Abstract

A spatial coherence analysis of light propagation in optical fibers illuminated with a laser source is presented. Modulus and phase of the complex degree of spatial coherence across the end cross section are measured by means of Michelson-type wave-front-reversing interferometry. Interference fringe patterns of a laser beam emerging from the output end of optical fibers are also photographed. Comparison of the measurement with theory enables us to characterize the modal content in a quasi-single-mode fiber.

© 1986 Optical Society of America

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References

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  1. C. Pask, A. W. Snyder, “The Van Cittert–Zernike theorem for optical fibers,” Opt. Commun. 9, 95–97 (1973).
    [Crossref]
  2. D. J. Carpenter, C. Pask, “Propagation of partial coherence along optical fibers,” Opt. Commun. 22, 99–102 (1977).
    [Crossref]
  3. S. Piazzolla, G. De Marchis, “Spatial coherence in optical fibers,” Opt. Commun. 32, 380–382 (1980).
    [Crossref]
  4. R. E. Epworth, “Phenomenon of modal noise in fiber systems,” in Technical Digest of the Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1979), pp. 106–108.
  5. B. Daino, G. De Marchis, S. Piazzolla, “Speckle and modal noise in optical fibers. Theory and experiment,” Opt. Acta 27, 1151–1159 (1980).
    [Crossref]
  6. E. G. Rawson, J. W. Goodman, R. E. Norton, “Frequency dependence of modal noise in multimode optical fibers,” J. Opt. Soc. Am. 70, 968–976 (1980).
    [Crossref]
  7. P. Spano, “Connection between spatial coherence and modal structure in optical fibers and semiconductor lasers,” Opt. Commun. 33, 265–270 (1980).
    [Crossref]
  8. P. Spano, G. De Marchis, G. Grosso, “Coherence properties and cutoff wavelength determination in dielectric waveguides,” Appl. Opt. 22, 1915–1917 (1983).
    [Crossref] [PubMed]
  9. M. Imai, Y. Ohtsuka, “Spatial coherence of laser light propagating in an optical fiber,” Opt. Quantum Electron. 14, 515–523 (1982).
    [Crossref]
  10. M. Imai, Y. Ohtsuka, “The influence of mode-coupling on the degree of coherence in an optical fiber,” Opt. Commun. 45, 331–335 (1983).
    [Crossref]
  11. M. Imai, K. Itoh, Y. Ohtsuka, “Measurements of complex degree of spatial coherence at the end face of an optical fiber,” Opt. Commun. 42, 97–100 (1982).
    [Crossref]
  12. M. Imai, S. Satoh, Y. Ohtsuka, “Spatial coherence in a coherently excited optical fiber and its application to mode analysis,” in Conference Digest of the 13th Congress of the International Commission for Optics (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 700–701.
  13. M. Imai, S. Satoh, Y. Ohtsuka, “Complex degree of spatial coherence in an optical fiber: theory and experiment,” J. Opt. Soc. Am. A 3, 86–93 (1986).
    [Crossref]
  14. D. Gloge, “Weakly guiding fibers,” Appl. Opt. 10, 2252–2258 (1971).
    [Crossref] [PubMed]
  15. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), pp. 62–77.
  16. A. W. Snyder, W. R. Young, “Modes of optical waveguides,” J. Opt. Soc. Am. 68, 297–309 (1978).
    [Crossref]

1986 (1)

1983 (2)

M. Imai, Y. Ohtsuka, “The influence of mode-coupling on the degree of coherence in an optical fiber,” Opt. Commun. 45, 331–335 (1983).
[Crossref]

P. Spano, G. De Marchis, G. Grosso, “Coherence properties and cutoff wavelength determination in dielectric waveguides,” Appl. Opt. 22, 1915–1917 (1983).
[Crossref] [PubMed]

1982 (2)

M. Imai, Y. Ohtsuka, “Spatial coherence of laser light propagating in an optical fiber,” Opt. Quantum Electron. 14, 515–523 (1982).
[Crossref]

