Abstract

An electro-optic probe tip that is made from LiTaO crystal to make tangentially two-dimensional electric-field (E-field) vector measurements is presented. We combine a new electro-optic modulation technique and a conventional one to resolve the two E-field components. The new modulation effect on the optical probing beam is caused by rotation of the principal axis the electro-optic crystal, which is proportional to the E-field. Inasmuch as there is no free charge involved in the axis rotation, rotation modulation of the axis can be as fast as conventional modulation. The principles are carefully derived, and an experimental system constructed, to measure two-dimensional E-field vectors on a test pattern. The results are in good agreement with those obtained with commercial software for electromagnetic simulation. The sensitivities of two tangential E-field components are 76 (mV/cm)/Hz and 0.8 (V/cm)/Hz, respectively. The root-mean-square error of an E-field directional measurement is 1.5°.

© 2000 Optical Society of America

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References

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  1. J. A. Valdmanis, G. Mourou, C. W. Gaabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41, 211–212 (1982).
    [Crossref]
  2. K. W. Chang, W. V. Sorin, “Electro-optic sampling of high speed nonlinear device,” in Ultrafast Electronics and Optoelectronics, J. Shah, U. Mishra, eds., Vol. 14 of OSA Procedings Series (Optical Society of America, Washington, D.C., 1993), pp. 220–223.
  3. J. A. Valdmanis, S. S. Pei, “A non-contact picosecond prober for intergrated circuit testing,” in Picosecond Electronics and Optoelectronics, F. J. Leonberger, C. H. Lee, F. Capasso, H. Morkoc, eds. (Springer-Verlag, New York, 1987).
    [Crossref]
  4. S. L. Huang, C. H. Lee, H.-L. A. Huang, “Real-time linear time-domain network analysis using picosecond photoconductive mixer and samplers,” IEEE Trans. Microwave Theory Tech. 43, 1281–1289 (1995).
    [Crossref]
  5. M. G. Li, E. V. Chauchard, C. H. Lee, H.-L. A. Hung, “Two-dimension field mapping of GaAs microstrip circuit by electro-optic sensing,” in Picosecond Electronics and Optoelectrics, F. J. Leonberger, C. H. Lee, F. Capasso, H. Morkoc, eds. (Springer-Verlag, New York, 1987), pp. 54–58.
  6. B. H. Kolner, D. M. Bloom, “Electrooptic sampling in GaAs integrated circuits,” IEEE J. Quantum Electron. QE-22, 79–93 (1986).
    [Crossref]
  7. M. S. Heutmaker, G. T. Harvey, “Electro-optic sampling of high-speed silicon integrated circuits using a GaAs probe tip,” Appl. Phys. Lett. 59, 146–148 (1991).
    [Crossref]
  8. D. L. Quang, D. Erasme, B. Huyart, “Fabry–Perot enhanced real-time electro-optic probing of MMICs,” Electron. Lett. 29, 498–499 (1993).
    [Crossref]
  9. H. Takahashi, S.-I. Aoshima, Y. Tsuchiya, “Sampling and real-time methods in electro-optic probing system,” IEEE Trans. Instrum. Meas. 44, 965–971 (1995).
    [Crossref]
  10. T. K. Ishii, Microwave Engineering, 2nd ed. (Harcourt Brace Jovanovich, San Diego, Calif., 1989).
  11. T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, E. M. Biebl, “Electro-optic near-field mapping of planar resonators,” IEEE Trans. Antennas Propag. 46, 284–291 (1998).
    [Crossref]
  12. K. Kamogawa, I. Toyoda, K. Nishikawa, T. Tokumitsu, “Characterization of a monolithic slot antenna using an electro-optic sampling technique,” IEEE Microwave Guided Wave Lett. 4, 414–416 (1994).
    [Crossref]
  13. Y. Imaizumi, M. Shinagawa, H. Ogawa, “Electric field distribution measurement of microstrip antenna and arrays using electro-optic sampling,” IEEE Trans. Microwave Theory Tech. 43, 2402–2047 (1995).
    [Crossref]
  14. W. K. Kuo, S. L. Huang, L. C. Chang, “On-wafer dual-beam electro-optic probing of electric-field vector,” in Digest of Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 142–143.
  15. W. K. Kuo, S. L. Huang, T. S. Horng, L. C. Chang, “Two-dimensional mapping of electric-field vector by electro-optic prober,” Opt. Commun. 149, 55–60 (1998).
    [Crossref]
  16. A. Yariv, P. Yeh, Optical Waves in Crystal (Wiley, New York, 1984).
  17. M. Y. Frankel, S. Gupta, J. A. Valdmanis, G. A. Mourou, “Terahertz attenuation and disperation characteristics of coplanar transmission lines,” IEEE Trans. Microwave Theory Tech. 39, 910–916 (1991).
    [Crossref]
  18. J. Nees, G. A. Mourou, “Noncontact electro-optic sampling with a GaAs injection laser,” Electron. Lett. 22, 918–919 (1986).
    [Crossref]
  19. W. M. Robertson, Optoelectronic Techniques for Microwave and Millimeter-Wave Engineering (Artech House, Boston, Mass., 1995).

