Abstract

We present a high-finesse optical cavity containing a LiTaO3 electro-optic crystal, devoted to free-space electric field characterization. Theoretical considerations will show that the modulation depth is directly related to the transversal components of the field to be measured, thus opening the way to vectorial mapping of the electric field using a single electro-optic crystal. Also, a discussion about noise and sensitivity will be given. As the latter increases with the effective cavity length, and bandwidth decreases, a trade-off is realized, allowing us to measure an electric field of 60  mV/m/Hz in a 110  MHz bandwidth. Cavity dimensions are less than 8mm3, giving an inner-crystal transverse spatial resolution of 70μm and allowing pigtailed systems to integrate.

© 2007 Optical Society of America

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References

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  1. B. H. Kolner and D. M. Bloom, "Electro-optic sampling in GaAs integrated circuits," IEEE J. Quantum Electron. 22, 79-93 (1986).
    [Crossref]
  2. K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, "Electro-optic 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. G. Gaborit, L. Duvillaret, N. Breuil, B. Crabos, and J.-L. Lasserre, "Low invasiveness, high-bandwidth vectorial pigtailed electro-optic sensors for high power electromagnetics measurements," in Proceedings of European Electromagnetics, EUROEM (Magdeburg, 2004), pp. 70-71.
  4. G. Roussy, K. Agbossou, and B. Dichtel, "Vector electric field measurement using a noninterfering sensor," Meas. Sci. Technol. 11, 1145-1151 (2000).
    [Crossref]
  5. M. Shinagawa, T. Nagatsuma, K. Ohno, and Y. Jin, "A real-time electro-optic handy probe using a continuous-wave laser," IEEE Trans. Microwave Theory Tech. 50, 1076-1080 (2001).
  6. S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, "Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field," IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
    [Crossref]
  7. S. T. Vohra and F. Bucholtz, "Fiber-optic ac electric-field sensor based on the electrostrictive effect," Opt. Lett. 17, 372-374 (1992).
    [Crossref] [PubMed]
  8. K. M. Bohnert and J. Nehring, "Fiber-optic sensing of electric field components," Appl. Opt. 27, 4814-4818 (1988).
    [Crossref] [PubMed]
  9. C. Li and T. Yoshino, "Optical voltage sensor based on electrooptic crystal multiplier," J. Lightwave Technol. 20, 843-849 (2002).
    [Crossref]
  10. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
  11. L. Duvillaret, S. Rialland, and J.-L. Coutaz, "Electro-optic sensors for electric-field measurements. I. Theoretical comparison among different modulation techniques," J. Opt. Soc. Am. B 19, 2692-2703 (2002).
    [Crossref]
  12. T. Meier, C. Kostrzewa, K. Petermann, and B. Schüppert, "Integrated optical E-field probes with segmented modulator electrodes," J. Lightwave Technol. 12, 1497-1503 (1994).
    [Crossref]
  13. D. H. Naghski, J. T. Boyd, H. E. Jackson, S. Sriram, S. A. Kingsley, and J. Latess, "An integrated photonic Mach-Zehnder interferometer with no electrodes for sensing electric fields," J. Lightwave Technol. 12, 1092-1098 (1994).
    [Crossref]
  14. 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]
  15. L. Duvillaret, S. Rialland, and J.-L. Coutaz, "Electro-optic sensors for electric-field measurements. II. Choice of the crystals and complete optimization of their orientation," J. Opt. Soc. Am. B 19, 2704-2715 (2002).
    [Crossref]
  16. G. Gaborit, G. Martin, L. Duvillaret, J.-L. Coutaz, C. T. Nguyen, R. Hierle, and J. Zyss, "Electro-optic probe based on an organic microcavity," IEEE Photon. Technol. Lett. 17, 2140-2142 (2005).
    [Crossref]
  17. J. Morville and D. Romanini, "Sensitive birefringence measurement in a high-finesse resonator using diode laser optical self-locking," Appl. Phys. B. 74, 495-501 (2005).
    [Crossref]
  18. A. Yariv, Optical Electronics, 4th ed. (Saunders, 1991).