M. Imai, K. Itoh, Y. Ohtsuka, “Measurements of complex degree of spatial coherence at the end face of an optical fiber,” Opt. Commun. 42, 97–100 (1982).
[Crossref]

1980 (4)

S. Piazzolla, G. De Marchis, “Spatial coherence in optical fibers,” Opt. Commun. 32, 380–382 (1980).
[Crossref]

B. Daino, G. De Marchis, S. Piazzolla, “Speckle and modal noise in optical fibers. Theory and experiment,” Opt. Acta 27, 1151–1159 (1980).
[Crossref]

E. G. Rawson, J. W. Goodman, R. E. Norton, “Frequency dependence of modal noise in multimode optical fibers,” J. Opt. Soc. Am. 70, 968–976 (1980).
[Crossref]

P. Spano, “Connection between spatial coherence and modal structure in optical fibers and semiconductor lasers,” Opt. Commun. 33, 265–270 (1980).
[Crossref]

1978 (1)

1977 (1)

D. J. Carpenter, C. Pask, “Propagation of partial coherence along optical fibers,” Opt. Commun. 22, 99–102 (1977).
[Crossref]

1973 (1)

C. Pask, A. W. Snyder, “The Van Cittert–Zernike theorem for optical fibers,” Opt. Commun. 9, 95–97 (1973).
[Crossref]

1971 (1)

Carpenter, D. J.

D. J. Carpenter, C. Pask, “Propagation of partial coherence along optical fibers,” Opt. Commun. 22, 99–102 (1977).
[Crossref]

Daino, B.

B. Daino, G. De Marchis, S. Piazzolla, “Speckle and modal noise in optical fibers. Theory and experiment,” Opt. Acta 27, 1151–1159 (1980).
[Crossref]

De Marchis, G.

P. Spano, G. De Marchis, G. Grosso, “Coherence properties and cutoff wavelength determination in dielectric waveguides,” Appl. Opt. 22, 1915–1917 (1983).
[Crossref] [PubMed]

B. Daino, G. De Marchis, S. Piazzolla, “Speckle and modal noise in optical fibers. Theory and experiment,” Opt. Acta 27, 1151–1159 (1980).
[Crossref]

S. Piazzolla, G. De Marchis, “Spatial coherence in optical fibers,” Opt. Commun. 32, 380–382 (1980).
[Crossref]

Epworth, R. E.

R. E. Epworth, “Phenomenon of modal noise in fiber systems,” in Technical Digest of the Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1979), pp. 106–108.

Gloge, D.

Goodman, J. W.

Grosso, G.

Imai, M.

M. Imai, S. Satoh, Y. Ohtsuka, “Complex degree of spatial coherence in an optical fiber: theory and experiment,” J. Opt. Soc. Am. A 3, 86–93 (1986).
[Crossref]

M. Imai, Y. Ohtsuka, “The influence of mode-coupling on the degree of coherence in an optical fiber,” Opt. Commun. 45, 331–335 (1983).
[Crossref]

M. Imai, Y. Ohtsuka, “Spatial coherence of laser light propagating in an optical fiber,” Opt. Quantum Electron. 14, 515–523 (1982).
[Crossref]

M. Imai, K. Itoh, Y. Ohtsuka, “Measurements of complex degree of spatial coherence at the end face of an optical fiber,” Opt. Commun. 42, 97–100 (1982).
[Crossref]

M. Imai, S. Satoh, Y. Ohtsuka, “Spatial coherence in a coherently excited optical fiber and its application to mode analysis,” in Conference Digest of the 13th Congress of the International Commission for Optics (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 700–701.

Itoh, K.

M. Imai, K. Itoh, Y. Ohtsuka, “Measurements of complex degree of spatial coherence at the end face of an optical fiber,” Opt. Commun. 42, 97–100 (1982).
[Crossref]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), pp. 62–77.

