Abstract

The doppler frequency shift produced in the various diffraction orders of a rotating radial diffraction grating allows such a device to be used as an optical modulator. The theory and performance of such devices is presented.

© 1970 Optical Society of America

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References

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  1. A. T. Forrester, J. Opt. Soc. Amer. 31, 253 (1961).
  2. T. Suzuki, R. Hioki, J. Opt. Soc. Amer. 57, 1551 (1967).
    [CrossRef]
  3. Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
    [CrossRef]
  4. J. W. Foreman et al., IEEE J. Quantum Electron. QE-2, 260 (1966).
    [CrossRef]
  5. R. J. Goldstein, D. K. Kreid, Appl. Mech., Trans. ASME 34, 813 (1967).
    [CrossRef]
  6. D. R. Herriott, U. S. Patent No. 3, 175,088 (1965).
  7. C. F. Buhrer, D. Baird, E. Conwell, Appl. Phys. Lett. 1, 46 (1962).
    [CrossRef]
  8. C. F. Buhrer, L. Ho, J. Zucker, Appl. Opt. 3, 517 (1964).
    [CrossRef]
  9. H. Z. Cummins, N. Knable, Proc. IEEE 51, 1246 (1963).
    [CrossRef]
  10. H. Z. Cummins, N. Knable, Y. Yeh, Phys. Rev. Lett. 12, 150 (1964).
    [CrossRef]
  11. M. Born, E. Wolf, Principles of Optics (Pergamon Press, New York, 1964).
  12. P. J. Magill, T. Young, Appl. Phys. Lett. 5, 13 (1964).
    [CrossRef]
  13. J. W. Foreman, Appl. Opt. 6, 821 (1967).
    [CrossRef] [PubMed]

1967

T. Suzuki, R. Hioki, J. Opt. Soc. Amer. 57, 1551 (1967).
[CrossRef]

R. J. Goldstein, D. K. Kreid, Appl. Mech., Trans. ASME 34, 813 (1967).
[CrossRef]

J. W. Foreman, Appl. Opt. 6, 821 (1967).
[CrossRef] [PubMed]

1966

J. W. Foreman et al., IEEE J. Quantum Electron. QE-2, 260 (1966).
[CrossRef]

1964

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

H. Z. Cummins, N. Knable, Y. Yeh, Phys. Rev. Lett. 12, 150 (1964).
[CrossRef]

P. J. Magill, T. Young, Appl. Phys. Lett. 5, 13 (1964).
[CrossRef]

C. F. Buhrer, L. Ho, J. Zucker, Appl. Opt. 3, 517 (1964).
[CrossRef]

1963

H. Z. Cummins, N. Knable, Proc. IEEE 51, 1246 (1963).
[CrossRef]

1962

C. F. Buhrer, D. Baird, E. Conwell, Appl. Phys. Lett. 1, 46 (1962).
[CrossRef]

1961

A. T. Forrester, J. Opt. Soc. Amer. 31, 253 (1961).

Baird, D.

C. F. Buhrer, D. Baird, E. Conwell, Appl. Phys. Lett. 1, 46 (1962).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, New York, 1964).

Buhrer, C. F.

C. F. Buhrer, L. Ho, J. Zucker, Appl. Opt. 3, 517 (1964).
[CrossRef]

C. F. Buhrer, D. Baird, E. Conwell, Appl. Phys. Lett. 1, 46 (1962).
[CrossRef]

Conwell, E.

C. F. Buhrer, D. Baird, E. Conwell, Appl. Phys. Lett. 1, 46 (1962).
[CrossRef]

Cummins, H. Z.

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

H. Z. Cummins, N. Knable, Y. Yeh, Phys. Rev. Lett. 12, 150 (1964).
[CrossRef]

H. Z. Cummins, N. Knable, Proc. IEEE 51, 1246 (1963).
[CrossRef]

Foreman, J. W.

J. W. Foreman, Appl. Opt. 6, 821 (1967).
[CrossRef] [PubMed]

J. W. Foreman et al., IEEE J. Quantum Electron. QE-2, 260 (1966).
[CrossRef]

Forrester, A. T.

