Abstract

A high resolution submillimeter interferometer system for measurement of electron densities in the 1014-cm−3ne ≤ 2 × 1015-cm−3 range has been developed for use in high density tokamaks. Phase modulation at ~1 MHz is accomplished by difference frequency mixing of two cavity tuned laser oscillators. The optically pumped CH3OH lasers, which operate on the 118.8-μm line, feature a novel output coupling design that permits good mode quality and low beam divergence. The beat signals are detected using a newly developed Ge:Li photoconductor, and a direct measurement of the phase shift is obtained from the time lag between probe and reference signals. The sensitivity of the resulting phase measurement is independent of the instantaneous phase and unaffected by fluctuations in the amplitude or in the frequency of the modulation.

© 1976 Optical Society of America

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References

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  1. R. R. Parker, Bull. Am. Phys. Soc. 20, 1572 (1975).
  2. K. Young, “Diagnostic Needs for Large Tokamak Plasmas,” in Conference on Diagnostics of High Temperature Plasmas (Knoxville, Tenn., 1976).
  3. M. Rosenbluh, R. J. Temkin, K. J. Button, Appl. Opt.15, 0000 (1976). (to be published).
    [CrossRef]
  4. H. R. Fetterman, H. R. Schlossberg, Microwave J. 17, 11 (1974).
  5. M. H. Heald, C. B. Wharton, Plasma Diagnostics With Microwaves (Wiley, New York, 1965).
  6. D. Véron, Opt. Commun. 10, 95 (1974).
    [CrossRef]
  7. D. T. Hodges, T. S. Hartwick, Appl. Phys. Lett. 23, 252 (1973).
    [CrossRef]
  8. S. M. Wolfe, MIT; unpublished.
  9. R. Ulrich, Infrared Phys. 7, 37 (1967).
    [CrossRef]
  10. R. Ulrich, K. F. Renk, L. Genzel, IEEE Trans. Microwave Theory Tech. MTT-11, 363 (1963).
    [CrossRef]
  11. J. Waldman, S. M. Wolfe, L. Darken, T. S. Chang (to be published).
  12. G. E. Stillman, C. M. Wolfe, I. Melngailis, C. D. Parker, P. E. Tannenwald, J. O. Dimmock, Appl. Phys. Lett. 3, 83 (1968).
    [CrossRef]
  13. B. J. H. Meddens, R. J. Taylor, MIT Plasma Physics Report PRR7411 (August1974).
  14. D. T. Hodges, Aerospace Corp., unpublished communication.

1975 (1)

R. R. Parker, Bull. Am. Phys. Soc. 20, 1572 (1975).

1974 (2)

H. R. Fetterman, H. R. Schlossberg, Microwave J. 17, 11 (1974).

D. Véron, Opt. Commun. 10, 95 (1974).
[CrossRef]

1973 (1)

D. T. Hodges, T. S. Hartwick, Appl. Phys. Lett. 23, 252 (1973).
[CrossRef]

1968 (1)

G. E. Stillman, C. M. Wolfe, I. Melngailis, C. D. Parker, P. E. Tannenwald, J. O. Dimmock, Appl. Phys. Lett. 3, 83 (1968).
[CrossRef]

1967 (1)

R. Ulrich, Infrared Phys. 7, 37 (1967).
[CrossRef]

1963 (1)

R. Ulrich, K. F. Renk, L. Genzel, IEEE Trans. Microwave Theory Tech. MTT-11, 363 (1963).
[CrossRef]

Button, K. J.

M. Rosenbluh, R. J. Temkin, K. J. Button, Appl. Opt.15, 0000 (1976). (to be published).
[CrossRef]

Chang, T. S.

J. Waldman, S. M. Wolfe, L. Darken, T. S. Chang (to be published).

Darken, L.

J. Waldman, S. M. Wolfe, L. Darken, T. S. Chang (to be published).

Dimmock, J. O.