1998 (2)

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, E. M. Biebl, “Electro-optic near-field mapping of planar resonators,” IEEE Trans. Antennas Propag. 46, 284–291 (1998).
[Crossref]

W. K. Kuo, S. L. Huang, T. S. Horng, L. C. Chang, “Two-dimensional mapping of electric-field vector by electro-optic prober,” Opt. Commun. 149, 55–60 (1998).
[Crossref]

1995 (3)

Y. Imaizumi, M. Shinagawa, H. Ogawa, “Electric field distribution measurement of microstrip antenna and arrays using electro-optic sampling,” IEEE Trans. Microwave Theory Tech. 43, 2402–2047 (1995).
[Crossref]

H. Takahashi, S.-I. Aoshima, Y. Tsuchiya, “Sampling and real-time methods in electro-optic probing system,” IEEE Trans. Instrum. Meas. 44, 965–971 (1995).
[Crossref]

S. L. Huang, C. H. Lee, H.-L. A. Huang, “Real-time linear time-domain network analysis using picosecond photoconductive mixer and samplers,” IEEE Trans. Microwave Theory Tech. 43, 1281–1289 (1995).
[Crossref]

1994 (1)

K. Kamogawa, I. Toyoda, K. Nishikawa, T. Tokumitsu, “Characterization of a monolithic slot antenna using an electro-optic sampling technique,” IEEE Microwave Guided Wave Lett. 4, 414–416 (1994).
[Crossref]

1993 (1)

D. L. Quang, D. Erasme, B. Huyart, “Fabry–Perot enhanced real-time electro-optic probing of MMICs,” Electron. Lett. 29, 498–499 (1993).
[Crossref]

1991 (2)

M. S. Heutmaker, G. T. Harvey, “Electro-optic sampling of high-speed silicon integrated circuits using a GaAs probe tip,” Appl. Phys. Lett. 59, 146–148 (1991).
[Crossref]

M. Y. Frankel, S. Gupta, J. A. Valdmanis, G. A. Mourou, “Terahertz attenuation and disperation characteristics of coplanar transmission lines,” IEEE Trans. Microwave Theory Tech. 39, 910–916 (1991).
[Crossref]

1986 (2)

J. Nees, G. A. Mourou, “Noncontact electro-optic sampling with a GaAs injection laser,” Electron. Lett. 22, 918–919 (1986).
[Crossref]

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

1982 (1)

J. A. Valdmanis, G. Mourou, C. W. Gaabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41, 211–212 (1982).
[Crossref]

Aoshima, S.-I.

H. Takahashi, S.-I. Aoshima, Y. Tsuchiya, “Sampling and real-time methods in electro-optic probing system,” IEEE Trans. Instrum. Meas. 44, 965–971 (1995).
[Crossref]

Biebl, E. M.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, E. M. Biebl, “Electro-optic near-field mapping of planar resonators,” IEEE Trans. Antennas Propag. 46, 284–291 (1998).
[Crossref]

Bloom, D. M.

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

Chang, K. W.

K. W. Chang, W. V. Sorin, “Electro-optic sampling of high speed nonlinear device,” in Ultrafast Electronics and Optoelectronics, J. Shah, U. Mishra, eds., Vol. 14 of OSA Procedings Series (Optical Society of America, Washington, D.C., 1993), pp. 220–223.

