Abstract

The influence of convex striations of vapor phase axial deposition (VAD) optical fibers on transmission characteristics has been analyzed. These convex striations are inherent in optical fibers made by VAD and cause refractive-index fluctuations in both radial and axial directions. The phase of the sinusoidal fluctuations in the radial direction varies periodically along the fiber axis. Numerical analysis shows that bandwidth degradation due to sinusoidal fluctuations in the radial direction can be alleviated by a periodic phase variation in the axial direction.

© 1981 Optical Society of America

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References

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  1. T. Izawa, S. Kobayashi, S. Sudo, F. Hanawa, “Continuous Fabrication of High Silica Fiber Preform,” in International Conference on Integrated Optics and Optical Fiber Communication (IOOC, Tokyo, 1977), Cl-1, pp. 375–378.
  2. S. Sudo, M. Kawachi, T. Edahiro, T. Izawa, T. Shioda, H. Gotoh, Electron. Lett. 14, 534 (1978).
    [CrossRef]
  3. T. Edahiro, S. Sudo, M. Kawachi, K. Jinguji, N. Inagaki, Electron. Lett. 15, 726 (1979).
    [CrossRef]
  4. S. Sudo, M. Kawachi, T. Edahiro, K. Chida, Electron. Lett. 16, 152 (1980).
    [CrossRef]
  5. J. A. Arnaud, W. Mammel, Electron. Lett. 12, 6 (1976).
    [CrossRef]
  6. R. Olshansky, Appl. Opt. 15, 782 (1976).
    [CrossRef] [PubMed]
  7. D. Marcuse, Appl. Opt. 18, 2073 (1979).
    [CrossRef] [PubMed]
  8. D. Marcuse, Appl. Opt. 18, 2229 (1979).
    [CrossRef] [PubMed]
  9. D. Marcuse, Appl. Opt. 18, 4003 (1979).
    [CrossRef] [PubMed]
  10. T. Matsumoto, “Effects of Index-Profile Distortion and Splicing Permutation on Fiber Bandwidth,” in Technical Digest, Institute of Electronics and Communication Engineers (IECE, Tokyo, 1980), pp. 31–36.
  11. Y. Daido, “Refractive-Index Profiling of Graded-Index Fiber Waveguides Attaining 100 MHz Bandwidth at 100 km,” in CLEOS, 26– 28 Feb. 1980, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1980), paper TUDD3.
  12. C. Pask, Opt. Quantum Electron. 12, 281 (1980).
    [CrossRef]
  13. D. Gloge, E. A. J. Marcatili, Bell. Syst. Tech. J. 52, 1563 (1973).
  14. D. H. Irving, A. E. Karbowiak, Electron. Lett. 15, 160 (1979).
    [CrossRef]
  15. L. G. Cohen, C. Lin, IEEE J. Quantum Electron. QE-14, 855 (1978).
    [CrossRef]
  16. K. Yoshida, S. Shibuya, K. Kokura, S. Sentsui, T. Kuroha, “Ultrawide Bandwidth Optical Fibers Fabricated by VAD Method,” paper presented at Sixth European Conference on Optical Communication, U.K., Sept. 1980, p. 6.

1980 (2)

S. Sudo, M. Kawachi, T. Edahiro, K. Chida, Electron. Lett. 16, 152 (1980).
[CrossRef]

C. Pask, Opt. Quantum Electron. 12, 281 (1980).
[CrossRef]

1979 (5)

D. H. Irving, A. E. Karbowiak, Electron. Lett. 15, 160 (1979).
[CrossRef]

T. Edahiro, S. Sudo, M. Kawachi, K. Jinguji, N. Inagaki, Electron. Lett. 15, 726 (1979).
[CrossRef]

D. Marcuse, Appl. Opt. 18, 2073 (1979).
[CrossRef] [PubMed]

D. Marcuse, Appl. Opt. 18, 2229 (1979).
[CrossRef] [PubMed]

D. Marcuse, Appl. Opt. 18, 4003 (1979).
[CrossRef] [PubMed]

1978 (2)

S. Sudo, M. Kawachi, T. Edahiro, T. Izawa, T. Shioda, H. Gotoh, Electron. Lett. 14, 534 (1978).
[CrossRef]

L. G. Cohen, C. Lin, IEEE J. Quantum Electron. QE-14, 855 (1978).
[CrossRef]

1976 (2)

R. Olshansky, Appl. Opt. 15, 782 (1976).
[CrossRef] [PubMed]

J. A. Arnaud, W. Mammel, Electron. Lett. 12, 6 (1976).
[CrossRef]

1973 (1)

D. Gloge, E. A. J. Marcatili, Bell. Syst. Tech. J. 52, 1563 (1973).

Arnaud, J. A.

