Abstract

We demonstrate microwave modulation of an optical beam by using the electro-optic effect in total internal reflection near the critical angle. An internally reflected mode-locked laser beam and a microwave field electro-optically interact near the surface of a KDP crystal to produce new modulation frequencies in the reflected beam. Its microwave sensitivity is approximately 3mV/Hz. This technique, described by the boundary-value problem of nonlinear optics, provides a sensitive method to study the physical nature of the electro-optic effect in total internal reflection. Fundamental optical and electrical properties of the electro-optic effect in total internal reflection are presented.

© 1992 Optical Society of America

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  1. H. J. Simon, C. H. Lee, Opt. Lett. 13, 440 (1988).
    [CrossRef] [PubMed]
  2. N. Bloembergen, C. H. Lee, Phys. Rev. Lett. 19, 835 (1967).
    [CrossRef]
  3. N. Bloembergen, H. J. Simon, C. H. Lee, Phys. Rev. 181, 1261 (1969).
    [CrossRef]
  4. P. P. Bey, J. F. Giuliani, H. Rabin, Phys. Rev. 184, 849 (1969).
    [CrossRef]
  5. N. Bloembergen, P. S. Pershan, Phys. Rev. 128, 606 (1962).
    [CrossRef]
  6. S. Kim, Jpn. J. Appl. Phys. Lett. 29, 1141 (1990).
    [CrossRef]
  7. M. R. Meadows, M. A. Handschy, N. A. Clark, Appl. Phys. Lett. 54, 1394 (1989).
    [CrossRef]
  8. M. Scibor-Rylski, Electron. Lett. 9, 304 (1973).
    [CrossRef]
  9. K. J. Weingarten, M. J. W. Rodwell, D. M. Bloom, IEEE J. Quantum Electron. 24, 198 (1988).
    [CrossRef]
  10. M. G. Li, E. A. Chauchard, C. H. Lee, H.-L. A. Hung, IEEE Trans. Microwave Theory Tech. 38, 1924 (1990).
    [CrossRef]

1990 (2)

S. Kim, Jpn. J. Appl. Phys. Lett. 29, 1141 (1990).
[CrossRef]

M. G. Li, E. A. Chauchard, C. H. Lee, H.-L. A. Hung, IEEE Trans. Microwave Theory Tech. 38, 1924 (1990).
[CrossRef]

1989 (1)

M. R. Meadows, M. A. Handschy, N. A. Clark, Appl. Phys. Lett. 54, 1394 (1989).
[CrossRef]

1988 (2)

K. J. Weingarten, M. J. W. Rodwell, D. M. Bloom, IEEE J. Quantum Electron. 24, 198 (1988).
[CrossRef]

H. J. Simon, C. H. Lee, Opt. Lett. 13, 440 (1988).
[CrossRef] [PubMed]

1973 (1)

M. Scibor-Rylski, Electron. Lett. 9, 304 (1973).
[CrossRef]

1969 (2)

N. Bloembergen, H. J. Simon, C. H. Lee, Phys. Rev. 181, 1261 (1969).
[CrossRef]

P. P. Bey, J. F. Giuliani, H. Rabin, Phys. Rev. 184, 849 (1969).
[CrossRef]

1967 (1)

N. Bloembergen, C. H. Lee, Phys. Rev. Lett. 19, 835 (1967).
[CrossRef]

1962 (1)

N. Bloembergen, P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Bey, P. P.

P. P. Bey, J. F. Giuliani, H. Rabin, Phys. Rev. 184, 849 (1969).
[CrossRef]

Bloembergen, N.

N. Bloembergen, H. J. Simon, C. H. Lee, Phys. Rev. 181, 1261 (1969).
[CrossRef]

N. Bloembergen, C. H. Lee, Phys. Rev. Lett. 19, 835 (1967).
[CrossRef]

N. Bloembergen, P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Bloom, D. M.

K. J. Weingarten, M. J. W. Rodwell, D. M. Bloom, IEEE J. Quantum Electron. 24, 198 (1988).
[CrossRef]

Chauchard, E. A.

M. G. Li, E. A. Chauchard, C. H. Lee, H.-L. A. Hung, IEEE Trans. Microwave Theory Tech. 38, 1924 (1990).
[CrossRef]

Clark, N. A.

M. R. Meadows, M. A. Handschy, N. A. Clark, Appl. Phys. Lett. 54, 1394 (1989).
[CrossRef]

Giuliani, J. F.

P. P. Bey, J. F. Giuliani, H. Rabin, Phys. Rev. 184, 849 (1969).
[CrossRef]

Handschy, M. A.

