Abstract

We used sub-μm-sized quartz fibers to probe a visible light, standing electromagnetic wave inside a laser ring cavity. By observing variations in the cavity’s irradiance decay lifetime, we observed the longitudinal shape of the standing wave.

© 1990 Optical Society of America

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References

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  1. M. Wind, H. Rapport, Eds., Handbook of Microwave Measurements, Vol. 1, (Polytechnic Press, Brooklyn, 1954 Section 2).
  2. J. M. Herbelin et al. “Sensitive Measurement of Photon Lifetime and True Reflectances in an Optical Cavity by a Phase-Shift Method,” Appl. Opt. 19, 144–147 (1980).
    [CrossRef] [PubMed]
  3. M. A. Kwok, J. M. Herbelin, R. H. Ueunten, “Cavity Phase Shift Method for High Reflectance Measurements at Mid-Infrared Wavelengths,” Opt. Eng. 21, 979–982 (1982).
    [CrossRef]
  4. D. Z. Anderson, J. C. Frisch, C. S. Masser, “Mirror Reflectometer Based on Optical Cavity Decay Time,” Appl. Opt. 23, 1238–1245 (1984).
    [CrossRef] [PubMed]
  5. W. S. Bickel, D. Z. Anderson at California Institute of Technology; unpublished research.
  6. A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston1976) pp. 79–80.
  7. Ref. 6, pp. 114–116.
  8. W. Mueller, H. Weber, “Decay Time of Optical Resonators,” Opt. Commun. 23, 440–442 (1977).
    [CrossRef]
  9. B. W. Bell, W. S. Bickel, “Single Fiber Light Scattering Matrix: An Experimental Determination,” Appl. Opt. 20, 3874–3879 (1981).
    [CrossRef] [PubMed]
  10. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1983), pp. 491–497.

1984 (1)

1982 (1)

M. A. Kwok, J. M. Herbelin, R. H. Ueunten, “Cavity Phase Shift Method for High Reflectance Measurements at Mid-Infrared Wavelengths,” Opt. Eng. 21, 979–982 (1982).
[CrossRef]

1981 (1)

1980 (1)

1977 (1)

W. Mueller, H. Weber, “Decay Time of Optical Resonators,” Opt. Commun. 23, 440–442 (1977).
[CrossRef]

Anderson, D. Z.

Bell, B. W.

Bickel, W. S.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1983), pp. 491–497.

Frisch, J. C.

Herbelin, J. M.

M. A. Kwok, J. M. Herbelin, R. H. Ueunten, “Cavity Phase Shift Method for High Reflectance Measurements at Mid-Infrared Wavelengths,” Opt. Eng. 21, 979–982 (1982).
[CrossRef]

J. M. Herbelin et al. “Sensitive Measurement of Photon Lifetime and True Reflectances in an Optical Cavity by a Phase-Shift Method,” Appl. Opt. 19, 144–147 (1980).
[CrossRef] [PubMed]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1983), pp. 491–497.

Kwok, M. A.

M. A. Kwok, J. M. Herbelin, R. H. Ueunten, “Cavity Phase Shift Method for High Reflectance Measurements at Mid-Infrared Wavelengths,” Opt. Eng. 21, 979–982 (1982).
[CrossRef]

Masser, C. S.

Mueller, W.

W. Mueller, H. Weber, “Decay Time of Optical Resonators,” Opt. Commun. 23, 440–442 (1977).
[CrossRef]

Ueunten, R. H.

M. A. Kwok, J. M. Herbelin, R. H. Ueunten, “Cavity Phase Shift Method for High Reflectance Measurements at Mid-Infrared Wavelengths,” Opt. Eng. 21, 979–982 (1982).
[CrossRef]

Weber, H.

W. Mueller, H. Weber, “Decay Time of Optical Resonators,” Opt. Commun. 23, 440–442 (1977).
[CrossRef]

Yariv, A.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston1976) pp. 79–80.

Appl. Opt. (3)

Opt. Commun. (1)

W. Mueller, H. Weber, “Decay Time of Optical Resonators,” Opt. Commun. 23, 440–442 (1977).
[CrossRef]

Opt. Eng. (1)

M. A. Kwok, J. M. Herbelin, R. H. Ueunten, “Cavity Phase Shift Method for High Reflectance Measurements at Mid-Infrared Wavelengths,” Opt. Eng. 21, 979–982 (1982).
[CrossRef]

Other (5)

M. Wind, H. Rapport, Eds., Handbook of Microwave Measurements, Vol. 1, (Polytechnic Press, Brooklyn, 1954 Section 2).

W. S. Bickel, D. Z. Anderson at California Institute of Technology; unpublished research.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston1976) pp. 79–80.

Ref. 6, pp. 114–116.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1983), pp. 491–497.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the basic laser ring cavity system needed to measure the irradiance decay lifetime.

Fig. 2
Fig. 2

Sketch showing a fiber at an arbitrary position in a standing wave, the irradiance amplitude of a standing wave, and the irradiance decay lifetime that will result for a given fiber position.

Fig. 3
Fig. 3

Sketch showing the relative scale of the fiber to the laser beam.

Fig. 4
Fig. 4

Standing wave phase structure in the longitudinal direction using experimental data taken with a 0.17-μm quartz fiber.

Fig. 5
Fig. 5

Standing wave phase structure in the longitudinal direction using experimental data taken with a 0.33 μm quartz fiber.

Equations (7)

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t c = 0 L [ J + ( x ) + J - ( x ) ] d x c ( x ) i ( 1 - R i ) [ J + ( x i ) + J - ( x i ) ] + 0 L a ( x ) [ j + ( x ) + J - ( x ) ] d x + other losses ,
t c = ( n L / c ) × [ 1 - R 2 R 3 R 4 V - ( 1 - R 2 ) exp ( - a x 2 ) - ( 1 - R 3 ) R 2 × exp ( - a x 3 ) - ( 1 - R 4 ) R 2 R 3 exp ( - a x 4 ) ] / [ a L ( 1 - R V ) ] ,
S T = 1 - [ ( C EXT - s f d A ) / detector area ] ,
t c = [ ( n L / c ) × A ] / [ a L × B ] ,
A = 1 - R 2 R 3 R 4 S T V - ( 1 - R 2 exp ( - a x 2 ) - ( 1 - R 3 ) R 2 exp ( - a x 3 ) - ( 1 - R 4 ) R 2 R 3 exp ( - a x 4 ) - ( 1 - S T ) R 2 R 3 R 4 exp ( - a x s ) - [ R 2 R 3 R 4 S R exp ( - 2 a x s ) ] × [ ( 1 - R 1 ) R 2 R 3 R 4 + ( 1 - R 2 ) R 3 R 4 exp ( a x 2 ) + ( 1 - R 3 ) R 4 exp ( a x 3 ) + ( 1 - R 4 ) exp ( a x 4 ) - ( 1 - R V ) exp ( a x s ) ] ,
B = 1 - R V S T - R V S R R 2 R 3 R 4 exp ( - a x s ) ,
I ( x ) = E ( x ) 2 sin [ 2 π ( x - x 0 ) / λ ] .

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