J. A. Arnaud, W. Mammel, Electron. Lett. 12, 6 (1976).
[CrossRef]

Chida, K.

S. Sudo, M. Kawachi, T. Edahiro, K. Chida, Electron. Lett. 16, 152 (1980).
[CrossRef]

Cohen, L. G.

L. G. Cohen, C. Lin, IEEE J. Quantum Electron. QE-14, 855 (1978).
[CrossRef]

Daido, Y.

Y. Daido, “Refractive-Index Profiling of Graded-Index Fiber Waveguides Attaining 100 MHz Bandwidth at 100 km,” in CLEOS, 26– 28 Feb. 1980, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1980), paper TUDD3.

Edahiro, T.

S. Sudo, M. Kawachi, T. Edahiro, K. Chida, Electron. Lett. 16, 152 (1980).
[CrossRef]

T. Edahiro, S. Sudo, M. Kawachi, K. Jinguji, N. Inagaki, Electron. Lett. 15, 726 (1979).
[CrossRef]

S. Sudo, M. Kawachi, T. Edahiro, T. Izawa, T. Shioda, H. Gotoh, Electron. Lett. 14, 534 (1978).
[CrossRef]

Gloge, D.

D. Gloge, E. A. J. Marcatili, Bell. Syst. Tech. J. 52, 1563 (1973).

Gotoh, H.

S. Sudo, M. Kawachi, T. Edahiro, T. Izawa, T. Shioda, H. Gotoh, Electron. Lett. 14, 534 (1978).
[CrossRef]

Hanawa, F.

T. Izawa, S. Kobayashi, S. Sudo, F. Hanawa, “Continuous Fabrication of High Silica Fiber Preform,” in International Conference on Integrated Optics and Optical Fiber Communication (IOOC, Tokyo, 1977), Cl-1, pp. 375–378.

Inagaki, N.

T. Edahiro, S. Sudo, M. Kawachi, K. Jinguji, N. Inagaki, Electron. Lett. 15, 726 (1979).
[CrossRef]

Irving, D. H.

D. H. Irving, A. E. Karbowiak, Electron. Lett. 15, 160 (1979).
[CrossRef]

Izawa, T.

S. Sudo, M. Kawachi, T. Edahiro, T. Izawa, T. Shioda, H. Gotoh, Electron. Lett. 14, 534 (1978).
[CrossRef]

T. Izawa, S. Kobayashi, S. Sudo, F. Hanawa, “Continuous Fabrication of High Silica Fiber Preform,” in International Conference on Integrated Optics and Optical Fiber Communication (IOOC, Tokyo, 1977), Cl-1, pp. 375–378.

Jinguji, K.

T. Edahiro, S. Sudo, M. Kawachi, K. Jinguji, N. Inagaki, Electron. Lett. 15, 726 (1979).
[CrossRef]

Karbowiak, A. E.

D. H. Irving, A. E. Karbowiak, Electron. Lett. 15, 160 (1979).
[CrossRef]

Kawachi, M.

S. Sudo, M. Kawachi, T. Edahiro, K. Chida, Electron. Lett. 16, 152 (1980).
[CrossRef]

T. Edahiro, S. Sudo, M. Kawachi, K. Jinguji, N. Inagaki, Electron. Lett. 15, 726 (1979).
[CrossRef]

S. Sudo, M. Kawachi, T. Edahiro, T. Izawa, T. Shioda, H. Gotoh, Electron. Lett. 14, 534 (1978).
[CrossRef]

Kobayashi, S.

T. Izawa, S. Kobayashi, S. Sudo, F. Hanawa, “Continuous Fabrication of High Silica Fiber Preform,” in International Conference on Integrated Optics and Optical Fiber Communication (IOOC, Tokyo, 1977), Cl-1, pp. 375–378.

Kokura, K.

