Abstract

We present a complete analysis of electro-optic sensors for electric field measurement based on three different modulation techniques: amplitude, phase, and polarization state modulation. We treat the most general case, considering both isotropic and anisotropic crystals and taking into account the absorption of the crystal. We derive the optimal configuration of experimental setups for the three studied modulation techniques, and we give the values of the variable physical parameters required to yield the best performance. Finally we compare the three modulation techniques and show that phase or polarization state modulations result in exactly the same performance while amplitude modulation gives slightly enhanced performance.

© 2002 Optical Society of America

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  1. J. A. Valdmanis, G. A. Mourou, and C. W. Gabel, “Subpicosecond electrical sampling,” IEEE J. Quantum Electron. 19, 664–667 (1983).
    [CrossRef]
  2. B. H. Kolner and D. M. Bloom, “Electro-optic sampling in GaAs integrated circuits,” IEEE J. Quantum Electron. 22, 79–93 (1986).
    [CrossRef]
  3. Z. Jiang and X.-C. Zhang, “Terahertz imaging via electro-optic effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
    [CrossRef]
  4. M. S. Litz, D. C. Judy, G. A. Huttlin, C. Lazard, L. F. Libelo, X.-C. Zhang, and Z. Lu, “A wideband, dielectric, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 72–78 (1997).
    [CrossRef]
  5. W. Thomann, M. Rottenkolber, and P. Russer, “Optimization of electro-optic sampling by volume-integral method,” IEEE Trans. Microwave Theory Tech. 41, 2393–2399 (1993).
    [CrossRef]
  6. Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (1999).
    [CrossRef]
  7. D. M. Zhang, M. B. Yi, X. J. Tian, W. Sun, A. L. Hou, J. Z. Sun, Y. G. Ma, W. J. Tian, and J. C. Shen, “External electro-optic measurement utilizing poled polymer-based asymmetric Fabry–Perot reflection film,” J. Appl. Phys. 86, 6184–6188 (1999).
    [CrossRef]
  8. 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]
  9. 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 orientations,” J. Opt. Soc. Am. B 19, 2704–2715 (2002).
    [CrossRef]
  10. Z. Jiang and X.-C. Zhang, “Single-shot spatiotemporal terahertz field imaging,” Opt. Lett. 23, 1114–1116 (1998).
    [CrossRef]
  11. S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electro-optic/magneto-optic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611–2616 (2000).
    [CrossRef]
  12. J. Latess, C. J. Lazard, “High-power, integrated photonic, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 79–84 (1997).
    [CrossRef]
  13. P. O. Müller, S. B. Alleston, A. J. Vickers, and D. Erasme, “An external electro-optic sampling technique based on the Fabry–Perot effect,” IEEE J. Quantum Electron. 35, 7–11 (1999).
    [CrossRef]
  14. A. Sasaki and T. Nagatsuma, “Millimeter-wave imaging using an electro-optic detector as a harmonic mixer,” IEEE J. Sel. Top. Quantum Electron. 6, 735–740 (2000).
    [CrossRef]
  15. 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]
  16. A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), pp. 16–29.
  17. J.-P. Perez, Optique, 5th ed. (Masson, Paris, 1996), pp. 210–226.
  18. J.-P. Perez, Optique, 5th ed. (Masson, Paris, 1996), pp. 321–326.

2002 (1)

2001 (1)

2000 (2)

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electro-optic/magneto-optic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611–2616 (2000).
[CrossRef]

A. Sasaki and T. Nagatsuma, “Millimeter-wave imaging using an electro-optic detector as a harmonic mixer,” IEEE J. Sel. Top. Quantum Electron. 6, 735–740 (2000).
[CrossRef]

1999 (4)

P. O. Müller, S. B. Alleston, A. J. Vickers, and D. Erasme, “An external electro-optic sampling technique based on the Fabry–Perot effect,” IEEE J. Quantum Electron. 35, 7–11 (1999).
[CrossRef]

Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (1999).
[CrossRef]

D. M. Zhang, M. B. Yi, X. J. Tian, W. Sun, A. L. Hou, J. Z. Sun, Y. G. Ma, W. J. Tian, and J. C. Shen, “External electro-optic measurement utilizing poled polymer-based asymmetric Fabry–Perot reflection film,” J. Appl. Phys. 86, 6184–6188 (1999).
[CrossRef]