2005 (2)

G. Gaborit, G. Martin, L. Duvillaret, J.-L. Coutaz, C. T. Nguyen, R. Hierle, and J. Zyss, "Electro-optic probe based on an organic microcavity," IEEE Photon. Technol. Lett. 17, 2140-2142 (2005).
[Crossref]

J. Morville and D. Romanini, "Sensitive birefringence measurement in a high-finesse resonator using diode laser optical self-locking," Appl. Phys. B. 74, 495-501 (2005).
[Crossref]

2002 (3)

2001 (1)

M. Shinagawa, T. Nagatsuma, K. Ohno, and Y. Jin, "A real-time electro-optic handy probe using a continuous-wave laser," IEEE Trans. Microwave Theory Tech. 50, 1076-1080 (2001).

2000 (4)

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, "Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field," IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[Crossref]

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, "Electro-optic 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]

G. Roussy, K. Agbossou, and B. Dichtel, "Vector electric field measurement using a noninterfering sensor," Meas. Sci. Technol. 11, 1145-1151 (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]

1994 (2)

T. Meier, C. Kostrzewa, K. Petermann, and B. Schüppert, "Integrated optical E-field probes with segmented modulator electrodes," J. Lightwave Technol. 12, 1497-1503 (1994).
[Crossref]

D. H. Naghski, J. T. Boyd, H. E. Jackson, S. Sriram, S. A. Kingsley, and J. Latess, "An integrated photonic Mach-Zehnder interferometer with no electrodes for sensing electric fields," J. Lightwave Technol. 12, 1092-1098 (1994).
[Crossref]

1992 (1)

1988 (1)

1986 (1)

B. H. Kolner and D. M. Bloom, "Electro-optic sampling in GaAs integrated circuits," IEEE J. Quantum Electron. 22, 79-93 (1986).
[Crossref]

Abe, M.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, "Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field," IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[Crossref]

Agbossou, K.

G. Roussy, K. Agbossou, and B. Dichtel, "Vector electric field measurement using a noninterfering sensor," Meas. Sci. Technol. 11, 1145-1151 (2000).
[Crossref]

Bloom, D. M.

B. H. Kolner and D. M. Bloom, "Electro-optic sampling in GaAs integrated circuits," IEEE J. Quantum Electron. 22, 79-93 (1986).
[Crossref]

Bohnert, K. M.

Boyd, J. T.

D. H. Naghski, J. T. Boyd, H. E. Jackson, S. Sriram, S. A. Kingsley, and J. Latess, "An integrated photonic Mach-Zehnder interferometer with no electrodes for sensing electric fields," J. Lightwave Technol. 12, 1092-1098 (1994).
[Crossref]

Breuil, N.

G. Gaborit, L. Duvillaret, N. Breuil, B. Crabos, and J.-L. Lasserre, "Low invasiveness, high-bandwidth vectorial pigtailed electro-optic sensors for high power electromagnetics measurements," in Proceedings of European Electromagnetics, EUROEM (Magdeburg, 2004), pp. 70-71.

Bucholtz, F.

Coutaz, J.-L.

Crabos, B.

G. Gaborit, L. Duvillaret, N. Breuil, B. Crabos, and J.-L. Lasserre, "Low invasiveness, high-bandwidth vectorial pigtailed electro-optic sensors for high power electromagnetics measurements," in Proceedings of European Electromagnetics, EUROEM (Magdeburg, 2004), pp. 70-71.

David, G.

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, "Electro-optic 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]

Dichtel, B.

G. Roussy, K. Agbossou, and B. Dichtel, "Vector electric field measurement using a noninterfering sensor," Meas. Sci. Technol. 11, 1145-1151 (2000).
[Crossref]

Duvillaret, L.

