Abstract

The light emerging from the output aperture of a laser should be spatially coherent even when the laser is operated far below its threshold and behaves substantially as a thermal source. The spatial coherence has been demonstrated experimentally by photoelectric correlation measurements at different pairs of points in the aperture.

© 1973 Optical Society of America

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References

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  1. H. Risken and H. D. Vollmer, Z. Phys. 201, 323 (1967); R. D. Hempstead and M. Lax, Phys. Rev. 161, 350 (1967); M. O. Scully and W. E. Lamb, Phys. Rev. 159, 208 (1967); Phys. Rev. 179, 368 (1969).
    [CrossRef]
  2. C. Freed and H. A. Haus, IEEE J. Quantum Electron. 2, 190 (1966); A. W. Smith and J. A. Armstrong, Phys. Rev. Lett. 16, 1169 (1966); F. T. Arecchi, G. S. Rodari, and A. Sona, Phys. Lett. 25A, 59 (1967); F. Davidson and L. Mandel, Phys. Lett. A 25A, 700 (1967); R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
    [CrossRef]
  3. See, for example, M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), Sec. 8.3.
  4. Reference 3, Sec. 10.4.
  5. F. Davidson, Phys. Rev. 185, 446 (1969); D. Meltzer and L. Mandel, IEEE J. Quantum Electron. 6, 661 (1970).
    [CrossRef]
  6. S. Chopra and L. Mandel, Rev. Sci. Instrum. 43, 1489 (1972).
    [CrossRef]
  7. See, for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
    [CrossRef]

1972 (1)

S. Chopra and L. Mandel, Rev. Sci. Instrum. 43, 1489 (1972).
[CrossRef]

1969 (1)

F. Davidson, Phys. Rev. 185, 446 (1969); D. Meltzer and L. Mandel, IEEE J. Quantum Electron. 6, 661 (1970).
[CrossRef]

1967 (1)

H. Risken and H. D. Vollmer, Z. Phys. 201, 323 (1967); R. D. Hempstead and M. Lax, Phys. Rev. 161, 350 (1967); M. O. Scully and W. E. Lamb, Phys. Rev. 159, 208 (1967); Phys. Rev. 179, 368 (1969).
[CrossRef]

1966 (1)

C. Freed and H. A. Haus, IEEE J. Quantum Electron. 2, 190 (1966); A. W. Smith and J. A. Armstrong, Phys. Rev. Lett. 16, 1169 (1966); F. T. Arecchi, G. S. Rodari, and A. Sona, Phys. Lett. 25A, 59 (1967); F. Davidson and L. Mandel, Phys. Lett. A 25A, 700 (1967); R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[CrossRef]

1965 (1)

See, for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

Born, M.

See, for example, M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), Sec. 8.3.

Chopra, S.

S. Chopra and L. Mandel, Rev. Sci. Instrum. 43, 1489 (1972).
[CrossRef]

Davidson, F.

F. Davidson, Phys. Rev. 185, 446 (1969); D. Meltzer and L. Mandel, IEEE J. Quantum Electron. 6, 661 (1970).
[CrossRef]

Freed, C.

C. Freed and H. A. Haus, IEEE J. Quantum Electron. 2, 190 (1966); A. W. Smith and J. A. Armstrong, Phys. Rev. Lett. 16, 1169 (1966); F. T. Arecchi, G. S. Rodari, and A. Sona, Phys. Lett. 25A, 59 (1967); F. Davidson and L. Mandel, Phys. Lett. A 25A, 700 (1967); R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Haus, H. A.

C. Freed and H. A. Haus, IEEE J. Quantum Electron. 2, 190 (1966); A. W. Smith and J. A. Armstrong, Phys. Rev. Lett. 16, 1169 (1966); F. T. Arecchi, G. S. Rodari, and A. Sona, Phys. Lett. 25A, 59 (1967); F. Davidson and L. Mandel, Phys. Lett. A 25A, 700 (1967); R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Mandel, L.

S. Chopra and L. Mandel, Rev. Sci. Instrum. 43, 1489 (1972).
[CrossRef]

See, for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

Risken, H.

