Abstract

The optical frequency domain technique has been used in the analysis of discrete and distributed reflections in an optical fiber. To study discrete reflections, three examples are shown on a single-mode fiber: the first involves one reflector, the second and third examples use two and three reflectors in sequence. Another investigation is conducted on a 500-m multimode fiber to detect distributed reflections. This technique is suitable for recognition of the positions and properties of discrete reflections along an optical fiber.

© 1984 Optical Society of America

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Corrections

Mehdi Shadaram and William L. Kuriger, "Using the optical frequency domain technique for the analysis of discrete and distributed reflections in an optical fiber: errata," Appl. Opt. 23, 1906-1906 (1984)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-23-12-1906

References

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  1. L. G. Cohen, H. W. Astle, Bell Syst. Tech. J. 55, 1509 (1976).
  2. F. P. Kapron, D. G. Kneller, P. M. Garel-Jones, in Technical Digest, Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981), paper WF2.
  3. R. I. MacDonald, Appl. Opt. 20, 1840 (1981).
    [CrossRef] [PubMed]
  4. D. L. Philen, I. A. White, IEEE J. Quantum Electron. QE-18, 1499 (1982).
    [CrossRef]
  5. A. J. Rogers, Appl. Opt. 20, 1060 (1981).
    [CrossRef] [PubMed]
  6. K. Aoyama, K. Nakagawa, IEEE J. Quantum Electron. QE-7, 862 (1981).
    [CrossRef]

1982 (1)

D. L. Philen, I. A. White, IEEE J. Quantum Electron. QE-18, 1499 (1982).
[CrossRef]

1981 (3)

1976 (1)

L. G. Cohen, H. W. Astle, Bell Syst. Tech. J. 55, 1509 (1976).

Aoyama, K.

K. Aoyama, K. Nakagawa, IEEE J. Quantum Electron. QE-7, 862 (1981).
[CrossRef]

Astle, H. W.

L. G. Cohen, H. W. Astle, Bell Syst. Tech. J. 55, 1509 (1976).

Cohen, L. G.

L. G. Cohen, H. W. Astle, Bell Syst. Tech. J. 55, 1509 (1976).

Garel-Jones, P. M.

F. P. Kapron, D. G. Kneller, P. M. Garel-Jones, in Technical Digest, Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981), paper WF2.

Kapron, F. P.

F. P. Kapron, D. G. Kneller, P. M. Garel-Jones, in Technical Digest, Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981), paper WF2.

Kneller, D. G.

F. P. Kapron, D. G. Kneller, P. M. Garel-Jones, in Technical Digest, Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981), paper WF2.

MacDonald, R. I.

Nakagawa, K.

K. Aoyama, K. Nakagawa, IEEE J. Quantum Electron. QE-7, 862 (1981).
[CrossRef]

Philen, D. L.

D. L. Philen, I. A. White, IEEE J. Quantum Electron. QE-18, 1499 (1982).
[CrossRef]

Rogers, A. J.

White, I. A.

D. L. Philen, I. A. White, IEEE J. Quantum Electron. QE-18, 1499 (1982).
[CrossRef]

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

L. G. Cohen, H. W. Astle, Bell Syst. Tech. J. 55, 1509 (1976).

IEEE J. Quantum Electron. (2)

D. L. Philen, I. A. White, IEEE J. Quantum Electron. QE-18, 1499 (1982).
[CrossRef]

K. Aoyama, K. Nakagawa, IEEE J. Quantum Electron. QE-7, 862 (1981).
[CrossRef]

Other (1)

F. P. Kapron, D. G. Kneller, P. M. Garel-Jones, in Technical Digest, Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981), paper WF2.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of an optical fiber (a) with discrete reflections along it, (b) with distributed reflections along it.

Fig. 2
Fig. 2

Characteristic of the reflected signal from one reflector at 100 m away from fiber input end: (a) phase vs frequency; (b) amplitude vs frequency.

Fig. 3
Fig. 3

Characteristic of the reflected signal from two reflectors at 100 and 200 m, respectively, from the fiber input end: (a) phase vs frequency; (b) amplitude vs frequency.

Fig. 4
Fig. 4

Characteristic of the reflected signal from three reflectors at 100, 200, and 300 m, respectively, from the fiber input end: (a) phase vs frequency; (b) amplitude vs frequency.

Fig. 5
Fig. 5

Characterisic of Rayleigh reflections from a 500-m fiber with no end reflection: (a) phase vs frequency; (b) amplitude vs frequency.

Fig. 6
Fig. 6

Characteristic of the combination of Rayleigh and end reflections from a 500-m fiber with end reflectivity of 0.01: (a) phase vs frequency; (b) amplitude vs fruency.

Equations (22)

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T = A cos ω t .
R disc = i = 1 n A i cos ( ω t - θ i ) ,
A i = A ( 1 - T i ) k = 1 i - 1 T k 2 ,
θ i = 2 N ω l i c ,
R disc = X disc cos ( ω t + θ disc ) ,
X disc = { i = 1 n A i cos θ i } 2 + { i = 1 n A i sin θ i } 2
θ disc = arctan i = 1 n A i sin θ i i = 1 n A i cos θ i .
R l = A S α s exp ( - 2 α l ) cos ( ω t - 2 N ω l c ) ,
R dist = X dist cos ( ω t - θ dist ) ,
X dist = X 1 2 + X 2 2 ,             θ dist = arctan X 1 X 2 ,
X 1 = 0 L A S α s exp ( K 1 l ) sin ( K 2 l ) d l X 2 = 0 L A S α s exp ( K 1 l ) cos ( K 2 l ) d l K 1 = - 2 α and K 2 = ( 2 N ω ) / c } .
X dist = A S α s K 1 2 + K 2 2 Y 1 2 + Y 2 2 ,
θ dist = arctan Y 1 Y 2 ,
Y 2 = exp ( K 1 L ) { K 1 cos ( K 2 L ) + K 2 sin ( K 2 L ) } - K 1 , Y 1 = exp ( K 1 L ) { K 1 sin ( K 2 L ) - K 2 cos ( K 2 L ) } + K 2 .
P T = P R + P F .
P F = A F cos ( ω t - θ F ) ,
A F = { i = 1 n A i exp ( - 2 α l i ) sin θ i } 2 + { i = 1 n A i exp ( - 2 α l i ) cos θ i } 2 ,
θ F = Arctan i - 1 n A i exp ( - 2 α l i ) sin θ i i = 1 n A i exp ( - 2 α l i ) cos θ i .
P T = A T cos ( ω t - θ T ) ,
A T = { A F cos θ F + A R cos θ R } 2 + { A F sin θ F + A R sin θ R } 2 ,
θ T = arctan A F sin θ F + A R sin θ R A F cos θ F + A R cos θ R .
D = c / ( 2 Δ f N ) ,

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