Chang, L. C.

W. K. Kuo, S. L. Huang, T. S. Horng, L. C. Chang, “Two-dimensional mapping of electric-field vector by electro-optic prober,” Opt. Commun. 149, 55–60 (1998).
[Crossref]

W. K. Kuo, S. L. Huang, L. C. Chang, “On-wafer dual-beam electro-optic probing of electric-field vector,” in Digest of Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 142–143.

Chauchard, E. V.

M. G. Li, E. V. Chauchard, C. H. Lee, H.-L. A. Hung, “Two-dimension field mapping of GaAs microstrip circuit by electro-optic sensing,” in Picosecond Electronics and Optoelectrics, F. J. Leonberger, C. H. Lee, F. Capasso, H. Morkoc, eds. (Springer-Verlag, New York, 1987), pp. 54–58.

Erasme, D.

D. L. Quang, D. Erasme, B. Huyart, “Fabry–Perot enhanced real-time electro-optic probing of MMICs,” Electron. Lett. 29, 498–499 (1993).
[Crossref]

Frankel, M. Y.

M. Y. Frankel, S. Gupta, J. A. Valdmanis, G. A. Mourou, “Terahertz attenuation and disperation characteristics of coplanar transmission lines,” IEEE Trans. Microwave Theory Tech. 39, 910–916 (1991).
[Crossref]

Gaabel, C. W.

J. A. Valdmanis, G. Mourou, C. W. Gaabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41, 211–212 (1982).
[Crossref]

Gupta, S.

M. Y. Frankel, S. Gupta, J. A. Valdmanis, G. A. Mourou, “Terahertz attenuation and disperation characteristics of coplanar transmission lines,” IEEE Trans. Microwave Theory Tech. 39, 910–916 (1991).
[Crossref]

Harvey, G. T.

M. S. Heutmaker, G. T. Harvey, “Electro-optic sampling of high-speed silicon integrated circuits using a GaAs probe tip,” Appl. Phys. Lett. 59, 146–148 (1991).
[Crossref]

Heutmaker, M. S.

M. S. Heutmaker, G. T. Harvey, “Electro-optic sampling of high-speed silicon integrated circuits using a GaAs probe tip,” Appl. Phys. Lett. 59, 146–148 (1991).
[Crossref]

Horng, T. S.

W. K. Kuo, S. L. Huang, T. S. Horng, L. C. Chang, “Two-dimensional mapping of electric-field vector by electro-optic prober,” Opt. Commun. 149, 55–60 (1998).
[Crossref]

Huang, H.-L. A.

S. L. Huang, C. H. Lee, H.-L. A. Huang, “Real-time linear time-domain network analysis using picosecond photoconductive mixer and samplers,” IEEE Trans. Microwave Theory Tech. 43, 1281–1289 (1995).
[Crossref]

Huang, S. L.

W. K. Kuo, S. L. Huang, T. S. Horng, L. C. Chang, “Two-dimensional mapping of electric-field vector by electro-optic prober,” Opt. Commun. 149, 55–60 (1998).
[Crossref]

S. L. Huang, C. H. Lee, H.-L. A. Huang, “Real-time linear time-domain network analysis using picosecond photoconductive mixer and samplers,” IEEE Trans. Microwave Theory Tech. 43, 1281–1289 (1995).
[Crossref]

W. K. Kuo, S. L. Huang, L. C. Chang, “On-wafer dual-beam electro-optic probing of electric-field vector,” in Digest of Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 142–143.

Hung, H.-L. A.

M. G. Li, E. V. Chauchard, C. H. Lee, H.-L. A. Hung, “Two-dimension field mapping of GaAs microstrip circuit by electro-optic sensing,” in Picosecond Electronics and Optoelectrics, F. J. Leonberger, C. H. Lee, F. Capasso, H. Morkoc, eds. (Springer-Verlag, New York, 1987), pp. 54–58.

Huyart, B.

D. L. Quang, D. Erasme, B. Huyart, “Fabry–Perot enhanced real-time electro-optic probing of MMICs,” Electron. Lett. 29, 498–499 (1993).
[Crossref]

Imaizumi, Y.