G. Gaborit, G. Martin, L. Duvillaret, J.-L. Coutaz, C. T. Nguyen, R. Hierle, and J. Zyss, "Electro-optic probe based on an organic microcavity," IEEE Photon. Technol. Lett. 17, 2140-2142 (2005).
[Crossref]

L. Duvillaret, S. Rialland, and J.-L. Coutaz, "Electro-optic sensors for electric-field measurements. II. Choice of the crystals and complete optimization of their orientation," J. Opt. Soc. Am. B 19, 2704-2715 (2002).
[Crossref]

L. Duvillaret, S. Rialland, and J.-L. Coutaz, "Electro-optic sensors for electric-field measurements. I. Theoretical comparison among different modulation techniques," J. Opt. Soc. Am. B 19, 2692-2703 (2002).
[Crossref]

G. Gaborit, L. Duvillaret, N. Breuil, B. Crabos, and J.-L. Lasserre, "Low invasiveness, high-bandwidth vectorial pigtailed electro-optic sensors for high power electromagnetics measurements," in Proceedings of European Electromagnetics, EUROEM (Magdeburg, 2004), pp. 70-71.

Gaborit, G.

G. Gaborit, G. Martin, L. Duvillaret, J.-L. Coutaz, C. T. Nguyen, R. Hierle, and J. Zyss, "Electro-optic probe based on an organic microcavity," IEEE Photon. Technol. Lett. 17, 2140-2142 (2005).
[Crossref]

G. Gaborit, L. Duvillaret, N. Breuil, B. Crabos, and J.-L. Lasserre, "Low invasiveness, high-bandwidth vectorial pigtailed electro-optic sensors for high power electromagnetics measurements," in Proceedings of European Electromagnetics, EUROEM (Magdeburg, 2004), pp. 70-71.

Hierle, R.

G. Gaborit, G. Martin, L. Duvillaret, J.-L. Coutaz, C. T. Nguyen, R. Hierle, and J. Zyss, "Electro-optic probe based on an organic microcavity," IEEE Photon. Technol. Lett. 17, 2140-2142 (2005).
[Crossref]

Jackson, H. E.

D. H. Naghski, J. T. Boyd, H. E. Jackson, S. Sriram, S. A. Kingsley, and J. Latess, "An integrated photonic Mach-Zehnder interferometer with no electrodes for sensing electric fields," J. Lightwave Technol. 12, 1092-1098 (1994).
[Crossref]

Jin, Y.

M. Shinagawa, T. Nagatsuma, K. Ohno, and Y. Jin, "A real-time electro-optic handy probe using a continuous-wave laser," IEEE Trans. Microwave Theory Tech. 50, 1076-1080 (2001).

Katehi, L. P. B.

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, "Electro-optic 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]

Kingsley, S. A.

D. H. Naghski, J. T. Boyd, H. E. Jackson, S. Sriram, S. A. Kingsley, and J. Latess, "An integrated photonic Mach-Zehnder interferometer with no electrodes for sensing electric fields," J. Lightwave Technol. 12, 1092-1098 (1994).
[Crossref]

Kishi, M.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, "Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field," IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[Crossref]

Kolner, B. H.

B. H. Kolner and D. M. Bloom, "Electro-optic sampling in GaAs integrated circuits," IEEE J. Quantum Electron. 22, 79-93 (1986).
[Crossref]

Kostrzewa, C.

T. Meier, C. Kostrzewa, K. Petermann, and B. Schüppert, "Integrated optical E-field probes with segmented modulator electrodes," J. Lightwave Technol. 12, 1497-1503 (1994).
[Crossref]

Lasserre, J.-L.

G. Gaborit, L. Duvillaret, N. Breuil, B. Crabos, and J.-L. Lasserre, "Low invasiveness, high-bandwidth vectorial pigtailed electro-optic sensors for high power electromagnetics measurements," in Proceedings of European Electromagnetics, EUROEM (Magdeburg, 2004), pp. 70-71.