K. Yoshida, S. Shibuya, K. Kokura, S. Sentsui, T. Kuroha, “Ultrawide Bandwidth Optical Fibers Fabricated by VAD Method,” paper presented at Sixth European Conference on Optical Communication, U.K., Sept. 1980, p. 6.

Kuroha, T.

K. Yoshida, S. Shibuya, K. Kokura, S. Sentsui, T. Kuroha, “Ultrawide Bandwidth Optical Fibers Fabricated by VAD Method,” paper presented at Sixth European Conference on Optical Communication, U.K., Sept. 1980, p. 6.

Lin, C.

L. G. Cohen, C. Lin, IEEE J. Quantum Electron. QE-14, 855 (1978).
[CrossRef]

Mammel, W.

J. A. Arnaud, W. Mammel, Electron. Lett. 12, 6 (1976).
[CrossRef]

Marcatili, E. A. J.

D. Gloge, E. A. J. Marcatili, Bell. Syst. Tech. J. 52, 1563 (1973).

Marcuse, D.

Matsumoto, T.

T. Matsumoto, “Effects of Index-Profile Distortion and Splicing Permutation on Fiber Bandwidth,” in Technical Digest, Institute of Electronics and Communication Engineers (IECE, Tokyo, 1980), pp. 31–36.

Olshansky, R.

Pask, C.

C. Pask, Opt. Quantum Electron. 12, 281 (1980).
[CrossRef]

Sentsui, S.

K. Yoshida, S. Shibuya, K. Kokura, S. Sentsui, T. Kuroha, “Ultrawide Bandwidth Optical Fibers Fabricated by VAD Method,” paper presented at Sixth European Conference on Optical Communication, U.K., Sept. 1980, p. 6.

Shibuya, S.

K. Yoshida, S. Shibuya, K. Kokura, S. Sentsui, T. Kuroha, “Ultrawide Bandwidth Optical Fibers Fabricated by VAD Method,” paper presented at Sixth European Conference on Optical Communication, U.K., Sept. 1980, p. 6.

Shioda, T.

S. Sudo, M. Kawachi, T. Edahiro, T. Izawa, T. Shioda, H. Gotoh, Electron. Lett. 14, 534 (1978).
[CrossRef]

Sudo, S.

S. Sudo, M. Kawachi, T. Edahiro, K. Chida, Electron. Lett. 16, 152 (1980).
[CrossRef]

T. Edahiro, S. Sudo, M. Kawachi, K. Jinguji, N. Inagaki, Electron. Lett. 15, 726 (1979).
[CrossRef]

S. Sudo, M. Kawachi, T. Edahiro, T. Izawa, T. Shioda, H. Gotoh, Electron. Lett. 14, 534 (1978).
[CrossRef]

T. Izawa, S. Kobayashi, S. Sudo, F. Hanawa, “Continuous Fabrication of High Silica Fiber Preform,” in International Conference on Integrated Optics and Optical Fiber Communication (IOOC, Tokyo, 1977), Cl-1, pp. 375–378.

Yoshida, K.

K. Yoshida, S. Shibuya, K. Kokura, S. Sentsui, T. Kuroha, “Ultrawide Bandwidth Optical Fibers Fabricated by VAD Method,” paper presented at Sixth European Conference on Optical Communication, U.K., Sept. 1980, p. 6.

Appl. Opt. (4)

Bell. Syst. Tech. J. (1)

D. Gloge, E. A. J. Marcatili, Bell. Syst. Tech. J. 52, 1563 (1973).

Electron. Lett. (5)

D. H. Irving, A. E. Karbowiak, Electron. Lett. 15, 160 (1979).
[CrossRef]

S. Sudo, M. Kawachi, T. Edahiro, T. Izawa, T. Shioda, H. Gotoh, Electron. Lett. 14, 534 (1978).
[CrossRef]

T. Edahiro, S. Sudo, M. Kawachi, K. Jinguji, N. Inagaki, Electron. Lett. 15, 726 (1979).
[CrossRef]

S. Sudo, M. Kawachi, T. Edahiro, K. Chida, Electron. Lett. 16, 152 (1980).
[CrossRef]

J. A. Arnaud, W. Mammel, Electron. Lett. 12, 6 (1976).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. G. Cohen, C. Lin, IEEE J. Quantum Electron. QE-14, 855 (1978).
[CrossRef]

Opt. Quantum Electron. (1)

C. Pask, Opt. Quantum Electron. 12, 281 (1980).
[CrossRef]

Other (4)

T. Izawa, S. Kobayashi, S. Sudo, F. Hanawa, “Continuous Fabrication of High Silica Fiber Preform,” in International Conference on Integrated Optics and Optical Fiber Communication (IOOC, Tokyo, 1977), Cl-1, pp. 375–378.