Z. Jiang and X.-C. Zhang, “Terahertz imaging via electro-optic effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
[CrossRef]

1998 (1)

1997 (2)

M. S. Litz, D. C. Judy, G. A. Huttlin, C. Lazard, L. F. Libelo, X.-C. Zhang, and Z. Lu, “A wideband, dielectric, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 72–78 (1997).
[CrossRef]

J. Latess, C. J. Lazard, “High-power, integrated photonic, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 79–84 (1997).
[CrossRef]

1996 (1)

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]

1993 (1)

W. Thomann, M. Rottenkolber, and P. Russer, “Optimization of electro-optic sampling by volume-integral method,” IEEE Trans. Microwave Theory Tech. 41, 2393–2399 (1993).
[CrossRef]

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]

1983 (1)

J. A. Valdmanis, G. A. Mourou, and C. W. Gabel, “Subpicosecond electrical sampling,” IEEE J. Quantum Electron. 19, 664–667 (1983).
[CrossRef]

Abe, M.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electro-optic/magneto-optic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611–2616 (2000).
[CrossRef]

Alleston, S. B.

P. O. Müller, S. B. Alleston, A. J. Vickers, and D. Erasme, “An external electro-optic sampling technique based on the Fabry–Perot effect,” IEEE J. Quantum Electron. 35, 7–11 (1999).
[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]

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]

Chen, Q.

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]

Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (1999).
[CrossRef]

Coutaz, J.-L.

Duvillaret, L.

Erasme, D.

P. O. Müller, S. B. Alleston, A. J. Vickers, and D. Erasme, “An external electro-optic sampling technique based on the Fabry–Perot effect,” IEEE J. Quantum Electron. 35, 7–11 (1999).
[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]

Gabel, C. W.

J. A. Valdmanis, G. A. Mourou, and C. W. Gabel, “Subpicosecond electrical sampling,” IEEE J. Quantum Electron. 19, 664–667 (1983).
[CrossRef]

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]

Hou, A. L.

D. M. Zhang, M. B. Yi, X. J. Tian, W. Sun, A. L. Hou, J. Z. Sun, Y. G. Ma, W. J. Tian, and J. C. Shen, “External electro-optic measurement utilizing poled polymer-based asymmetric Fabry–Perot reflection film,” J. Appl. Phys. 86, 6184–6188 (1999).
[CrossRef]

Huttlin, G. A.

M. S. Litz, D. C. Judy, G. A. Huttlin, C. Lazard, L. F. Libelo, X.-C. Zhang, and Z. Lu, “A wideband, dielectric, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 72–78 (1997).
[CrossRef]

Jiang, Z.

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]

Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (1999).
[CrossRef]

Z. Jiang and X.-C. Zhang, “Terahertz imaging via electro-optic effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
[CrossRef]

Z. Jiang and X.-C. Zhang, “Single-shot spatiotemporal terahertz field imaging,” Opt. Lett. 23, 1114–1116 (1998).
[CrossRef]

Judy, D. C.

M. S. Litz, D. C. Judy, G. A. Huttlin, C. Lazard, L. F. Libelo, X.-C. Zhang, and Z. Lu, “A wideband, dielectric, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 72–78 (1997).
[CrossRef]

Kishi, M.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electro-optic/magneto-optic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611–2616 (2000).
[CrossRef]

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]

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]

Latess, J.

J. Latess, C. J. Lazard, “High-power, integrated photonic, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 79–84 (1997).
[CrossRef]

Lazard, C.

M. S. Litz, D. C. Judy, G. A. Huttlin, C. Lazard, L. F. Libelo, X.-C. Zhang, and Z. Lu, “A wideband, dielectric, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 72–78 (1997).
[CrossRef]

Lazard, C. J.

J. Latess, C. J. Lazard, “High-power, integrated photonic, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 79–84 (1997).
[CrossRef]

Libelo, L. F.

M. S. Litz, D. C. Judy, G. A. Huttlin, C. Lazard, L. F. Libelo, X.-C. Zhang, and Z. Lu, “A wideband, dielectric, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 72–78 (1997).
[CrossRef]

Litz, M. S.

