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.

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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, Jr., 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, Jr., 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

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

1969

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

1967

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, Jr., Phys. Rev. 159, 208 (1967); Phys. Rev. 179, 368 (1969).
[CrossRef]

1966

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, Jr., and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[CrossRef]

1965

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, Jr., 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, Jr., 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, Jr., 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, Jr., 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.

Other

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, Jr., Phys. Rev. 159, 208 (1967); Phys. Rev. 179, 368 (1969).
[CrossRef]

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, Jr., and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[CrossRef]

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

Reference 3, Sec. 10.4.

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

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]

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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 ) ] ,