Latess, J.

D. H. Naghski, J. T. Boyd, H. E. Jackson, S. Sriram, S. A. Kingsley, and J. Latess, "An integrated photonic Mach-Zehnder interferometer with no electrodes for sensing electric fields," J. Lightwave Technol. 12, 1092-1098 (1994).
[Crossref]

Li, C.

C. Li and T. Yoshino, "Optical voltage sensor based on electrooptic crystal multiplier," J. Lightwave Technol. 20, 843-849 (2002).
[Crossref]

Martin, G.

G. Gaborit, G. Martin, L. Duvillaret, J.-L. Coutaz, C. T. Nguyen, R. Hierle, and J. Zyss, "Electro-optic probe based on an organic microcavity," IEEE Photon. Technol. Lett. 17, 2140-2142 (2005).
[Crossref]

Meier, T.

T. Meier, C. Kostrzewa, K. Petermann, and B. Schüppert, "Integrated optical E-field probes with segmented modulator electrodes," J. Lightwave Technol. 12, 1497-1503 (1994).
[Crossref]

Morville, J.

J. Morville and D. Romanini, "Sensitive birefringence measurement in a high-finesse resonator using diode laser optical self-locking," Appl. Phys. B. 74, 495-501 (2005).
[Crossref]

Nagatsuma, T.

M. Shinagawa, T. Nagatsuma, K. Ohno, and Y. Jin, "A real-time electro-optic handy probe using a continuous-wave laser," IEEE Trans. Microwave Theory Tech. 50, 1076-1080 (2001).

Naghski, D. H.

D. H. Naghski, J. T. Boyd, H. E. Jackson, S. Sriram, S. A. Kingsley, and J. Latess, "An integrated photonic Mach-Zehnder interferometer with no electrodes for sensing electric fields," J. Lightwave Technol. 12, 1092-1098 (1994).
[Crossref]

Nehring, J.

Nguyen, C. T.

G. Gaborit, G. Martin, L. Duvillaret, J.-L. Coutaz, C. T. Nguyen, R. Hierle, and J. Zyss, "Electro-optic probe based on an organic microcavity," IEEE Photon. Technol. Lett. 17, 2140-2142 (2005).
[Crossref]

Ohara, T.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, "Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field," IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[Crossref]

Ohno, K.

M. Shinagawa, T. Nagatsuma, K. Ohno, and Y. Jin, "A real-time electro-optic handy probe using a continuous-wave laser," IEEE Trans. Microwave Theory Tech. 50, 1076-1080 (2001).

Papapolymerou, I.

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, "Electro-optic 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]

Petermann, K.

T. Meier, C. Kostrzewa, K. Petermann, and B. Schüppert, "Integrated optical E-field probes with segmented modulator electrodes," J. Lightwave Technol. 12, 1497-1503 (1994).
[Crossref]

Rialland, S.

Romanini, D.

J. Morville and D. Romanini, "Sensitive birefringence measurement in a high-finesse resonator using diode laser optical self-locking," Appl. Phys. B. 74, 495-501 (2005).
[Crossref]

Roussy, G.

G. Roussy, K. Agbossou, and B. Dichtel, "Vector electric field measurement using a noninterfering sensor," Meas. Sci. Technol. 11, 1145-1151 (2000).
[Crossref]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

Schüppert, B.

T. Meier, C. Kostrzewa, K. Petermann, and B. Schüppert, "Integrated optical E-field probes with segmented modulator electrodes," J. Lightwave Technol. 12, 1497-1503 (1994).
[Crossref]

Shinagawa, M.

M. Shinagawa, T. Nagatsuma, K. Ohno, and Y. Jin, "A real-time electro-optic handy probe using a continuous-wave laser," IEEE Trans. Microwave Theory Tech. 50, 1076-1080 (2001).

Sriram, S.

