Abstract

We present a simple method to determine both direction of the electric field component to which an electro-optic sensor is sensitive and sensitivity to this component. For this purpose we introduce the concept of an electro-optic sensitivity vector. This work is done for electro-optic sensors working as amplitude modulators, as phase modulators, or as polarization state modulators. The method applies to any anisotropic crystal, regardless of crystallographic group. After defining three kinds of electro-optic sensor geometry that allow longitudinal, transversal or fully vectorial electric field probing, we make a comparative study of several commonly used electro-optic crystals. We derive the optimal orientations of the crystals with respect to the optical probe beam that lead to high-performance electro-optic sensors. We also treat isotropic crystals in the case of polarization state modulators. In contrast to anisotropic crystals that are sensitive to a unique electric field component, we show that isotropic crystals are sensitive to two orthogonal electric field components simultaneously.

© 2002 Optical Society of America

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References

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  1. H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
    [CrossRef]
  2. K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, “Electrooptic mapping and finite-element modeling of the near-field pattern of a microstrip patch antenna,” IEEE Trans. Microwave Theory Tech. 48, 288–294 (2000).
    [CrossRef]
  3. M. Shinagawa and T. Nagatsuma, “An automated electro-optic probing system for ultrahigh-speed IC’s,” IEEE Trans. Instrum. Meas. 43, 843–847 (1994).
    [CrossRef]
  4. M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
    [CrossRef]
  5. Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987).
  6. J. Xu, L. Zhou, and M. Thakur, “Electro-optic modulation using an organic single crystal film in a Fabry–Perot cavity,” Appl. Phys. Lett. 72, 153–154 (1998).
    [CrossRef]
  7. Y. Shi, W. Lin, D. J. Olson, J. H. Bechtel, H. Zhang, W. H. Steier, C. Zhang, and L. R. Dalton, “Electro-optic polymer modulators with 0.8 V half-wave voltage,” Appl. Phys. Lett. 77, 1–3 (2000).
    [CrossRef]
  8. I. P. Kaminow and E. H. Turner, “Linear electro-optical materials,” in Handbook of Lasers, R. J. Pressley, ed. (Chemical Rubber, Cleveland, Ohio, 1971), pp. 447–459.
  9. M. J. Gunning and R. E. Raab, “Algebraic determination of the principal refractive indices and axes in the electro-optic effect,” Appl. Opt. 37, 8438–8447 (1998).
    [CrossRef]
  10. P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18, 313–318 (2001).
    [CrossRef]
  11. Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B 18, 823–831 (2001).
    [CrossRef]
  12. P. Uhd Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
    [CrossRef]
  13. W. Mertin, “Two-dimensional field mapping of monolithic microwave integrated circuits using electro-optic sampling techniques,” Opt. Quantum Electron. 28, 801–817 (1996).
    [CrossRef]
  14. B. H. Hoerman, B. M. Nichols, M. J. Nystrom, and B. W. Wessels, “Dynamic response of the electro-optic effect in epitaxial KNbO3,” Appl. Phys. Lett. 75, 2707–2709 (1999).
    [CrossRef]
  15. Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 4, pp. 53–57.
  16. L. Duvillaret, S. Rialland, and J.-L. Coutaz, “Electro-optic sensors for electric field measurements. I. Theoretical comparison between different modulation techniques,” J. Opt. Soc. Am. B 19, 2692–2703 (2002).
    [CrossRef]
  17. Ph. Prêtre, L.-M. Wu, R. A. Hill, and A. Knoesen, “Characterization of electro-optic polymer films by use of decal-deposited reflection Fabry–Perot microcavities,” J. Opt. Soc. Am. B 15, 379–392 (1998).
    [CrossRef]
  18. K. D. Singer, S. J. Lalama, J. E. Sohn, and R. D. Small, “Electro-optic organic materials,” in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987), pp. 435–468.
  19. F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, “Electro-optic properties of the organic salt 4-N,N-dimethylamino-4′-N′-methylstilbazolium tosylate,” Appl. Phys. Lett. 69, 13–15 (1996).
    [CrossRef]
  20. K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77, 486–488 (2000).
    [CrossRef]
  21. An error appears in relation (29) of Ref. 11. The numerical coefficient of the last term should be 4/6 instead of 2/6. This leads to a corrected expression (36) of Ref. 11 equal to that of relation (21) in this paper.
  22. A. Yariv, Optical Electronics, 4th ed. (Saunders, Orlando, Fla., 1991), Chap. 9, Table 9-1, pp. 312–314.
  23. Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
    [CrossRef]
  24. S. Sohma, H. Takahashi, T. Taniuchi, and H. Ito, “Organic nonlinear crystal DAST growth and its device applications,” Chem. Phys. 245, 359 (1999).
    [CrossRef]
  25. DAST belongs to the monoclinic m-Cc group, exhibiting ten different nonvanishing electro-optic coefficients. Among them, only six have been measured.19

