenico, “Oxygen-octahedra ferroelectrics. II. Electro-optical and nonlinear-optical device applications,” J. Appl. Phys. 40, 735–752 (1969).
[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, 388–398 (1966).
[CrossRef]

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

Yagi, S.

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, M. Sasaura, and K. Fujiura, “Fast response variable focal-length length lenses using KTa1−xNbxO3 crystals,” Appl. Phys. Express 4, 022501 (2011).
[CrossRef]

Yamagata, Y.

T. Kaneko, Y. Yamagata, T. Idogaki, T. Hattori, and T. Higuchi, “3-Dimensional specific thickness glass diaphragm lens for dynamic focusing,” IEICE Trans. Electron. E78-C, 123–127 (1995).

Yamaguchi, M.

T. Khayim, M. Yamaguchi, D. S. Kim, and T. Kobayashi, “Femtosecond optical pulse generation from a CW laser using an electrooptic phase modulator featuring lens modulation,” IEEE J. Quantum Electron. 35, 1412–1418 (1999).
[CrossRef]

Ye, M.

Am. Ceram. Soc. Bull.

W. A. Banner, E. F. Dearborn, and L. G. Van Uitert, “Growth of potassium tantalate niobate single crystals for optical application,” Am. Ceram. Soc. Bull. 44, 9–11 (1965).

Appl. Opt.

Appl. Phys. Express

T. Imai, S. Yagi, S. Toyoda, J. Miyazu, K. Naganuma, M. Sasaura, and K. Fujiura, “Fast response variable focal-length length lenses using KTa1−xNbxO3 crystals,” Appl. Phys. Express 4, 022501 (2011).
[CrossRef]

Appl. Phys. Lett.

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

Eur. Phys. J. E

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: an application of electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
[CrossRef]

IEEE J. Quantum Electron.

T. Khayim, M. Yamaguchi, D. S. Kim, and T. Kobayashi, “Femtosecond optical pulse generation from a CW laser using an electrooptic phase modulator featuring lens modulation,” IEEE J. Quantum Electron. 35, 1412–1418 (1999).
[CrossRef]

IEICE Trans. Electron.

T. Kaneko, Y. Yamagata, T. Idogaki, T. Hattori, and T. Higuchi, “3-Dimensional specific thickness glass diaphragm lens for dynamic focusing,” IEICE Trans. Electron. E78-C, 123–127 (1995).

J. Appl. Phys.

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, 388–398 (1966).
[CrossRef]

S. H. Wemple and M. DiDomenico, “Oxygen-octahedra ferroelectrics. II. Electro-optical and nonlinear-optical device applications,” J. Appl. Phys. 40, 735–752 (1969).
[CrossRef]

J. Phys. Soc. Japan

H. Uwe and T. Sakudo, “Electrostriction and stress-induced ferroelectricity in KTaO3,” J. Phys. Soc. Japan 38, 183–189 (1975).
[CrossRef]

J. Phys. Soc. Jpn.

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]

Japanese J. Appl. Phys.

T. Shibaguchi and H. Funato, “Lead-lanthanum zirconate-titanate (PLZT) electrooptic variable focal-length lens with stripe electrodes,” Japanese J. Appl. Phys. 31, 3196–3200 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev. B

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

Other

F. Jona and G. Shirane, Ferroelectric Crystals (Macmillan, 1962).

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Figures (11)

Fig. 1.
Fig. 1.

Structure of KTN EO varifocal lens.

Fig. 2.
Fig. 2.

Calculated optical path distributions obtained using Eq. (4).

Fig. 3.
Fig. 3.

Variations of our varifocal lenses.

Fig. 4.
Fig. 4.

Calculated optical path distributions for the configuration shown in Fig. 3(d).

Fig. 5.
Fig. 5.

Experimental setup for evaluating focus shifts made by a KTN varifocal lens.

Fig. 6.
Fig. 6.

Optical path distribution for configuration (a) measured with a Michelson interferometer.

Fig. 7.
Fig. 7.

Light intensity distributions obtained with the setup in Fig. 1 for configuration (a), which shows a focus shift of 40 mm.

Fig. 8.
Fig. 8.

Voltage dependence of the focus shift for configuration (d). The solid line is theoretical.

Fig. 9.
Fig. 9.

Time evolution of transmitting power through the pinhole for configuration (a), which indicates a 1 μs response for a KTN varifocal lens.

Fig. 10.
Fig. 10.

Strain distributions calculated by the conventional method and our new method. The left two figures show the horizontal expansion ratio, and the right two figures show the vertical expansion ratio.

Fig. 11.
Fig. 11.

Refractive index distributions obtained experimentally and calculated using the two methods. Note the bumps in the top and the bottom center regions and the dent at the center.

Tables (1)

Tables Icon

Table 1. Assumed Parameters

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

β1x2+β2y2+β3z2+2β4yz+2β5zx+2β6xy=1,
Δnx=12n03Δβ1,Δny=12n03Δβ2,
Δβ1=s11Ex2+s12Ez2,Δβ2=s12Ex2+s12Ez2,
Δsx=0TΔnxdz=12n03(s110TEx2dz+s120TEz2dz),Δsy=0TΔnydz=12n03(s120TEx2dz+s120TEz2dz),
Δf=f2F,
eij=QijmnPmPn=ε2QijmnEmEn,
Δβij=g(S)ijklPkPl+πijklekl,
Δβij=(g(S)ijkl+πijmnQmnkl)PkPl=g(T)ijklPkPl=s(T)ijklEkEl,
Flocal=12PiEi+12eijcijklekl+eijαijklPkPl,
Fblock=Vc(12eijcijklekleijcijmnQmnklPkPl)dV.

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