M. S. Litz, D. C. Judy, G. A. Huttlin, C. Lazard, L. F. Libelo, X.-C. Zhang, and Z. Lu, “A wideband, dielectric, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 72–78 (1997).
[CrossRef]

Lu, Z.

M. S. Litz, D. C. Judy, G. A. Huttlin, C. Lazard, L. F. Libelo, X.-C. Zhang, and Z. Lu, “A wideband, dielectric, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 72–78 (1997).
[CrossRef]

Ma, Y. G.

D. M. Zhang, M. B. Yi, X. J. Tian, W. Sun, A. L. Hou, J. Z. Sun, Y. G. Ma, W. J. Tian, and J. C. Shen, “External electro-optic measurement utilizing poled polymer-based asymmetric Fabry–Perot reflection film,” J. Appl. Phys. 86, 6184–6188 (1999).
[CrossRef]

Mourou, G. A.

J. A. Valdmanis, G. A. Mourou, and C. W. Gabel, “Subpicosecond electrical sampling,” IEEE J. Quantum Electron. 19, 664–667 (1983).
[CrossRef]

Müller, P. O.

P. O. Müller, S. B. Alleston, A. J. Vickers, and D. Erasme, “An external electro-optic sampling technique based on the Fabry–Perot effect,” IEEE J. Quantum Electron. 35, 7–11 (1999).
[CrossRef]

Nagatsuma, T.

A. Sasaki and T. Nagatsuma, “Millimeter-wave imaging using an electro-optic detector as a harmonic mixer,” IEEE J. Sel. Top. Quantum Electron. 6, 735–740 (2000).
[CrossRef]

Ohara, T.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electro-optic/magneto-optic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611–2616 (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]

Rialland, S.

Rottenkolber, M.

W. Thomann, M. Rottenkolber, and P. Russer, “Optimization of electro-optic sampling by volume-integral method,” IEEE Trans. Microwave Theory Tech. 41, 2393–2399 (1993).
[CrossRef]

Russer, P.

W. Thomann, M. Rottenkolber, and P. Russer, “Optimization of electro-optic sampling by volume-integral method,” IEEE Trans. Microwave Theory Tech. 41, 2393–2399 (1993).
[CrossRef]

Sasaki, A.

A. Sasaki and T. Nagatsuma, “Millimeter-wave imaging using an electro-optic detector as a harmonic mixer,” IEEE J. Sel. Top. Quantum Electron. 6, 735–740 (2000).
[CrossRef]

Shen, J. C.

D. M. Zhang, M. B. Yi, X. J. Tian, W. Sun, A. L. Hou, J. Z. Sun, Y. G. Ma, W. J. Tian, and J. C. Shen, “External electro-optic measurement utilizing poled polymer-based asymmetric Fabry–Perot reflection film,” J. Appl. Phys. 86, 6184–6188 (1999).
[CrossRef]

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]

Sun, F. G.

Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (1999).
[CrossRef]

Sun, J. Z.

D. M. Zhang, M. B. Yi, X. J. Tian, W. Sun, A. L. Hou, J. Z. Sun, Y. G. Ma, W. J. Tian, and J. C. Shen, “External electro-optic measurement utilizing poled polymer-based asymmetric Fabry–Perot reflection film,” J. Appl. Phys. 86, 6184–6188 (1999).
[CrossRef]

Sun, W.

D. M. Zhang, M. B. Yi, X. J. Tian, W. Sun, A. L. Hou, J. Z. Sun, Y. G. Ma, W. J. Tian, and J. C. Shen, “External electro-optic measurement utilizing poled polymer-based asymmetric Fabry–Perot reflection film,” J. Appl. Phys. 86, 6184–6188 (1999).
[CrossRef]

Tani, M.

Thomann, W.

W. Thomann, M. Rottenkolber, and P. Russer, “Optimization of electro-optic sampling by volume-integral method,” IEEE Trans. Microwave Theory Tech. 41, 2393–2399 (1993).
[CrossRef]

Tian, W. J.

D. M. Zhang, M. B. Yi, X. J. Tian, W. Sun, A. L. Hou, J. Z. Sun, Y. G. Ma, W. J. Tian, and J. C. Shen, “External electro-optic measurement utilizing poled polymer-based asymmetric Fabry–Perot reflection film,” J. Appl. Phys. 86, 6184–6188 (1999).
[CrossRef]

Tian, X. J.