2002 (1)

2001 (3)

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18, 313–318 (2001).
[CrossRef]

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B 18, 823–831 (2001).
[CrossRef]

2000 (4)

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
[CrossRef]

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, “Electrooptic mapping and finite-element modeling of the near-field pattern of a microstrip patch antenna,” IEEE Trans. Microwave Theory Tech. 48, 288–294 (2000).
[CrossRef]

Y. Shi, W. Lin, D. J. Olson, J. H. Bechtel, H. Zhang, W. H. Steier, C. Zhang, and L. R. Dalton, “Electro-optic polymer modulators with 0.8 V half-wave voltage,” Appl. Phys. Lett. 77, 1–3 (2000).
[CrossRef]

K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77, 486–488 (2000).
[CrossRef]

1999 (2)

B. H. Hoerman, B. M. Nichols, M. J. Nystrom, and B. W. Wessels, “Dynamic response of the electro-optic effect in epitaxial KNbO3,” Appl. Phys. Lett. 75, 2707–2709 (1999).
[CrossRef]

S. Sohma, H. Takahashi, T. Taniuchi, and H. Ito, “Organic nonlinear crystal DAST growth and its device applications,” Chem. Phys. 245, 359 (1999).
[CrossRef]

1998 (3)

1996 (4)

P. Uhd Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

W. Mertin, “Two-dimensional field mapping of monolithic microwave integrated circuits using electro-optic sampling techniques,” Opt. Quantum Electron. 28, 801–817 (1996).
[CrossRef]

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, “Electro-optic properties of the organic salt 4-N,N-dimethylamino-4′-N′-methylstilbazolium tosylate,” Appl. Phys. Lett. 69, 13–15 (1996).
[CrossRef]

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
[CrossRef]

1994 (1)

M. Shinagawa and T. Nagatsuma, “An automated electro-optic probing system for ultrahigh-speed IC’s,” IEEE Trans. Instrum. Meas. 43, 843–847 (1994).
[CrossRef]

Bakker, H. J.

Bechtel, J. H.

Y. Shi, W. Lin, D. J. Olson, J. H. Bechtel, H. Zhang, W. H. Steier, C. Zhang, and L. R. Dalton, “Electro-optic polymer modulators with 0.8 V half-wave voltage,” Appl. Phys. Lett. 77, 1–3 (2000).
[CrossRef]

Bosshard, Ch.

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, “Electro-optic properties of the organic salt 4-N,N-dimethylamino-4′-N′-methylstilbazolium tosylate,” Appl. Phys. Lett. 69, 13–15 (1996).
[CrossRef]

Chang, D.

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Chang, Y.

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Chen, Q.

Coutaz, J.-L.

Dalton, L. R.

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Y. Shi, W. Lin, D. J. Olson, J. H. Bechtel, H. Zhang, W. H. Steier, C. Zhang, and L. R. Dalton, “Electro-optic polymer modulators with 0.8 V half-wave voltage,” Appl. Phys. Lett. 77, 1–3 (2000).
[CrossRef]

David, G.