Y. Imaizumi, M. Shinagawa, H. Ogawa, “Electric field distribution measurement of microstrip antenna and arrays using electro-optic sampling,” IEEE Trans. Microwave Theory Tech. 43, 2402–2047 (1995).
[Crossref]

Ishii, T. K.

T. K. Ishii, Microwave Engineering, 2nd ed. (Harcourt Brace Jovanovich, San Diego, Calif., 1989).

Kamogawa, K.

K. Kamogawa, I. Toyoda, K. Nishikawa, T. Tokumitsu, “Characterization of a monolithic slot antenna using an electro-optic sampling technique,” IEEE Microwave Guided Wave Lett. 4, 414–416 (1994).
[Crossref]

Kolner, B. H.

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

Kuo, W. K.

W. K. Kuo, S. L. Huang, T. S. Horng, L. C. Chang, “Two-dimensional mapping of electric-field vector by electro-optic prober,” Opt. Commun. 149, 55–60 (1998).
[Crossref]

W. K. Kuo, S. L. Huang, L. C. Chang, “On-wafer dual-beam electro-optic probing of electric-field vector,” in Digest of Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 142–143.

Kurz, H.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, E. M. Biebl, “Electro-optic near-field mapping of planar resonators,” IEEE Trans. Antennas Propag. 46, 284–291 (1998).
[Crossref]

Lee, C. H.

S. L. Huang, C. H. Lee, H.-L. A. Huang, “Real-time linear time-domain network analysis using picosecond photoconductive mixer and samplers,” IEEE Trans. Microwave Theory Tech. 43, 1281–1289 (1995).
[Crossref]

M. G. Li, E. V. Chauchard, C. H. Lee, H.-L. A. Hung, “Two-dimension field mapping of GaAs microstrip circuit by electro-optic sensing,” in Picosecond Electronics and Optoelectrics, F. J. Leonberger, C. H. Lee, F. Capasso, H. Morkoc, eds. (Springer-Verlag, New York, 1987), pp. 54–58.

Li, M. G.

M. G. Li, E. V. Chauchard, C. H. Lee, H.-L. A. Hung, “Two-dimension field mapping of GaAs microstrip circuit by electro-optic sensing,” in Picosecond Electronics and Optoelectrics, F. J. Leonberger, C. H. Lee, F. Capasso, H. Morkoc, eds. (Springer-Verlag, New York, 1987), pp. 54–58.

Loffler, T.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, E. M. Biebl, “Electro-optic near-field mapping of planar resonators,” IEEE Trans. Antennas Propag. 46, 284–291 (1998).
[Crossref]

Mourou, G.

J. A. Valdmanis, G. Mourou, C. W. Gaabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41, 211–212 (1982).
[Crossref]

Mourou, G. A.

M. Y. Frankel, S. Gupta, J. A. Valdmanis, G. A. Mourou, “Terahertz attenuation and disperation characteristics of coplanar transmission lines,” IEEE Trans. Microwave Theory Tech. 39, 910–916 (1991).
[Crossref]

J. Nees, G. A. Mourou, “Noncontact electro-optic sampling with a GaAs injection laser,” Electron. Lett. 22, 918–919 (1986).
[Crossref]

Nees, J.

J. Nees, G. A. Mourou, “Noncontact electro-optic sampling with a GaAs injection laser,” Electron. Lett. 22, 918–919 (1986).
[Crossref]

Nishikawa, K.

K. Kamogawa, I. Toyoda, K. Nishikawa, T. Tokumitsu, “Characterization of a monolithic slot antenna using an electro-optic sampling technique,” IEEE Microwave Guided Wave Lett. 4, 414–416 (1994).
[Crossref]

Ogawa, H.

Y. Imaizumi, M. Shinagawa, H. Ogawa, “Electric field distribution measurement of microstrip antenna and arrays using electro-optic sampling,” IEEE Trans. Microwave Theory Tech. 43, 2402–2047 (1995).
[Crossref]

Pei, S. S.

J. A. Valdmanis, S. S. Pei, “A non-contact picosecond prober for intergrated circuit testing,” in Picosecond Electronics and Optoelectronics, F. J. Leonberger, C. H. Lee, F. Capasso, H. Morkoc, eds. (Springer-Verlag, New York, 1987).
[Crossref]

Pfeifer, T.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, E. M. Biebl, “Electro-optic near-field mapping of planar resonators,” IEEE Trans. Antennas Propag. 46, 284–291 (1998).
[Crossref]

Quang, D. L.