M. R. Meadows, M. A. Handschy, N. A. Clark, Appl. Phys. Lett. 54, 1394 (1989).
[CrossRef]

Hung, H.-L. A.

M. G. Li, E. A. Chauchard, C. H. Lee, H.-L. A. Hung, IEEE Trans. Microwave Theory Tech. 38, 1924 (1990).
[CrossRef]

Kim, S.

S. Kim, Jpn. J. Appl. Phys. Lett. 29, 1141 (1990).
[CrossRef]

Lee, C. H.

M. G. Li, E. A. Chauchard, C. H. Lee, H.-L. A. Hung, IEEE Trans. Microwave Theory Tech. 38, 1924 (1990).
[CrossRef]

H. J. Simon, C. H. Lee, Opt. Lett. 13, 440 (1988).
[CrossRef] [PubMed]

N. Bloembergen, H. J. Simon, C. H. Lee, Phys. Rev. 181, 1261 (1969).
[CrossRef]

N. Bloembergen, C. H. Lee, Phys. Rev. Lett. 19, 835 (1967).
[CrossRef]

Li, M. G.

M. G. Li, E. A. Chauchard, C. H. Lee, H.-L. A. Hung, IEEE Trans. Microwave Theory Tech. 38, 1924 (1990).
[CrossRef]

Meadows, M. R.

M. R. Meadows, M. A. Handschy, N. A. Clark, Appl. Phys. Lett. 54, 1394 (1989).
[CrossRef]

Pershan, P. S.

N. Bloembergen, P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Rabin, H.

P. P. Bey, J. F. Giuliani, H. Rabin, Phys. Rev. 184, 849 (1969).
[CrossRef]

Rodwell, M. J. W.

K. J. Weingarten, M. J. W. Rodwell, D. M. Bloom, IEEE J. Quantum Electron. 24, 198 (1988).
[CrossRef]

Scibor-Rylski, M.

M. Scibor-Rylski, Electron. Lett. 9, 304 (1973).
[CrossRef]

Simon, H. J.

H. J. Simon, C. H. Lee, Opt. Lett. 13, 440 (1988).
[CrossRef] [PubMed]

N. Bloembergen, H. J. Simon, C. H. Lee, Phys. Rev. 181, 1261 (1969).
[CrossRef]

Weingarten, K. J.

K. J. Weingarten, M. J. W. Rodwell, D. M. Bloom, IEEE J. Quantum Electron. 24, 198 (1988).
[CrossRef]

Appl. Phys. Lett. (1)

M. R. Meadows, M. A. Handschy, N. A. Clark, Appl. Phys. Lett. 54, 1394 (1989).
[CrossRef]

Electron. Lett. (1)

M. Scibor-Rylski, Electron. Lett. 9, 304 (1973).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. J. Weingarten, M. J. W. Rodwell, D. M. Bloom, IEEE J. Quantum Electron. 24, 198 (1988).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

M. G. Li, E. A. Chauchard, C. H. Lee, H.-L. A. Hung, IEEE Trans. Microwave Theory Tech. 38, 1924 (1990).
[CrossRef]

Jpn. J. Appl. Phys. Lett. (1)

S. Kim, Jpn. J. Appl. Phys. Lett. 29, 1141 (1990).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (3)

N. Bloembergen, H. J. Simon, C. H. Lee, Phys. Rev. 181, 1261 (1969).
[CrossRef]

P. P. Bey, J. F. Giuliani, H. Rabin, Phys. Rev. 184, 849 (1969).
[CrossRef]

N. Bloembergen, P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Phys. Rev. Lett. (1)

N. Bloembergen, C. H. Lee, Phys. Rev. Lett. 19, 835 (1967).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Light internally reflects off the prism-KDP interface while an electrical signal (Emicrowave) is applied to the coplanar waveguide transmission line. In the KDP crystal, interaction of optical and microwave fields generates orthogonally polarized light that reflects back into the prism.

Fig. 2
Fig. 2

Angular dependence of the electro-optic signal peaks at the critical angle θc. The solid curve is the theory showing the angular dependence of relation (2); experimental data are plotted as filled circles.

Fig. 3
Fig. 3

Electro-optic (EO) signal varying with the input beam’s linear polarization angle. The signal drops to zero when the input light is s polarized (0°) or p polarized (90°) and is strongest when the input beam is polarized at 45°.

Equations (2)

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E R , NL = - 4 π d ˜ ˜ : E ¯ RF E ¯ opt ( T cos θ T + S cos θ S ) ( T cos θ T + R cos θ R ,
S Δ ω 10 log ( d 36 2 E RF 2 E I , | | 2 E I , 2 F R , | | L 2 F T , L 2 F R , | | NL 2 ) ,

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