D. H. Naghski, J. T. Boyd, H. E. Jackson, S. Sriram, S. A. Kingsley, and J. Latess, "An integrated photonic Mach-Zehnder interferometer with no electrodes for sensing electric fields," J. Lightwave Technol. 12, 1092-1098 (1994).
[Crossref]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

Tsuchiya, M.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, "Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field," IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[Crossref]

Vohra, S. T.

Wakana, S.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, "Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field," IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[Crossref]

Whitaker, J. F.

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, "Electro-optic 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]

Yamazaki, E.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, "Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field," IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[Crossref]

Yang, K.

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, "Electro-optic 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]

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Saunders, 1991).

Yook, J.-G.

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, "Electro-optic 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]

Yoshino, T.

C. Li and T. Yoshino, "Optical voltage sensor based on electrooptic crystal multiplier," J. Lightwave Technol. 20, 843-849 (2002).
[Crossref]

Zyss, J.

G. Gaborit, G. Martin, L. Duvillaret, J.-L. Coutaz, C. T. Nguyen, R. Hierle, and J. Zyss, "Electro-optic probe based on an organic microcavity," IEEE Photon. Technol. Lett. 17, 2140-2142 (2005).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B. (1)

J. Morville and D. Romanini, "Sensitive birefringence measurement in a high-finesse resonator using diode laser optical self-locking," Appl. Phys. B. 74, 495-501 (2005).
[Crossref]

Appl. Phys. Lett. (1)

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]

IEEE J. Quantum Electron. (1)

B. H. Kolner and D. M. Bloom, "Electro-optic sampling in GaAs integrated circuits," IEEE J. Quantum Electron. 22, 79-93 (1986).
[Crossref]

IEEE Photon. Technol. Lett. (1)

G. Gaborit, G. Martin, L. Duvillaret, J.-L. Coutaz, C. T. Nguyen, R. Hierle, and J. Zyss, "Electro-optic probe based on an organic microcavity," IEEE Photon. Technol. Lett. 17, 2140-2142 (2005).
[Crossref]

IEEE Trans. Microwave Theory Tech. (3)

K. Yang, G. David, J.-G. Yook, I. Papapolymerou, L. P. B. Katehi, and J. F. Whitaker, "Electro-optic 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]

M. Shinagawa, T. Nagatsuma, K. Ohno, and Y. Jin, "A real-time electro-optic handy probe using a continuous-wave laser," IEEE Trans. Microwave Theory Tech. 50, 1076-1080 (2001).

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, "Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field," IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[Crossref]

J. Lightwave Technol. (3)

C. Li and T. Yoshino, "Optical voltage sensor based on electrooptic crystal multiplier," J. Lightwave Technol. 20, 843-849 (2002).
[Crossref]

T. Meier, C. Kostrzewa, K. Petermann, and B. Schüppert, "Integrated optical E-field probes with segmented modulator electrodes," J. Lightwave Technol. 12, 1497-1503 (1994).
[Crossref]

D. H. Naghski, J. T. Boyd, H. E. Jackson, S. Sriram, S. A. Kingsley, and J. Latess, "An integrated photonic Mach-Zehnder interferometer with no electrodes for sensing electric fields," J. Lightwave Technol. 12, 1092-1098 (1994).
[Crossref]

J. Opt. Soc. Am. B (2)

Meas. Sci. Technol. (1)

G. Roussy, K. Agbossou, and B. Dichtel, "Vector electric field measurement using a noninterfering sensor," Meas. Sci. Technol. 11, 1145-1151 (2000).
[Crossref]

Opt. Lett. (1)

Other (3)

G. Gaborit, L. Duvillaret, N. Breuil, B. Crabos, and J.-L. Lasserre, "Low invasiveness, high-bandwidth vectorial pigtailed electro-optic sensors for high power electromagnetics measurements," in Proceedings of European Electromagnetics, EUROEM (Magdeburg, 2004), pp. 70-71.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

A. Yariv, Optical Electronics, 4th ed. (Saunders, 1991).

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Figures (9)

Fig. 1
Fig. 1

Transformation of the (x, y, z) electro-optic crystal axes to the new coordinate system (X, Y, Z), with Z aligned to the wave vector k . A first φ rotation about the z axis transforms the x(y) direction into the x ( y ) direction. A second θ rotation about the y axis changes the z direction into the k direction.