D. L. Quang, D. Erasme, B. Huyart, “Fabry–Perot enhanced real-time electro-optic probing of MMICs,” Electron. Lett. 29, 498–499 (1993).
[Crossref]

Robertson, W. M.

W. M. Robertson, Optoelectronic Techniques for Microwave and Millimeter-Wave Engineering (Artech House, Boston, Mass., 1995).

Roskos, H. G.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, E. M. Biebl, “Electro-optic near-field mapping of planar resonators,” IEEE Trans. Antennas Propag. 46, 284–291 (1998).
[Crossref]

Shinagawa, M.

Y. Imaizumi, M. Shinagawa, H. Ogawa, “Electric field distribution measurement of microstrip antenna and arrays using electro-optic sampling,” IEEE Trans. Microwave Theory Tech. 43, 2402–2047 (1995).
[Crossref]

Singer, M.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, E. M. Biebl, “Electro-optic near-field mapping of planar resonators,” IEEE Trans. Antennas Propag. 46, 284–291 (1998).
[Crossref]

Sorin, W. V.

K. W. Chang, W. V. Sorin, “Electro-optic sampling of high speed nonlinear device,” in Ultrafast Electronics and Optoelectronics, J. Shah, U. Mishra, eds., Vol. 14 of OSA Procedings Series (Optical Society of America, Washington, D.C., 1993), pp. 220–223.

Takahashi, H.

H. Takahashi, S.-I. Aoshima, Y. Tsuchiya, “Sampling and real-time methods in electro-optic probing system,” IEEE Trans. Instrum. Meas. 44, 965–971 (1995).
[Crossref]

Tokumitsu, T.

K. Kamogawa, I. Toyoda, K. Nishikawa, T. Tokumitsu, “Characterization of a monolithic slot antenna using an electro-optic sampling technique,” IEEE Microwave Guided Wave Lett. 4, 414–416 (1994).
[Crossref]

Toyoda, I.

K. Kamogawa, I. Toyoda, K. Nishikawa, T. Tokumitsu, “Characterization of a monolithic slot antenna using an electro-optic sampling technique,” IEEE Microwave Guided Wave Lett. 4, 414–416 (1994).
[Crossref]

Tsuchiya, Y.

H. Takahashi, S.-I. Aoshima, Y. Tsuchiya, “Sampling and real-time methods in electro-optic probing system,” IEEE Trans. Instrum. Meas. 44, 965–971 (1995).
[Crossref]

Valdmanis, J. A.

M. Y. Frankel, S. Gupta, J. A. Valdmanis, G. A. Mourou, “Terahertz attenuation and disperation characteristics of coplanar transmission lines,” IEEE Trans. Microwave Theory Tech. 39, 910–916 (1991).
[Crossref]

J. A. Valdmanis, G. Mourou, C. W. Gaabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41, 211–212 (1982).
[Crossref]

J. A. Valdmanis, S. S. Pei, “A non-contact picosecond prober for intergrated circuit testing,” in Picosecond Electronics and Optoelectronics, F. J. Leonberger, C. H. Lee, F. Capasso, H. Morkoc, eds. (Springer-Verlag, New York, 1987).
[Crossref]

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystal (Wiley, New York, 1984).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystal (Wiley, New York, 1984).

Appl. Phys. Lett. (2)

J. A. Valdmanis, G. Mourou, C. W. Gaabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41, 211–212 (1982).
[Crossref]

M. S. Heutmaker, G. T. Harvey, “Electro-optic sampling of high-speed silicon integrated circuits using a GaAs probe tip,” Appl. Phys. Lett. 59, 146–148 (1991).
[Crossref]

Electron. Lett. (2)

D. L. Quang, D. Erasme, B. Huyart, “Fabry–Perot enhanced real-time electro-optic probing of MMICs,” Electron. Lett. 29, 498–499 (1993).
[Crossref]

J. Nees, G. A. Mourou, “Noncontact electro-optic sampling with a GaAs injection laser,” Electron. Lett. 22, 918–919 (1986).
[Crossref]

IEEE J. Quantum Electron. (1)