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, “Electrooptic mapping and finite-element modeling of the near-field pattern of a microstrip patch antenna,” IEEE Trans. Microwave Theory Tech. 48, 288–294 (2000).
[CrossRef]

Duvillaret, L.

Erlig, H.

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Fetterman, H. R.

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Follonier, S.

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, “Electro-optic properties of the organic salt 4-N,N-dimethylamino-4′-N′-methylstilbazolium tosylate,” Appl. Phys. Lett. 69, 13–15 (1996).
[CrossRef]

Gunning, M. J.

Günter, P.

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, “Electro-optic properties of the organic salt 4-N,N-dimethylamino-4′-N′-methylstilbazolium tosylate,” Appl. Phys. Lett. 69, 13–15 (1996).
[CrossRef]

Helm, H.

P. Uhd Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Hill, R. A.

Hoerman, B. H.

B. H. Hoerman, B. M. Nichols, M. J. Nystrom, and B. W. Wessels, “Dynamic response of the electro-optic effect in epitaxial KNbO3,” Appl. Phys. Lett. 75, 2707–2709 (1999).
[CrossRef]

Ito, H.

S. Sohma, H. Takahashi, T. Taniuchi, and H. Ito, “Organic nonlinear crystal DAST growth and its device applications,” Chem. Phys. 245, 359 (1999).
[CrossRef]

Jepsen, P. Uhd

P. Uhd Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Jiang, Z.

Kaminow, I. P.

I. P. Kaminow and E. H. Turner, “Linear electro-optical materials,” in Handbook of Lasers, R. J. Pressley, ed. (Chemical Rubber, Cleveland, Ohio, 1971), pp. 447–459.

Katehi, L. P. B.

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, “Electrooptic mapping and finite-element modeling of the near-field pattern of a microstrip patch antenna,” IEEE Trans. Microwave Theory Tech. 48, 288–294 (2000).
[CrossRef]

K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77, 486–488 (2000).
[CrossRef]

Keiding, S. R.

P. Uhd Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Knoesen, A.

Knöpfle, G.

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, “Electro-optic properties of the organic salt 4-N,N-dimethylamino-4′-N′-methylstilbazolium tosylate,” Appl. Phys. Lett. 69, 13–15 (1996).
[CrossRef]

Kobayashi, T.

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
[CrossRef]

Lalama, S. J.

K. D. Singer, S. J. Lalama, J. E. Sohn, and R. D. Small, “Electro-optic organic materials,” in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987), pp. 435–468.

Lin, W.

Y. Shi, W. Lin, D. J. Olson, J. H. Bechtel, H. Zhang, W. H. Steier, C. Zhang, and L. R. Dalton, “Electro-optic polymer modulators with 0.8 V half-wave voltage,” Appl. Phys. Lett. 77, 1–3 (2000).
[CrossRef]

Litz, M.

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
[CrossRef]

Mertin, W.

W. Mertin, “Two-dimensional field mapping of monolithic microwave integrated circuits using electro-optic sampling techniques,” Opt. Quantum Electron. 28, 801–817 (1996).
[CrossRef]

Morimoto, A.

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
[CrossRef]

Murata, H.

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
[CrossRef]

Nagatsuma, T.

M. Shinagawa and T. Nagatsuma, “An automated electro-optic probing system for ultrahigh-speed IC’s,” IEEE Trans. Instrum. Meas. 43, 843–847 (1994).
[CrossRef]

Nichols, B. M.

B. H. Hoerman, B. M. Nichols, M. J. Nystrom, and B. W. Wessels, “Dynamic response of the electro-optic effect in epitaxial KNbO3,” Appl. Phys. Lett. 75, 2707–2709 (1999).
[CrossRef]

Nienhuys, H.-K.

Nystrom, M. J.

B. H. Hoerman, B. M. Nichols, M. J. Nystrom, and B. W. Wessels, “Dynamic response of the electro-optic effect in epitaxial KNbO3,” Appl. Phys. Lett. 75, 2707–2709 (1999).
[CrossRef]

Oh, M.-C.

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Olson, D. J.