Norton, R. E.

Ohtsuka, Y.

M. Imai, S. Satoh, Y. Ohtsuka, “Complex degree of spatial coherence in an optical fiber: theory and experiment,” J. Opt. Soc. Am. A 3, 86–93 (1986).
[Crossref]

M. Imai, Y. Ohtsuka, “The influence of mode-coupling on the degree of coherence in an optical fiber,” Opt. Commun. 45, 331–335 (1983).
[Crossref]

M. Imai, Y. Ohtsuka, “Spatial coherence of laser light propagating in an optical fiber,” Opt. Quantum Electron. 14, 515–523 (1982).
[Crossref]

M. Imai, K. Itoh, Y. Ohtsuka, “Measurements of complex degree of spatial coherence at the end face of an optical fiber,” Opt. Commun. 42, 97–100 (1982).
[Crossref]

M. Imai, S. Satoh, Y. Ohtsuka, “Spatial coherence in a coherently excited optical fiber and its application to mode analysis,” in Conference Digest of the 13th Congress of the International Commission for Optics (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 700–701.

Pask, C.

D. J. Carpenter, C. Pask, “Propagation of partial coherence along optical fibers,” Opt. Commun. 22, 99–102 (1977).
[Crossref]

C. Pask, A. W. Snyder, “The Van Cittert–Zernike theorem for optical fibers,” Opt. Commun. 9, 95–97 (1973).
[Crossref]

Piazzolla, S.

S. Piazzolla, G. De Marchis, “Spatial coherence in optical fibers,” Opt. Commun. 32, 380–382 (1980).
[Crossref]

B. Daino, G. De Marchis, S. Piazzolla, “Speckle and modal noise in optical fibers. Theory and experiment,” Opt. Acta 27, 1151–1159 (1980).
[Crossref]

Rawson, E. G.

Satoh, S.

M. Imai, S. Satoh, Y. Ohtsuka, “Complex degree of spatial coherence in an optical fiber: theory and experiment,” J. Opt. Soc. Am. A 3, 86–93 (1986).
[Crossref]

M. Imai, S. Satoh, Y. Ohtsuka, “Spatial coherence in a coherently excited optical fiber and its application to mode analysis,” in Conference Digest of the 13th Congress of the International Commission for Optics (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 700–701.

Snyder, A. W.

A. W. Snyder, W. R. Young, “Modes of optical waveguides,” J. Opt. Soc. Am. 68, 297–309 (1978).
[Crossref]

C. Pask, A. W. Snyder, “The Van Cittert–Zernike theorem for optical fibers,” Opt. Commun. 9, 95–97 (1973).
[Crossref]

Spano, P.

P. Spano, G. De Marchis, G. Grosso, “Coherence properties and cutoff wavelength determination in dielectric waveguides,” Appl. Opt. 22, 1915–1917 (1983).
[Crossref] [PubMed]

P. Spano, “Connection between spatial coherence and modal structure in optical fibers and semiconductor lasers,” Opt. Commun. 33, 265–270 (1980).
[Crossref]

Young, W. R.

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

B. Daino, G. De Marchis, S. Piazzolla, “Speckle and modal noise in optical fibers. Theory and experiment,” Opt. Acta 27, 1151–1159 (1980).
[Crossref]

Opt. Commun. (6)

M. Imai, Y. Ohtsuka, “The influence of mode-coupling on the degree of coherence in an optical fiber,” Opt. Commun. 45, 331–335 (1983).
[Crossref]

M. Imai, K. Itoh, Y. Ohtsuka, “Measurements of complex degree of spatial coherence at the end face of an optical fiber,” Opt. Commun. 42, 97–100 (1982).
[Crossref]

P. Spano, “Connection between spatial coherence and modal structure in optical fibers and semiconductor lasers,” Opt. Commun. 33, 265–270 (1980).
[Crossref]