D. M. Zhang, M. B. Yi, X. J. Tian, W. Sun, A. L. Hou, J. Z. Sun, Y. G. Ma, W. J. Tian, and J. C. Shen, “External electro-optic measurement utilizing poled polymer-based asymmetric Fabry–Perot reflection film,” J. Appl. Phys. 86, 6184–6188 (1999).
[CrossRef]

Tsuchiya, M.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electro-optic/magneto-optic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611–2616 (2000).
[CrossRef]

Valdmanis, J. A.

J. A. Valdmanis, G. A. Mourou, and C. W. Gabel, “Subpicosecond electrical sampling,” IEEE J. Quantum Electron. 19, 664–667 (1983).
[CrossRef]

Vickers, A. J.

P. O. Müller, S. B. Alleston, A. J. Vickers, and D. Erasme, “An external electro-optic sampling technique based on the Fabry–Perot effect,” IEEE J. Quantum Electron. 35, 7–11 (1999).
[CrossRef]

Wakana, S.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electro-optic/magneto-optic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611–2616 (2000).
[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]

Yamazaki, E.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electro-optic/magneto-optic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611–2616 (2000).
[CrossRef]

Yi, M. B.

D. M. Zhang, M. B. Yi, X. J. Tian, W. Sun, A. L. Hou, J. Z. Sun, Y. G. Ma, W. J. Tian, and J. C. Shen, “External electro-optic measurement utilizing poled polymer-based asymmetric Fabry–Perot reflection film,” J. Appl. Phys. 86, 6184–6188 (1999).
[CrossRef]

Zhang, D. M.

D. M. Zhang, M. B. Yi, X. J. Tian, W. Sun, A. L. Hou, J. Z. Sun, Y. G. Ma, W. J. Tian, and J. C. Shen, “External electro-optic measurement utilizing poled polymer-based asymmetric Fabry–Perot reflection film,” J. Appl. Phys. 86, 6184–6188 (1999).
[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]

Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (1999).
[CrossRef]

Z. Jiang and X.-C. Zhang, “Terahertz imaging via electro-optic effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
[CrossRef]

Z. Jiang and X.-C. Zhang, “Single-shot spatiotemporal terahertz field imaging,” Opt. Lett. 23, 1114–1116 (1998).
[CrossRef]

M. S. Litz, D. C. Judy, G. A. Huttlin, C. Lazard, L. F. Libelo, X.-C. Zhang, and Z. Lu, “A wideband, dielectric, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 72–78 (1997).
[CrossRef]

Appl. Phys. Lett. (2)

Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (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]

IEEE J. Quantum Electron. (3)

P. O. Müller, S. B. Alleston, A. J. Vickers, and D. Erasme, “An external electro-optic sampling technique based on the Fabry–Perot effect,” IEEE J. Quantum Electron. 35, 7–11 (1999).
[CrossRef]

J. A. Valdmanis, G. A. Mourou, and C. W. Gabel, “Subpicosecond electrical sampling,” IEEE J. Quantum Electron. 19, 664–667 (1983).
[CrossRef]

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

IEEE J. Sel. Top. Quantum Electron. (1)

A. Sasaki and T. Nagatsuma, “Millimeter-wave imaging using an electro-optic detector as a harmonic mixer,” IEEE J. Sel. Top. Quantum Electron. 6, 735–740 (2000).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (3)

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electro-optic/magneto-optic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611–2616 (2000).
[CrossRef]

Z. Jiang and X.-C. Zhang, “Terahertz imaging via electro-optic effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
[CrossRef]

W. Thomann, M. Rottenkolber, and P. Russer, “Optimization of electro-optic sampling by volume-integral method,” IEEE Trans. Microwave Theory Tech. 41, 2393–2399 (1993).
[CrossRef]

J. Appl. Phys. (1)

D. M. Zhang, M. B. Yi, X. J. Tian, W. Sun, A. L. Hou, J. Z. Sun, Y. G. Ma, W. J. Tian, and J. C. Shen, “External electro-optic measurement utilizing poled polymer-based asymmetric Fabry–Perot reflection film,” J. Appl. Phys. 86, 6184–6188 (1999).
[CrossRef]

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

Opt. Lett. (1)

Proc. SPIE (2)

M. S. Litz, D. C. Judy, G. A. Huttlin, C. Lazard, L. F. Libelo, X.-C. Zhang, and Z. Lu, “A wideband, dielectric, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 72–78 (1997).
[CrossRef]

J. Latess, C. J. Lazard, “High-power, integrated photonic, electric field sensor,” in Intense Microwave Pulses V, H. E. Brandt, ed., Proc. SPIE 3158, 79–84 (1997).
[CrossRef]

Other (3)

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), pp. 16–29.