Y. Shi, W. Lin, D. J. Olson, J. H. Bechtel, H. Zhang, W. H. Steier, C. Zhang, and L. R. Dalton, “Electro-optic polymer modulators with 0.8 V half-wave voltage,” Appl. Phys. Lett. 77, 1–3 (2000).
[CrossRef]

Pan, F.

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, “Electro-optic properties of the organic salt 4-N,N-dimethylamino-4′-N′-methylstilbazolium tosylate,” Appl. Phys. Lett. 69, 13–15 (1996).
[CrossRef]

Papapolymerou, I.

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, “Electrooptic mapping and finite-element modeling of the near-field pattern of a microstrip patch antenna,” IEEE Trans. Microwave Theory Tech. 48, 288–294 (2000).
[CrossRef]

Planken, P. C. M.

Prêtre, Ph.

Raab, R. E.

Rialland, S.

Schall, M.

P. Uhd Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Schyja, V.

P. Uhd Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Shen, Y. R.

Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 4, pp. 53–57.

Shi, Y.

Y. Shi, W. Lin, D. J. Olson, J. H. Bechtel, H. Zhang, W. H. Steier, C. Zhang, and L. R. Dalton, “Electro-optic polymer modulators with 0.8 V half-wave voltage,” Appl. Phys. Lett. 77, 1–3 (2000).
[CrossRef]

Shinagawa, M.

M. Shinagawa and T. Nagatsuma, “An automated electro-optic probing system for ultrahigh-speed IC’s,” IEEE Trans. Instrum. Meas. 43, 843–847 (1994).
[CrossRef]

Singer, K. D.

K. D. Singer, S. J. Lalama, J. E. Sohn, and R. D. Small, “Electro-optic organic materials,” in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987), pp. 435–468.

Small, R. D.

K. D. Singer, S. J. Lalama, J. E. Sohn, and R. D. Small, “Electro-optic organic materials,” in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987), pp. 435–468.

Sohma, S.

S. Sohma, H. Takahashi, T. Taniuchi, and H. Ito, “Organic nonlinear crystal DAST growth and its device applications,” Chem. Phys. 245, 359 (1999).
[CrossRef]

Sohn, J. E.

K. D. Singer, S. J. Lalama, J. E. Sohn, and R. D. Small, “Electro-optic organic materials,” in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987), pp. 435–468.

Spreiter, R.

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, “Electro-optic properties of the organic salt 4-N,N-dimethylamino-4′-N′-methylstilbazolium tosylate,” Appl. Phys. Lett. 69, 13–15 (1996).
[CrossRef]

Steier, W. H.

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Y. Shi, W. Lin, D. J. Olson, J. H. Bechtel, H. Zhang, W. H. Steier, C. Zhang, and L. R. Dalton, “Electro-optic polymer modulators with 0.8 V half-wave voltage,” Appl. Phys. Lett. 77, 1–3 (2000).
[CrossRef]

Szep, A.

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Takahashi, H.

S. Sohma, H. Takahashi, T. Taniuchi, and H. Ito, “Organic nonlinear crystal DAST growth and its device applications,” Chem. Phys. 245, 359 (1999).
[CrossRef]

Tani, M.

Taniuchi, T.

S. Sohma, H. Takahashi, T. Taniuchi, and H. Ito, “Organic nonlinear crystal DAST growth and its device applications,” Chem. Phys. 245, 359 (1999).
[CrossRef]

Thakur, M.

J. Xu, L. Zhou, and M. Thakur, “Electro-optic modulation using an organic single crystal film in a Fabry–Perot cavity,” Appl. Phys. Lett. 72, 153–154 (1998).
[CrossRef]

Tsap, B.

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Turner, E. H.

I. P. Kaminow and E. H. Turner, “Linear electro-optical materials,” in Handbook of Lasers, R. J. Pressley, ed. (Chemical Rubber, Cleveland, Ohio, 1971), pp. 447–459.

Wenckebach, T.

Wessels, B. W.

