Abstract

A new technique for three-dimensional (3D) electric-field (e-field) vector measurement is presented. Three laser beams with different propagation paths in an electro-optic (EO) crystal were used to resolve 3D components of e-field vectors. We adopted a special geometric shape of bismuth silicon oxide EO crystal so that the three beams would propagate within it. A sensitivity of 0.6 V/cm Hz was achieved. A commercial Ansoft Maxwell 3D field simulator was also used to verify our measurements.

© 1999 Optical Society of America

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References

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  1. M. S. Heutmaker and G. T. Harvey, Appl. Phys. Lett. 59, 146 (1991).
    [CrossRef]
  2. D. L. Quang, D. Erasme, and B. Huyart, IEEE Trans. Microwave Theory Tech. 43, 1031 (1995).
    [CrossRef]
  3. T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
    [CrossRef]
  4. T. Ishii, Microwave Engineering, 2nd ed. (Harcourt Brace Jovanovitch, San Diego, Calif., 1989).
  5. K. K. Kamoga, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guide Wave Lett. 4, 414 (1994).
    [CrossRef]
  6. W. K. Kuo, S. L. Huang, T. S. Horng, and L. C. Chang, Opt. Commun. 149, 55 (1998).
    [CrossRef]
  7. A. Yariv and P. Yeh, Optical Waves in Crystal (Wiley, New York, 1984).
  8. R. Hofmann and H. J. Pfleiderer, Microelectron. Eng. 31, 377 (1996).
    [CrossRef]

1998 (2)

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

W. K. Kuo, S. L. Huang, T. S. Horng, and L. C. Chang, Opt. Commun. 149, 55 (1998).
[CrossRef]

1996 (1)

R. Hofmann and H. J. Pfleiderer, Microelectron. Eng. 31, 377 (1996).
[CrossRef]

1995 (1)

D. L. Quang, D. Erasme, and B. Huyart, IEEE Trans. Microwave Theory Tech. 43, 1031 (1995).
[CrossRef]

1994 (1)

K. K. Kamoga, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guide Wave Lett. 4, 414 (1994).
[CrossRef]

1991 (1)

M. S. Heutmaker and G. T. Harvey, Appl. Phys. Lett. 59, 146 (1991).
[CrossRef]

Biebl, E. M.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

Chang, L. C.

W. K. Kuo, S. L. Huang, T. S. Horng, and L. C. Chang, Opt. Commun. 149, 55 (1998).
[CrossRef]

Erasme, D.

D. L. Quang, D. Erasme, and B. Huyart, IEEE Trans. Microwave Theory Tech. 43, 1031 (1995).
[CrossRef]

Harvey, G. T.

M. S. Heutmaker and G. T. Harvey, Appl. Phys. Lett. 59, 146 (1991).
[CrossRef]

Heutmaker, M. S.

M. S. Heutmaker and G. T. Harvey, Appl. Phys. Lett. 59, 146 (1991).
[CrossRef]

Hofmann, R.

R. Hofmann and H. J. Pfleiderer, Microelectron. Eng. 31, 377 (1996).
[CrossRef]

Horng, T. S.

W. K. Kuo, S. L. Huang, T. S. Horng, and L. C. Chang, Opt. Commun. 149, 55 (1998).
[CrossRef]

Huang, S. L.

W. K. Kuo, S. L. Huang, T. S. Horng, and L. C. Chang, Opt. Commun. 149, 55 (1998).
[CrossRef]

Huyart, B.

D. L. Quang, D. Erasme, and B. Huyart, IEEE Trans. Microwave Theory Tech. 43, 1031 (1995).
[CrossRef]

Ishii, T.

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

Kamoga, K. K.

K. K. Kamoga, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guide Wave Lett. 4, 414 (1994).
[CrossRef]

Kuo, W. K.

W. K. Kuo, S. L. Huang, T. S. Horng, and L. C. Chang, Opt. Commun. 149, 55 (1998).
[CrossRef]

Kurz, H.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

Loffler, T.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

Nishikawa, K.

K. K. Kamoga, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guide Wave Lett. 4, 414 (1994).
[CrossRef]

Pfeifer, T.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

Pfleiderer, H. J.

R. Hofmann and H. J. Pfleiderer, Microelectron. Eng. 31, 377 (1996).
[CrossRef]

Quang, D. L.

D. L. Quang, D. Erasme, and B. Huyart, IEEE Trans. Microwave Theory Tech. 43, 1031 (1995).
[CrossRef]

Roskos, H. G.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

Singer, M.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

Tokumitsu, T.

K. K. Kamoga, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guide Wave Lett. 4, 414 (1994).
[CrossRef]

Toyoda, I.

K. K. Kamoga, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guide Wave Lett. 4, 414 (1994).
[CrossRef]

Yariv, A.

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

Yeh, P.

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

Appl. Phys. Lett. (1)

M. S. Heutmaker and G. T. Harvey, Appl. Phys. Lett. 59, 146 (1991).
[CrossRef]

IEEE Microwave Guide Wave Lett. (1)

K. K. Kamoga, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guide Wave Lett. 4, 414 (1994).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

D. L. Quang, D. Erasme, and B. Huyart, IEEE Trans. Microwave Theory Tech. 43, 1031 (1995).
[CrossRef]

Microelectron. Eng. (1)

R. Hofmann and H. J. Pfleiderer, Microelectron. Eng. 31, 377 (1996).
[CrossRef]

Opt. Commun. (1)

W. K. Kuo, S. L. Huang, T. S. Horng, and L. C. Chang, Opt. Commun. 149, 55 (1998).
[CrossRef]

Other (2)

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

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

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Figures (4)

Fig. 1
Fig. 1

Geometric shape of the EOP and the three laser beams. Beam 1 is along the y direction, beam 2 is on the xy plane, and beam 3 is on the yz plane.

Fig. 2
Fig. 2

Schematic illustration of the experimental setup for 3D e-field vector measurement.

Fig. 3
Fig. 3

DUT pattern and 3D simulation structure for the electromagnetic simulator. See text for definitions.

Fig. 4
Fig. 4

Comparison between the measured and the simulation results.

Equations (7)

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

rij=0-r22r130r22r1300r330r510r5100-r2200.
x21no2-r22Ey+r13Ez+y21no2+r22Ey+r13Ez+z21ne2+r33Ez+2r51Exyz+2r51Eyxz-2r22Ezxy=1,
rij=000000000r41000r41000r41.
x2n2+y2n2+z2n2+2r41Exyz+2r41Eyxz+2r41Ezxy=1,
x2n2+z2n2+2r41Eyxz=1.
Φi=kixEx+kiyEykizEz.
ExuEyuEzu=k1xk1yk1zk2xk2yk2zk3xk3yk3z-1Φ1Φ2Φ3.

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