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

IEEE Microwave Guided Wave Lett. (1)

K. Kamogawa, I. Toyoda, K. Nishikawa, T. Tokumitsu, “Characterization of a monolithic slot antenna using an electro-optic sampling technique,” IEEE Microwave Guided Wave Lett. 4, 414–416 (1994).
[Crossref]

IEEE Trans. Antennas Propag. (1)

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, E. M. Biebl, “Electro-optic near-field mapping of planar resonators,” IEEE Trans. Antennas Propag. 46, 284–291 (1998).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

H. Takahashi, S.-I. Aoshima, Y. Tsuchiya, “Sampling and real-time methods in electro-optic probing system,” IEEE Trans. Instrum. Meas. 44, 965–971 (1995).
[Crossref]

IEEE Trans. Microwave Theory Tech. (3)

S. L. Huang, C. H. Lee, H.-L. A. Huang, “Real-time linear time-domain network analysis using picosecond photoconductive mixer and samplers,” IEEE Trans. Microwave Theory Tech. 43, 1281–1289 (1995).
[Crossref]

Y. Imaizumi, M. Shinagawa, H. Ogawa, “Electric field distribution measurement of microstrip antenna and arrays using electro-optic sampling,” IEEE Trans. Microwave Theory Tech. 43, 2402–2047 (1995).
[Crossref]

M. Y. Frankel, S. Gupta, J. A. Valdmanis, G. A. Mourou, “Terahertz attenuation and disperation characteristics of coplanar transmission lines,” IEEE Trans. Microwave Theory Tech. 39, 910–916 (1991).
[Crossref]

Opt. Commun. (1)

W. K. Kuo, S. L. Huang, T. S. Horng, L. C. Chang, “Two-dimensional mapping of electric-field vector by electro-optic prober,” Opt. Commun. 149, 55–60 (1998).
[Crossref]

Other (7)

A. Yariv, P. Yeh, Optical Waves in Crystal (Wiley, New York, 1984).

W. M. Robertson, Optoelectronic Techniques for Microwave and Millimeter-Wave Engineering (Artech House, Boston, Mass., 1995).

W. K. Kuo, S. L. Huang, L. C. Chang, “On-wafer dual-beam electro-optic probing of electric-field vector,” in Digest of Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 142–143.

M. G. Li, E. V. Chauchard, C. H. Lee, H.-L. A. Hung, “Two-dimension field mapping of GaAs microstrip circuit by electro-optic sensing,” in Picosecond Electronics and Optoelectrics, F. J. Leonberger, C. H. Lee, F. Capasso, H. Morkoc, eds. (Springer-Verlag, New York, 1987), pp. 54–58.

K. W. Chang, W. V. Sorin, “Electro-optic sampling of high speed nonlinear device,” in Ultrafast Electronics and Optoelectronics, J. Shah, U. Mishra, eds., Vol. 14 of OSA Procedings Series (Optical Society of America, Washington, D.C., 1993), pp. 220–223.

J. A. Valdmanis, S. S. Pei, “A non-contact picosecond prober for intergrated circuit testing,” in Picosecond Electronics and Optoelectronics, F. J. Leonberger, C. H. Lee, F. Capasso, H. Morkoc, eds. (Springer-Verlag, New York, 1987).
[Crossref]

T. K. Ishii, Microwave Engineering, 2nd ed. (Harcourt Brace Jovanovich, San Diego, Calif., 1989).

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Figures (12)

Fig. 1
Fig. 1

External EO probing system with a HR probe tip.

Fig. 2
Fig. 2

Side view of a TIR probe tip and illustration of the four segments for the probe beam.

Fig. 3
Fig. 3

Comparison of results of calculating E x responses of the HR- and TIR-type probe tips.

Fig. 4
Fig. 4

TIR probe tip with four inclined planes.

Fig. 5
Fig. 5

Setup of the experimental system.

Fig. 6
Fig. 6

CCD image of two TIR beam spots and the DUT pattern.

Fig. 7
Fig. 7

Arrangement of the CPSTL and the EO probe tip for comparison of the E z responses for beams B1 and B2.

Fig. 8
Fig. 8

Comparison of experimental results of the E z responses for beams B1 and B2.

Fig. 9
Fig. 9

Experimental result of the E x response for beam B1.