A. T. Forrester, J. Opt. Soc. Amer. 31, 253 (1961).

Goldstein, R. J.

R. J. Goldstein, D. K. Kreid, Appl. Mech., Trans. ASME 34, 813 (1967).
[CrossRef]

Herriott, D. R.

D. R. Herriott, U. S. Patent No. 3, 175,088 (1965).

Hioki, R.

T. Suzuki, R. Hioki, J. Opt. Soc. Amer. 57, 1551 (1967).
[CrossRef]

Ho, L.

Knable, N.

H. Z. Cummins, N. Knable, Y. Yeh, Phys. Rev. Lett. 12, 150 (1964).
[CrossRef]

H. Z. Cummins, N. Knable, Proc. IEEE 51, 1246 (1963).
[CrossRef]

Kreid, D. K.

R. J. Goldstein, D. K. Kreid, Appl. Mech., Trans. ASME 34, 813 (1967).
[CrossRef]

Magill, P. J.

P. J. Magill, T. Young, Appl. Phys. Lett. 5, 13 (1964).
[CrossRef]

Suzuki, T.

T. Suzuki, R. Hioki, J. Opt. Soc. Amer. 57, 1551 (1967).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, New York, 1964).

Yeh, Y.

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

H. Z. Cummins, N. Knable, Y. Yeh, Phys. Rev. Lett. 12, 150 (1964).
[CrossRef]

Young, T.

P. J. Magill, T. Young, Appl. Phys. Lett. 5, 13 (1964).
[CrossRef]

Zucker, J.

Appl. Mech., Trans. ASME

R. J. Goldstein, D. K. Kreid, Appl. Mech., Trans. ASME 34, 813 (1967).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

P. J. Magill, T. Young, Appl. Phys. Lett. 5, 13 (1964).
[CrossRef]

C. F. Buhrer, D. Baird, E. Conwell, Appl. Phys. Lett. 1, 46 (1962).
[CrossRef]

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

IEEE J. Quantum Electron.

J. W. Foreman et al., IEEE J. Quantum Electron. QE-2, 260 (1966).
[CrossRef]

J. Opt. Soc. Amer.

A. T. Forrester, J. Opt. Soc. Amer. 31, 253 (1961).

T. Suzuki, R. Hioki, J. Opt. Soc. Amer. 57, 1551 (1967).
[CrossRef]

Phys. Rev. Lett.

H. Z. Cummins, N. Knable, Y. Yeh, Phys. Rev. Lett. 12, 150 (1964).
[CrossRef]

Proc. IEEE

H. Z. Cummins, N. Knable, Proc. IEEE 51, 1246 (1963).
[CrossRef]

Other

D. R. Herriott, U. S. Patent No. 3, 175,088 (1965).

M. Born, E. Wolf, Principles of Optics (Pergamon Press, New York, 1964).

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Figures (6)

Fig. 1
Fig. 1

Laser doppler velocimeter.

Fig. 2
Fig. 2

Optical frequency shifting with a moving grating.

Fig. 3
Fig. 3

Use of a radial grating.

Fig. 4
Fig. 4

Apparatus for investigation of radial grating modulator performance.

Fig. 5
Fig. 5

Typical heterodyne signal.

Fig. 6
Fig. 6

Frequency shift vs rotation rate.

Equations (6)

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

ν D = 2 V sin ( θ / 2 ) / λ 0 ,
T ( y 1 , t ) = 1 + cos [ ( 2 π / a ) ( y 1 υ t ) ] .
ψ ( s , t ) = e i 2 π ν 0 t { δ ( s ) + 1 2 exp [ i ( 2 π / a ) υ t ] δ [ s + ( 2 π / a ) ] + 1 2 exp [ i ( 2 π / a ) υ t ] δ [ s ( 2 π / a ) ] } ,
ν ( r ) = ν 0 + ( υ / a )
ν = ν 0 + ( ω / K ) .
θ θ 0 = m λ / a ,

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