H. Risken and H. D. Vollmer, Z. Phys. 201, 323 (1967); R. D. Hempstead and M. Lax, Phys. Rev. 161, 350 (1967); M. O. Scully and W. E. Lamb, Phys. Rev. 159, 208 (1967); Phys. Rev. 179, 368 (1969).
[CrossRef]

Vollmer, H. D.

H. Risken and H. D. Vollmer, Z. Phys. 201, 323 (1967); R. D. Hempstead and M. Lax, Phys. Rev. 161, 350 (1967); M. O. Scully and W. E. Lamb, Phys. Rev. 159, 208 (1967); Phys. Rev. 179, 368 (1969).
[CrossRef]

Wolf, E.

See, for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

See, for example, M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), Sec. 8.3.

IEEE J. Quantum Electron. (1)

C. Freed and H. A. Haus, IEEE J. Quantum Electron. 2, 190 (1966); A. W. Smith and J. A. Armstrong, Phys. Rev. Lett. 16, 1169 (1966); F. T. Arecchi, G. S. Rodari, and A. Sona, Phys. Lett. 25A, 59 (1967); F. Davidson and L. Mandel, Phys. Lett. A 25A, 700 (1967); R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Phys. Rev. (1)

F. Davidson, Phys. Rev. 185, 446 (1969); D. Meltzer and L. Mandel, IEEE J. Quantum Electron. 6, 661 (1970).
[CrossRef]

Rev. Mod. Phys. (1)

See, for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

Rev. Sci. Instrum. (1)

S. Chopra and L. Mandel, Rev. Sci. Instrum. 43, 1489 (1972).
[CrossRef]

Z. Phys. (1)

H. Risken and H. D. Vollmer, Z. Phys. 201, 323 (1967); R. D. Hempstead and M. Lax, Phys. Rev. 161, 350 (1967); M. O. Scully and W. E. Lamb, Phys. Rev. 159, 208 (1967); Phys. Rev. 179, 368 (1969).
[CrossRef]

Other (2)

See, for example, M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), Sec. 8.3.

Reference 3, Sec. 10.4.

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Figures (1)

Fig. 1
Fig. 1

Arrangement of apparatus.

Tables (1)

Tables Icon

Table I Coherence of light collected by separated fibers.

Equations (12)

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V ( r , t ) = j = 0 V j ( r , t ) ,
γ j j ( r 1 , r 2 ) V j * ( r 1 , r ) V j ( r 2 , t ) / [ I j ( r 1 ) I j ( r 2 ) ] 1 2 ,   I j ( r ) V j * ( r , t ) V j ( r , t ) ,
γ i j ( r 1 , r 2 ) V i * ( r 1 , t ) V j ( r 2 , t ) / [ I i ( r 1 ) I j ( r 2 ) ] 1 2
  I ( r ) V * ( r , t ) V ( r , t )
  I ( r ) j V j * ( r , t ) V j ( r , t ) = j I j ( r ) ,
V * ( r 1 , t ) V ( r 2 , t ) j V j * ( r 1 , t ) V j ( r 2 , t ) .
γ ( r 1 , r 2 ) V * ( r 1 , t ) V ( r 2 , t ) / [ I ( r 1 ) I ( r 2 ) ] 1 2
γ ( r 1 , r 2 ) j V j * ( r 1 , t ) V j ( r 2 , t ) / [ i I i ( r 1 ) i I i ( r 2 ) ] 1 2 = j γ j j ( r 1 , r 2 ) [ I j ( r 1 ) I j ( r 2 ) / i I i ( r 1 ) i I i ( r 2 ) ] 1 2 .
I j ( r ) = α j I ( r ) ( 0 α j < ¯ 1 ) ,
j α j = 1 ,
γ ( r 1 , r 2 ) j γ j j ( r 1 , r 2 ) α j .
( number of events ) = n s ( R 2 + ρ 2 ) Δ τ × [ 1 + | γ ( r 1 , r 2 ) | 2 R 1 R 2 / ( R 1 + ρ 1 ) ( R 2 + ρ 2 ) ] ,