B. H. Hoerman, B. M. Nichols, M. J. Nystrom, and B. W. Wessels, “Dynamic response of the electro-optic effect in epitaxial KNbO3,” Appl. Phys. Lett. 75, 2707–2709 (1999).
[CrossRef]

Whitaker, J. F.

K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77, 486–488 (2000).
[CrossRef]

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, “Electrooptic mapping and finite-element modeling of the near-field pattern of a microstrip patch antenna,” IEEE Trans. Microwave Theory Tech. 48, 288–294 (2000).
[CrossRef]

Winnewisser, C.

P. Uhd Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Wong, M. S.

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, “Electro-optic properties of the organic salt 4-N,N-dimethylamino-4′-N′-methylstilbazolium tosylate,” Appl. Phys. Lett. 69, 13–15 (1996).
[CrossRef]

Wu, L.-M.

Wu, Q.

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
[CrossRef]

Xu, J.

J. Xu, L. Zhou, and M. Thakur, “Electro-optic modulation using an organic single crystal film in a Fabry–Perot cavity,” Appl. Phys. Lett. 72, 153–154 (1998).
[CrossRef]

Yamamoto, S.

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
[CrossRef]

Yang, K.

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, “Electrooptic mapping and finite-element modeling of the near-field pattern of a microstrip patch antenna,” IEEE Trans. Microwave Theory Tech. 48, 288–294 (2000).
[CrossRef]

K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77, 486–488 (2000).
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Saunders, Orlando, Fla., 1991), Chap. 9, Table 9-1, pp. 312–314.

Yook, J.-G.

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, “Electrooptic mapping and finite-element modeling of the near-field pattern of a microstrip patch antenna,” IEEE Trans. Microwave Theory Tech. 48, 288–294 (2000).
[CrossRef]

Zhang, C.

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Y. Shi, W. Lin, D. J. Olson, J. H. Bechtel, H. Zhang, W. H. Steier, C. Zhang, and L. R. Dalton, “Electro-optic polymer modulators with 0.8 V half-wave voltage,” Appl. Phys. Lett. 77, 1–3 (2000).
[CrossRef]

Zhang, H.

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Y. Shi, W. Lin, D. J. Olson, J. H. Bechtel, H. Zhang, W. H. Steier, C. Zhang, and L. R. Dalton, “Electro-optic polymer modulators with 0.8 V half-wave voltage,” Appl. Phys. Lett. 77, 1–3 (2000).
[CrossRef]

Zhang, X.-C.

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B 18, 823–831 (2001).
[CrossRef]

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
[CrossRef]

Zhou, L.

J. Xu, L. Zhou, and M. Thakur, “Electro-optic modulation using an organic single crystal film in a Fabry–Perot cavity,” Appl. Phys. Lett. 72, 153–154 (1998).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (6)

J. Xu, L. Zhou, and M. Thakur, “Electro-optic modulation using an organic single crystal film in a Fabry–Perot cavity,” Appl. Phys. Lett. 72, 153–154 (1998).
[CrossRef]

Y. Shi, W. Lin, D. J. Olson, J. H. Bechtel, H. Zhang, W. H. Steier, C. Zhang, and L. R. Dalton, “Electro-optic polymer modulators with 0.8 V half-wave voltage,” Appl. Phys. Lett. 77, 1–3 (2000).
[CrossRef]

B. H. Hoerman, B. M. Nichols, M. J. Nystrom, and B. W. Wessels, “Dynamic response of the electro-optic effect in epitaxial KNbO3,” Appl. Phys. Lett. 75, 2707–2709 (1999).
[CrossRef]

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, “Electro-optic properties of the organic salt 4-N,N-dimethylamino-4′-N′-methylstilbazolium tosylate,” Appl. Phys. Lett. 69, 13–15 (1996).
[CrossRef]

K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77, 486–488 (2000).
[CrossRef]

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
[CrossRef]

Chem. Phys. (1)

S. Sohma, H. Takahashi, T. Taniuchi, and H. Ito, “Organic nonlinear crystal DAST growth and its device applications,” Chem. Phys. 245, 359 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
[CrossRef]