J.-P. Perez, Optique, 5th ed. (Masson, Paris, 1996), pp. 210–226.

J.-P. Perez, Optique, 5th ed. (Masson, Paris, 1996), pp. 321–326.

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Figures (12)

Fig. 1
Fig. 1

Generic detection system for the use of PSM: EO, electro-optic, crystal; PBS, polarizing beam splitter; PD, photodiode.

Fig. 2
Fig. 2

Representation of any polarization state of the probe beam in terms of ellipticity ξb/a, optical power density I, and orientation χ, and in terms of magnitudes A1 and A2 and phase retardation ϕ.

Fig. 3
Fig. 3

Optimal experimental setup for the use of PSM: P, polarizer; EO, electro-optic crystal; PBS, polarizing beam splitter; PD, photodiode.

Fig. 4
Fig. 4

Fabry–Pérot interferometer used for AM: EO, electro-optic crystal; M, mirror.

Fig. 5
Fig. 5

Power transmission coefficient versus optical frequency of a 10-finesse Fabry–Pérot interferometer with the optimal operation point for AM.

Fig. 6
Fig. 6

Case of signal-independent noise: optimal reflection coefficient R (solid curve) of the cavity mirrors and associated finesse F (dashed curve) of the interferometer versus absorption factor αL of the EO crystal.

Fig. 7
Fig. 7

Case of signal-independent noise: figure of merit of AM versus absorption factor αL of the EO crystal.

Fig. 8
Fig. 8

Case of signal-proportional noise: optimal mean reflection coefficient R (solid curve) of the cavity mirrors and associated finesse F (dashed curve) of the interferometer versus absorption factor αL of the EO crystal. Heavy curves are relative to measurements performed in reflection while light curves are relative to measurements performed in transmission.

Fig. 9
Fig. 9

Case of signal-proportional noise: figure of merit of AM versus the absorption factor αL of the EO crystal for measurements both in reflection (heavy curve) and in transmission (light curve).

Fig. 10
Fig. 10

Case of noise proportional to the square root of the signal: optimal mean reflection coefficient R (solid curve) of the cavity mirrors and associated finesse F (dashed curve) of the interferometer versus absorption factor αL of the EO crystal. Heavy curves are relative to measurements performed in reflection while light curves are relative to measurements performed in transmission.

Fig. 11
Fig. 11

Case of noise proportional to the square root of the signal: figure of merit of AM versus the absorption factor αL of the EO crystal for measurements both in reflection (heavy curve) and in transmission (light curve).

Fig. 12
Fig. 12

Mach–Zehnder interferometer used for PM with power transmission and reflection coefficients of the two beam splitters: EO electro-optic crystal; M, mirror; BS, beam splitter.

Tables (5)

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Table 1 Figure of Merit, Expression of Normalized Optical Power Detected on Path 1, and Associated Optimal Values of Variable Parameters in Case of Polarization State Modulation

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Table 2 Figure of Merit, Expression of Normalized Optical Power, and Associated Optimal Values of Variable Parameters for Measurements Performed in Transmission in Case of Amplitude Modulation

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Table 3 Figure of Merit, Expression of Normalized Optical Power, and Associated Optimal Values of Adjustable Parameters for Measurements Performed in Reflection in Case of Amplitude Modulation

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Table 4 Figure of Merit, Expression of Normalized Optical Power Detected on Principal Path, and Associated Optimal Values of Variable Parameters in Case of Phase Modulation

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Table 5 Figures of Merit for PSM, AM, and PM in Case of a Fully Transparent Electro-Optic Crystal

Equations (54)