Fig. 10
Fig. 10

Angle error in measurement of the E-field direction.

Fig. 11
Fig. 11

Test pattern for measurement of the 2-D E-field vector.

Fig. 12
Fig. 12

Results of measurement of the 2-D E-field vector.

Equations (22)

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

rij=0-r22r130r22r1300r330r510r5100-r2200,
1no2+r13Ezx2+1ne2+r33Ezz2=1,
Δn=kΔnEz,
ΔIΔn,HR=Io2πλ kΔn2LEz,
x2no2+z2ne2+2r51Exxz=1.
Δθr51Ex1/no2-1/ne2=kΔθEx.
E1E2=cosπ/4sinπ/4-sinπ/4cosπ/4expjΨ001×cos ΔθRsin ΔθR-sin ΔθRcos ΔθRexpjΓR001×cos ΔθR-sin ΔθRsin ΔθRcos ΔθRcos ΔθIsin ΔθI-sin ΔθIcos ΔθI×expjΓI001cos ΔθI-sin ΔθIsin ΔθIcos ΔθI10Io.
ΓI=2πne-noL/λ.
1ΔθI-ΔθI1expjΓI0011-ΔθIΔθI1=expjΓI+ΔθI21-expjΓIΔθI1-expjΓIΔθI1+expjΓIΔθI2expjΓI1-expjΓIΔθI1-expjΓIΔθI1.
E1E2=Io2expjΓI+ΓR+Ψ-expjΓI+ΓRΔθR+expjΓIΔθR-ΔθI+ΔθI-expjΓI+ΓR+Ψ-expjΓI+ΓRΔθR+expjΓIΔθR-ΔθI+ΔθI.
ΔIθ,HR=|E1|2-|E2|2=2Io-ΔθR cosΓI+ΓR+ΔθR-ΔθI×cos ΓI+ΔθIcosΓI+ΓR+Ψ+-ΔθR sinΓI+ΓR+ΔθR-ΔθIsin ΓI×sinΓI+ΓR+Ψ.
ΔIΔθ,HR=4Iocos Γ-1cosΓ+ΨΔθ.
Ψ=-Γ±mπ  m an integer
|ΔIΔθ,HR|=4Io1-cos ΓkΔθEx.
|ΔIΔθ,HR|=0L=nλ/ne-no4IokΔθExL=n+1/2λ/ne-no.
ΔIΔn,TIR=Io2πλi=14 kΔni2LiEz,
ΔIΔθ,TIR=2Io-Δθ4 cosi=14 Γi+Δθ4-Δθ3×cosi=13 Γi+Δθ3-Δθ2cosi=12 Γi+Δθ2-Δθ1cos Γ1+Δθ1cosi=14 Γi+Ψ+-Δθ4 sini=14 Γi+Δθ4-Δθ3sini=13 Γi+Δθ3-Δθ2sini=12 Γi+Δθ2-Δθ1sin Γ1sini=14 Γi+Ψ,
Γi=2πne-noLiλ, i=2, 3.
1003+1003×1.14+33+33×1.141003+1003×0.283+33+33×1.14=2.71.
E1E2=cosπ/4sinπ/4-sinπ/4cosπ/4expjφ001cos-αsin-α-sin-αcos-αexpjδ001cos-α-sin-αsin-αcos-α×cos αsin α-sin αcos αexpjδ001cos α-sin αsin αcos α1/21/2IoIo2exp j2δ+φ+α1-expjδ21-expjφ+1-exp j2δ+φ+α1-expjδ21+expjφ+1=Io2A+B+iC+DA-B+iC-D,
A=α1-2 cos δ+cos 2δ+1, B=cos2δ+φ-αcos φ-2 cosδ+φ+cos2δ+φ, C=α-2 sin δ+sin 2δ, D=sin2δ+φ-αsin φ-2 sinδ+φ+sin2δ+φ,
ΔI=|E1|2-|E2|2=Io4A+B2+C+D2-A-B2+C-D2=IoAB+CDIoα1-2 cos δ+cos 2δcos2δ+φ-αcos φ-2 cosδ+φ+cos2δ+φ+cos2δ+φ+α-2 sin δ+sin 2δsin2δ+φ=Io cos2δ+φ,

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