K. Yoshida, S. Shibuya, K. Kokura, S. Sentsui, T. Kuroha, “Ultrawide Bandwidth Optical Fibers Fabricated by VAD Method,” paper presented at Sixth European Conference on Optical Communication, U.K., Sept. 1980, p. 6.

T. Matsumoto, “Effects of Index-Profile Distortion and Splicing Permutation on Fiber Bandwidth,” in Technical Digest, Institute of Electronics and Communication Engineers (IECE, Tokyo, 1980), pp. 31–36.

Y. Daido, “Refractive-Index Profiling of Graded-Index Fiber Waveguides Attaining 100 MHz Bandwidth at 100 km,” in CLEOS, 26– 28 Feb. 1980, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1980), paper TUDD3.

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Figures (8)

Fig. 1
Fig. 1

Striations in VAD fibers.

Fig. 2
Fig. 2

Photographs of the index fluctuations in radial direction at cross section bb′ in Fig. 1.

Fig. 3
Fig. 3

Refractive-index profile with radial fluctuations (N = 50).

Fig. 4
Fig. 4

Bandwidth of fiber with radial fluctuations as a function of the number of fluctuations N.

Fig. 5
Fig. 5

Bandwidth of fiber with only radial fluctuation (dot–broken line) and with both radial and axial fluctuations (solid line). The broken line shows the bandwidth without index fluctuations.

Fig. 6
Fig. 6

Bandwidth of fiber with only radial fluctuation (dot–broken line) and with both radial and axial fluctuations (solid line). Broken line shows the bandwidth without index fluctuations.

Fig. 7
Fig. 7

Experimental setup to measure the wavelength dependence of the bandwidth using a fiber Raman laser.

Fig. 8
Fig. 8

Bandwidth of the VAD fiber measured by semiconductor lasers and a fiber Raman laser.

Equations (15)

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R 1 R 2 [ k 2 n 2 ( r ) β m l 2 m 2 r 2 ] 1 / 2 d r = ( l + ½ ) π ,
τ m l = 1 c d β m l d k ,
τ m l = k n 1 N 1 c β m l { 1 ( 1 + y 4 ) R 1 R 2 [ n 1 2 n 2 ( r ) ] n 1 2 K ( r ) d r R 1 R 2 d r K ( r ) d r } ,
K ( r ) = k 2 n 2 ( r ) β m l 2 m 2 r 2 ,
y = 2 n 1 N 1 λ Δ d Δ d λ ;
τ m l = k n 1 N 1 c β m l { 1 ( 1 + y 4 ) i = 1 M [ n 1 2 n 2 ( r i ) ] ( r i R 1 ) ( R 2 r i ) k 2 n 2 ( r i ) β m l 2 m 2 / r i 2 i = 1 M ( r i R 1 ) ( R 2 r i ) k 2 n 2 ( r i ) β m l m 2 / r i 2 } ,
r i = ( R 1 + R 2 ) 2 + ( R 2 R 1 ) 2 cos ( 2 i 1 ) π 2 M .
σ = [ 1 N T m l ( τ m l τ a υ ) 2 ] 1 / 2 ,
τ a υ = 1 N T m l τ m l ,
B = 1 π σ ln 2 2 = 0.187 σ .
n 2 ( r ) = n 1 2 [ 1 2 Δ f ( r ) ] ,
f ( r ) = ( r a ) α ɛ ( 1 r a ) cos ( 2 π N r 2 a 2 ) ;
ɛ = ɛ 0 sin ( 2 π z Λ ) ,
t = 0 Λ τ m l ( z ) d z = j = 1 N z ( j 1 ) Λ N z j Λ N z τ m l ( z ) d z Λ N z j = 1 N z τ m l ( j Λ N z ) ,
τ ̂ m l = 1 N z j = 1 N z τ m l ( j Λ N z ) .

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