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ϕcry=2πLλ[n+(EΩ)n(EΩ)]=2πLλΔn(0)ϕ0+2πLλ[Δn(EΩ)Δn(0)]ϕE,
A1A2 exp(-jϕ).
I=A12+A22,
ξ2=1-1-Λ21+1-Λ2,
Λ=2A1A2 sin ϕA12+A22,
tan(2χ)=2A1A2 cos ϕA12-A22.
A12=cos2 χ+ξ2 sin2 χ1+ξ2×I,
A22=sin2 χ+ξ2 cos2 χ1+ξ2×I,
sin-2 ϕ=(ξ2+ξ-2)sin2 χ cos2 χ+sin4 χ+cos4 χ.
κ1/200(ηκ)1/2 exp[-j(ϕ0+ϕE)],
κ1/2A1(ηκ)1/2A2 exp(-jΔϕ),
R-Θ·M1/2·RΘ-Ψ·M1/4·RΨ-Φ·M1/4·RΦ,
P˜1=κ(P¯+ΔP),
P˜2=κ(P¯-ΔP),
P¯=1+η4-1-η4ζ,
ΔP=[η(1-ζ2)]1/22(a cos Δϕ+b sin Δϕ)-1+η4ζ-1-η4c,
ζ=-1-ξ21+ξ2 cos 2χ,
a=cos 2(Ψ-Φ)cos(4Θ-2Ψ)sin 2Φ-sin(4Θ-2Ψ)cos 2Φ,
b=sin 2(Ψ-Φ)cos(4Θ-2Ψ),
c=cos 2(Ψ-Φ)cos(4Θ-2Ψ)cos 2Φ+sin(4Θ-2Ψ)sin 2Φ.
a=cos(4Θ-2Ψ)sin 2Ψ,
b=sin(4Θ-2Ψ),
c=cos(4Θ-2Ψ)cos 2Ψ.
cos Δϕ=±b(1-c2)-1/2.
ΔPϕE2[η(1-ζ2)(1-c2)]1/2-c4[(1+η)ζ-(1-η)].
c=-ζ=-(1-ησ)/(1+ησ).
(1-ξ2)/(1+ξ2)cos 2χ=-(1-ησ)/(1+ησ).
cos(4Θ-2Ψ)cos 2Ψ=-(1-ησ)/(1+ησ).
sin(4Θ-2Ψ)
=±2ησ/21+ησcosarcsin1+tan2 χ[(ξ2+ξ-2)tan2 χ+tan4 χ+1]1/2+ϕ0.
ξ=0,
χ=±arctan(η-σ/2),
Ψ=12 arccos±(1-ησ)(1+η2σ-2ησ cos 2ϕ0)1/2,
Θ=14 arccos-1-ησ1+ησ±2ησ sin 2ϕ0(1+ησ)(1+η2σ-2ησ cos 2ϕ0)1/2.
TFP=TFπR2 11+2Fπ2 sin2(ϕ0+ϕE+ϕr),
ϕE=2πLλ[n(EΩ)-n(0)],
FFSRΔf=πR exp(-αL)1-R exp(-2αL),
FSR=c2nL.
RFP+TFP+AFP=1.
AFP
=[1-exp(-αL)]p=0+T1R1int(p/2)R2int[(p+1)/2] exp(-αL)
=T1[1-exp(-αL)][1+R2 exp(-αL)]1-R2 exp(-2αL).
SϕETFPϕE=RFPϕE=TFπR2 334πF.
P˜t34 TFπR21+3FπϕE
P˜r1-T1[1-exp(-αL)][1+R2 exp(-αL)]1-R2 exp(-2αL)-34 TFπR21+3FπϕE.
It(t0)=I0(1-R2)R1int[νt+L/2L]R2int(νt/2L) exp(-ανt),
It(t0)=I0 1-R2R2 exp(-t/τ)τ=nL/cαL-ln R.
fc=12πτ=FSR(αL-ln R)π.
R2R1+1-R1+RαL.
R2R1+45 1-R1+RαL.
Δϕ=2π(n-1)Lλ-ϕ0,
P˜p=R1(1-R2)+κR2(1-R1)+2[κR1R2(1-R1)×(1-R2)]1/2 cos Δϕ,
P˜c=κ(1-R1)(1-R2)+R1R2-2[κR1R2(1-R1)×(1-R2)]1/2 cos Δϕ.
ϕ02π[n(EΩ=0)-1]Lλ+π2[π].

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