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophores,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

M. Shinagawa and T. Nagatsuma, “An automated electro-optic probing system for ultrahigh-speed IC’s,” IEEE Trans. Instrum. Meas. 43, 843–847 (1994).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, “Electrooptic mapping and finite-element modeling of the near-field pattern of a microstrip patch antenna,” IEEE Trans. Microwave Theory Tech. 48, 288–294 (2000).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Quantum Electron. (1)

W. Mertin, “Two-dimensional field mapping of monolithic microwave integrated circuits using electro-optic sampling techniques,” Opt. Quantum Electron. 28, 801–817 (1996).
[CrossRef]

Phys. Rev. E (1)

P. Uhd Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Other (7)

Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987).

I. P. Kaminow and E. H. Turner, “Linear electro-optical materials,” in Handbook of Lasers, R. J. Pressley, ed. (Chemical Rubber, Cleveland, Ohio, 1971), pp. 447–459.

K. D. Singer, S. J. Lalama, J. E. Sohn, and R. D. Small, “Electro-optic organic materials,” in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987), pp. 435–468.

Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 4, pp. 53–57.

DAST belongs to the monoclinic m-Cc group, exhibiting ten different nonvanishing electro-optic coefficients. Among them, only six have been measured.19

An error appears in relation (29) of Ref. 11. The numerical coefficient of the last term should be 4/6 instead of 2/6. This leads to a corrected expression (36) of Ref. 11 equal to that of relation (21) in this paper.

A. Yariv, Optical Electronics, 4th ed. (Saunders, Orlando, Fla., 1991), Chap. 9, Table 9-1, pp. 312–314.

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Figures (10)

Fig. 1
Fig. 1

Index ellipsoid of the EO crystal in absence of applied electric field with polar angles θ and φ of the light beam wave vector k.

Fig. 2
Fig. 2

Transformation of the eigendielectric referential (x, y, z) of the EO crystal to the new coordinate system (X, Y, Z) linked to the wave vector k.

Fig. 3
Fig. 3

Ellipse, defined as intersection of the plane of polarization of the optical beam and the index ellipsoid, and its principal indices of refraction without (a) and with (b) an applied electric field E in the case of an anisotropic crystal.

Fig. 4
Fig. 4

One-, two-, or three-dimensional electric field measurements by, respectively, a longitudinal EO sensor (a), a transversal EO sensor (b), or a fully vectorial EO sensor (c). EK represents the unique electric field component to which the EO sensor reacts and T is the ternary symmetry axis of the X, Y, Z coordinate system.

Fig. 5
Fig. 5

Circle (without applied electric field, in dashed curve) and ellipse (with applied electric field E, in solid curve), defined as intersection of the plane of polarization of the optical beam and the index ellipsoid, and its principal indices of refraction, in the case of an isotropic crystal.

Fig. 6
Fig. 6

Ellipse formed by the values of δEΩ2 obtained for a unitary electric field lying in the plane perpendicular to e, represented together with the sensitivity vectors ΔKM and ΔKN and with the principal sensitivity vectors ΔKa and ΔKb.

Fig. 7
Fig. 7

LiTaO3 crystal: moduli K-, K+, and ΔK of the three sensitivity vectors, normalized to the maximal value of 340 pm/V and represented as shaded areas ranging from black to white, versus the polar angles θ and φ of the wave vector. Thick contour lines indicate Λ values 2° apart from 0° (L), 54.57° (V), and 90° (T).

Fig. 8
Fig. 8

KNbO3 crystal: moduli K-, K+, and ΔK of the three sensitivity vectors, normalized to the maximal value of 1540 pm/V and represented as shaded areas ranging from black to white, versus the polar angles θ and φ of the wave vector. Thick contour lines indicate Λ values 2° apart from 0° (L), 54.57° (V), and 90° (T).

Fig. 9
Fig. 9

KTP crystal: moduli K-, K+, and ΔK of the three sensitivity vectors, normalized to the maximal value of 225 pm/V and represented as shaded areas ranging from black to white, versus the polar angles θ and φ of the wave vector. Thick contour lines indicate Λ values 2° apart from 0° (L), 54.57° (V), and 90° (T).