C. Pask, A. W. Snyder, “The Van Cittert–Zernike theorem for optical fibers,” Opt. Commun. 9, 95–97 (1973).
[Crossref]

D. J. Carpenter, C. Pask, “Propagation of partial coherence along optical fibers,” Opt. Commun. 22, 99–102 (1977).
[Crossref]

S. Piazzolla, G. De Marchis, “Spatial coherence in optical fibers,” Opt. Commun. 32, 380–382 (1980).
[Crossref]

Opt. Quantum Electron. (1)

M. Imai, Y. Ohtsuka, “Spatial coherence of laser light propagating in an optical fiber,” Opt. Quantum Electron. 14, 515–523 (1982).
[Crossref]

Other (3)

R. E. Epworth, “Phenomenon of modal noise in fiber systems,” in Technical Digest of the Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1979), pp. 106–108.

M. Imai, S. Satoh, Y. Ohtsuka, “Spatial coherence in a coherently excited optical fiber and its application to mode analysis,” in Conference Digest of the 13th Congress of the International Commission for Optics (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 700–701.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), pp. 62–77.

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of superposing the fields radiating from the two axially symmetrical points at the fiber output end.

Fig. 2
Fig. 2

Optical arrangement of a Michelson-type wave-front-reversing interferometer.

Fig. 3
Fig. 3

Interference fringe pattern of a plane wave front from a quasi-single-mode fiber in which the modal content of (a1/a0)2 = (a2/a0)2 = (a3/a0)2 ≈ 0 is assumed.

Fig. 4
Fig. 4

Calibrated (a) modulus and (b) phase plotted as a function of the normalized core radius x/A.

Fig. 5
Fig. 5

Interference fringe pattern at the image plane of the end cross section of a 2.2-m-long optical fiber.

Fig. 6
Fig. 6

300-times plots of modulus taken at the normalized radius x/A = ±0.6.

Fig. 7
Fig. 7

Measured (a) modulus and (b) phase of the complex degree of spatial coherence for the short fiber of 2.2-m length.

Fig. 8
Fig. 8

Calculated (a) modulus and (b) phase of the complex degree of spatial coherence for the same fiber as in Fig. 7.

Fig. 9
Fig. 9

Interference fringe pattern at the image plane of the end cross section of an optical fiber approximately 400 m long.

Fig. 10
Fig. 10

Measured (a) modulus and (b) phase of the complex degree of spatial coherence for the same fiber as in Fig. 9.

Fig. 11
Fig. 11

Calculated (a) modulus and (b) phase of the complex degree of spatial coherence for the same fiber as in Fig. 9.

Equations (5)

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E ( r , t ) = k a k e k ( x , y ) exp [ j ϕ ( t τ k z ) + j ( ω c t β k z ) ] .
I t ( x , 0 ) = [ E ( x , 0 , z , t ) + E ( x , 0 , z , t + τ ) ] × ( c . c ) = I 0 ( x ) + I 0 ( x ) + 2 I 0 ( x ) I 0 ( x ) | μ ( x , x ) | × cos [ arg μ ( x , x ) + ψ ( x , x ) + ω c τ ] .
I t ( x , π / 2 ) = I 0 ( x ) + I 0 ( x ) + 2 I 0 ( x ) I 0 ( x ) | μ ( x , x ) | × sin [ arg μ ( x , x ) + ψ ( x , x ) + ω c τ ] .
| μ ( x , x ) | = { [ I t ( x , 0 ) I 0 ( x ) I 0 ( x ) ] 2 + [ I t ( x , π / 2 ) I 0 ( x ) I 0 ( x ) ] 2 } 1 / 2 × { 2 [ I 0 ( x ) I 0 ( x ) ] 1 / 2 } 1
arg μ ( x , x ) = tan 1 [ I t ( x , π / 2 ) I 0 ( x ) I 0 ( x ) I t ( x , 0 ) I 0 ( x ) I 0 ( x ) ] ψ ( x , x ) ω c τ .

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