G. E. Stillman, C. M. Wolfe, I. Melngailis, C. D. Parker, P. E. Tannenwald, J. O. Dimmock, Appl. Phys. Lett. 3, 83 (1968).
[CrossRef]

Fetterman, H. R.

H. R. Fetterman, H. R. Schlossberg, Microwave J. 17, 11 (1974).

Genzel, L.

R. Ulrich, K. F. Renk, L. Genzel, IEEE Trans. Microwave Theory Tech. MTT-11, 363 (1963).
[CrossRef]

Hartwick, T. S.

D. T. Hodges, T. S. Hartwick, Appl. Phys. Lett. 23, 252 (1973).
[CrossRef]

Heald, M. H.

M. H. Heald, C. B. Wharton, Plasma Diagnostics With Microwaves (Wiley, New York, 1965).

Hodges, D. T.

D. T. Hodges, T. S. Hartwick, Appl. Phys. Lett. 23, 252 (1973).
[CrossRef]

D. T. Hodges, Aerospace Corp., unpublished communication.

Meddens, B. J. H.

B. J. H. Meddens, R. J. Taylor, MIT Plasma Physics Report PRR7411 (August1974).

Melngailis, I.

G. E. Stillman, C. M. Wolfe, I. Melngailis, C. D. Parker, P. E. Tannenwald, J. O. Dimmock, Appl. Phys. Lett. 3, 83 (1968).
[CrossRef]

Parker, C. D.

G. E. Stillman, C. M. Wolfe, I. Melngailis, C. D. Parker, P. E. Tannenwald, J. O. Dimmock, Appl. Phys. Lett. 3, 83 (1968).
[CrossRef]

Parker, R. R.

R. R. Parker, Bull. Am. Phys. Soc. 20, 1572 (1975).

Renk, K. F.

R. Ulrich, K. F. Renk, L. Genzel, IEEE Trans. Microwave Theory Tech. MTT-11, 363 (1963).
[CrossRef]

Rosenbluh, M.

M. Rosenbluh, R. J. Temkin, K. J. Button, Appl. Opt.15, 0000 (1976). (to be published).
[CrossRef]

Schlossberg, H. R.

H. R. Fetterman, H. R. Schlossberg, Microwave J. 17, 11 (1974).

Stillman, G. E.

G. E. Stillman, C. M. Wolfe, I. Melngailis, C. D. Parker, P. E. Tannenwald, J. O. Dimmock, Appl. Phys. Lett. 3, 83 (1968).
[CrossRef]

Tannenwald, P. E.

G. E. Stillman, C. M. Wolfe, I. Melngailis, C. D. Parker, P. E. Tannenwald, J. O. Dimmock, Appl. Phys. Lett. 3, 83 (1968).
[CrossRef]

Taylor, R. J.

B. J. H. Meddens, R. J. Taylor, MIT Plasma Physics Report PRR7411 (August1974).

Temkin, R. J.

M. Rosenbluh, R. J. Temkin, K. J. Button, Appl. Opt.15, 0000 (1976). (to be published).
[CrossRef]

Ulrich, R.

R. Ulrich, Infrared Phys. 7, 37 (1967).
[CrossRef]

R. Ulrich, K. F. Renk, L. Genzel, IEEE Trans. Microwave Theory Tech. MTT-11, 363 (1963).
[CrossRef]

Véron, D.

D. Véron, Opt. Commun. 10, 95 (1974).
[CrossRef]

Waldman, J.

J. Waldman, S. M. Wolfe, L. Darken, T. S. Chang (to be published).

Wharton, C. B.

M. H. Heald, C. B. Wharton, Plasma Diagnostics With Microwaves (Wiley, New York, 1965).

Wolfe, C. M.

G. E. Stillman, C. M. Wolfe, I. Melngailis, C. D. Parker, P. E. Tannenwald, J. O. Dimmock, Appl. Phys. Lett. 3, 83 (1968).
[CrossRef]

Wolfe, S. M.