Fig. 10
Fig. 10

ZnTe crystal: moduli ΔKa and ΔKb of the two principal sensitivity vectors, normalized to the maximal value of 115 pm/V and represented as shaded areas ranging from black to white every 5%, versus the polar angles θ and φ of the wave vector (parallels and meridians are represented in gray every 10°). Angle Λ between the wave vector and e is represented as shaded areas ranging from black (0°) to white (90°) every 5°.

Tables (2)

Tables Icon

Table 1 High-Frequency Values of the EO Tensor Coefficients, Refractive Indicesa, Microwave Dielectric Constants, and Other Physical Characteristicsb of the Crystals Considered

Tables Icon

Table 2 Main Parameters for the Most Interesting Practical EO Sensor Configurations

Equations (38)

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(xyz)·αϕϕβδδχ·xyz=1,
α=1/nx2+r1jEΩj,β=1/ny2+r2jEΩj,
χ=1/nz2+r3jEΩj,δ=r4jEΩj,
=r5jEΩj,ϕ=r6jEΩj.
(XYZ)·AFEFBDEDC·XYZ=1,
AFEFBDEDCRθ;Y×Rφ;z×αϕϕβδδχ×R-φ;z×R-θ;Y,
AX2+2FXY+BY2=1.
A=(α cos2 φ+β sin2 φ+ϕ sin 2φ)cos2 θ+χ sin2 θ-( cos φ+δ sin φ)sin 2θ,
B=α sin2 φ+β cos2 φ-ϕ sin 2φ,
F=β-α2 sin 2φ+ϕ cos 2φcos θ+( sin φ-δ cos φ)sin θ.
n±=2A+B±[(A-B)2+4F2]1/21/2.
δn±(E1+E2)δn±(E1)+δn±(E2).
δn±(EΩ)n±(EΩ)-n±(0)n±(EΩ)|0·EΩK±·EΩ.
Λ=arccos|Kx sin θ cos φ+Ky sin θ sin φ+Kz cos θK.
δn±(EΩ)=r41n34{L·EΩ[(M·EΩ)2+4(N·EΩ)2]1/2},
L=(sin 2θ sin φ, sin 2θ cos φ, sin2 θ sin 2φ),
M=(-sin 2θ sin φ,-sin 2θ cos φ,(1+cos2 θ)sin 2φ),
N=(-sin θ cos φ, sin θ sin φ, cos θ cos 2φ).
tan(2Ψ)=2FA-B=2 N·EΩM·EΩ.
δEΩδn-(EΩ)-δn+(EΩ)=[(ΔKM·EΩ)2+(ΔKN·EΩ)2]1/2,
ΔKM=r41n32 M,
ΔKN=r41n3N.
δEΩ=[(ΔKa·EΩ)2+(ΔKb·EΩ)2]1/2.
ΔKa2=r412n62(U+V),
ΔKb2=r412n62(U-V);
U=γ2+cos2 θ cos2 2φ+sin2 θ(1+cos2 θ),
V=[cos4 θ cos4 2φ+(γ2-sin4 θ)2+2 cos2 θ cos2 2φ(γ2+sin4 θ)]1/2,
γ=1+cos2 θ2 sin 2φ.
θ=arctancos 2φtan θ 1+1+cos2 θ2 cos2 θ tan 2φ21/2,
φ=arctan1+cos2 θ2 cos2 θ tan 2φ-φ.
Λ=arccos|sin 2θ| cos2 θ(1+cos2 2φ)+γ sin 2φcos θ4κ+sin2 2θ.
ΔKa=r41n3e100,
ΔKb=0,
ΔKa=r41n3e1¯10,
ΔKb=r41n32 e001.
δEΩ=r41n3EΩ2(1+3 sin2 ϕ)1/2.
ΔKa=ΔKb=2/3r41n3.
δEΩ=2/3r41n3EΩ.

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