Fig. 2
Fig. 2

(Color online) Sketch of the cavity. Black stripes represent dielectric mirrors.

Fig. 3
Fig. 3

(Color online) Experimental setup.

Fig. 4
Fig. 4

QuickField electrostatic simulations of the E-field distribution in a 2 m m × 2 m m LiTaO 3 crystal sandwiched between two electrodes 3.6   mm distant. (a) Schematic of the simulation and (b) ratio between E y and E z with respect to the position inside the crystal following the dashed line in (a) from spot A to spot B, then to spots C and D and back to spot A.

Fig. 5
Fig. 5

Experimental measurement of noise as a function of the injected optical power for the photodiode. Solid and dashed lines correspond to the best fits with respectively linear and square-root dependences to the optical power. This measurement is performed with a resolution bandwidth of 200   Hz .

Fig. 6
Fig. 6

Modulation (black circles) and radiation (triangles) as a function of frequency. Theoretical response for E-field on z axis at low frequencies ( f = 247   kHz ) and for unidirectional E-field at high frequencies ( f = 100   MHz ) regimes are also shown. The inset shows the transmitted power (crosses) through the electrodes with an input power of 1   mW .

Fig. 7
Fig. 7

Modulation depth at 247   kHz for a polarization of p = 0 ° ( r 33 probing) of the incident laser and two directions of the applied field, E z (black circles), E y (triangles).

Fig. 8
Fig. 8

Modulation depth at 247   kHz for a polarization of p = 90 ° ( r 13 , r 22 probing) of the incident laser and two directions of the applied field, E z (black circles), E y (triangles).

Fig. 9
Fig. 9

Evolution of parameters A and r as functions of frequency.

Equations (19)

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

d = P mod u l a t e d P a v e r a g e .
A X 2 + 2 G X Y + B Y 2 = 1 ,
A = 1 n e 2 + r 33 E z ,
B = 1 n o 2 + r 22 E y + r 13 E z ,
G = r 51 E y ,
n ± = 2 A + B ± ( A B ) 2 + 4 G 2 .
n + = n e + δ n + ( E ) n e 1 2 n e 3 r 33 E z ,
n = n o + δ n ( E ) n o 1 2 n o 3 ( r 22 E y + r 13 E z ) .
T ( E ) = ( ( 1 R ) F π R ) 2 1 1 + ( 2 F π ) 2 sin 2 ( 2 π λ L n e f f ( E ) ) ,
max [ δ T ( E ) ] = max [ T n e f f δ n e f f ( E ) ] 3 3 F L 2 λ δ n e f f ( E ) ,
d = max [ δ T ( E e f f ) ] 0.75 T max 2 3 F L λ δ n e f f ( E e f f ) ,
d ( r 33 ) 3 F n e 3 L λ r 33 E z ,
d ( r 13 , r 22 ) 3 F n o 3 L λ ( r 13 E z + r 22 E y ) .
E p a r a s i t i c = E m a i n / A .
q = d ( r 33 , E E z ) d ( r 33 , E E y ) = E E / A = A .
S / N = R l o a d ( P o p t d ) 2 10 ( N ( dBm ) / 10 ) ,
E min 10 N ( dBm ) / 20 3 R l o a d P o p t F n e 3 r 33 L λ .
r = d ( r 33 ) d ( r 13 , r 22 ) r 33 r 13 .
d ( r 13 , r 22 ; E E z ) d ( r 13 , r 22 ; E E y ) = r 13 r 22 7.5 .

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