J. Waldman, S. M. Wolfe, L. Darken, T. S. Chang (to be published).

S. M. Wolfe, MIT; unpublished.

Young, K.

K. Young, “Diagnostic Needs for Large Tokamak Plasmas,” in Conference on Diagnostics of High Temperature Plasmas (Knoxville, Tenn., 1976).

Appl. Phys. Lett. (2)

D. T. Hodges, T. S. Hartwick, Appl. Phys. Lett. 23, 252 (1973).
[CrossRef]

G. E. Stillman, C. M. Wolfe, I. Melngailis, C. D. Parker, P. E. Tannenwald, J. O. Dimmock, Appl. Phys. Lett. 3, 83 (1968).
[CrossRef]

Bull. Am. Phys. Soc. (1)

R. R. Parker, Bull. Am. Phys. Soc. 20, 1572 (1975).

IEEE Trans. Microwave Theory Tech. (1)

R. Ulrich, K. F. Renk, L. Genzel, IEEE Trans. Microwave Theory Tech. MTT-11, 363 (1963).
[CrossRef]

Infrared Phys. (1)

R. Ulrich, Infrared Phys. 7, 37 (1967).
[CrossRef]

Microwave J. (1)

H. R. Fetterman, H. R. Schlossberg, Microwave J. 17, 11 (1974).

Opt. Commun. (1)

D. Véron, Opt. Commun. 10, 95 (1974).
[CrossRef]

Other (7)

S. M. Wolfe, MIT; unpublished.

M. H. Heald, C. B. Wharton, Plasma Diagnostics With Microwaves (Wiley, New York, 1965).

K. Young, “Diagnostic Needs for Large Tokamak Plasmas,” in Conference on Diagnostics of High Temperature Plasmas (Knoxville, Tenn., 1976).

M. Rosenbluh, R. J. Temkin, K. J. Button, Appl. Opt.15, 0000 (1976). (to be published).
[CrossRef]

J. Waldman, S. M. Wolfe, L. Darken, T. S. Chang (to be published).

B. J. H. Meddens, R. J. Taylor, MIT Plasma Physics Report PRR7411 (August1974).

D. T. Hodges, Aerospace Corp., unpublished communication.

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Figures (3)

Fig. 1
Fig. 1

Dual beam modulated interferometer system. Two optically pumped lasers are operated at frequencies differing by Δω. Mixing the two outputs in detector D1 provides a modulated signal x ~ cos(Δωt), while detector D2 sees a similar signal y ~ cos(Δωt + ϕ) with an additional phase shift due to the plasma. The magnitude of this phase shift is then obtained directly from comparison of the two signals.

Fig. 2
Fig. 2

Laser mode shape. The mode is linearly polarized, and the shape is consistent with the EH11 dielectric waveguide mode. This mode is well suited for efficient mixing.

Fig. 3
Fig. 3

The 1.0-MHz modulation signal. The spectrum analyzer trace shows a single beat signal at 1 MHz with a width of less than 30 kHz. The small peaks at the second harmonic represent a slight nonlinearity in the detector response. Single transverse mode operation is verified by the presence of only one beat signal.

Equations (5)

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R c = Γ c 2 = 1 - Γ i 2 = T i .
R = 1 - T = Γ 2 = 1 / ( 1 + Z 0 2 Ω 2 ) ,
T = T 1 T 2 [ 1 - ( R 1 R 2 ) 1 / 2 ] + 4 ( R 1 R 2 ) 1 / 2 sin 2 ( ϕ + δ ) ,
T 1 = n T R + [ ( 1 + n ) / 2 ] 2 T , R 1 = 1 - T 1 , T 2 = 4 n ( 1 + n ) 2 , R 2 = ( 1 - n 1 + n ) 2 , δ = 1 2 cos - 1 ( 1 + R 1 - n T 1 2 ( R 1 ) 1 / 2 ) ,
Δ ν Δ l = ν l = 2.5 × 10 12 1 m = 2.5 MHz / μ m .

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