Abstract

A simplified method for the measurement of mode conversion coefficients and mode dependent losses is proposed. The method utilizes sinusoidally modulated light instead of optical pulses and is applied to step-index multimode fibers. The results obtained by frequency domain measurement agree satisfactorily with those obtained by time domain measurement. It is confirmed that frequency domain measurements make it simple to obtain mode conversion coefficients and mode dependent losses. Experiments also show that mode dependent losses in the fibers are roughly independent of the mode order, and that the dynamic equilibrium is attained after propagation over a few kilometers even in available step-index fibers.

© 1981 Optical Society of America

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References

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  1. S. D. Personik, Bell Syst. Tech. J. 50, 843 (1971).
  2. D. Marcuse, Bell Syst. Tech. J. 51, 1199 (1972).
  3. R. Olshansky, Appl. Opt. 14, 935 (1975).
    [PubMed]
  4. S. Kawakami, M. Ikeda, IEEE J. Quantum Electron. QE-14, 608 (1978).
    [CrossRef]
  5. S. Kawakami, Optical Waveguides (Asakura, Tokyo, 1980), Chap. 8 (in Japanese).
  6. D. B. Keck, Appl. Opt. 13, 1882 (1974).
    [CrossRef] [PubMed]
  7. R. Olshansky, S. M. Oaks, Appl. Opt. 17, 1830 (1978).
    [CrossRef] [PubMed]
  8. W. A. Gambling, D. N. Payne, H. Matsumura, Appl. Opt. 14, 1538 (1975).
    [CrossRef] [PubMed]
  9. L. Jeunhomme, J. P. Pocholle, Electron. Lett. 11, 425 (1975).
    [CrossRef]
  10. S. Kawakami, Electron. Lett. 13, 706 (1977).
    [CrossRef]
  11. M. Miyagi, S. Kawakami, M. Ohashi, S. Nishida, Appl. Opt. 17, 3238 (1978).
    [CrossRef] [PubMed]
  12. M. Ohashi, M.S. Thesis, Tohoku U., Sendai, Japan (1979).
  13. D. Marcuse, Bell Syst. Tech. J. 51, 1199 (1972).
  14. S. Kawakami, S. Nishida, IEEE J. Quantum Electron. QE-10, 879 (1974).
    [CrossRef]
  15. R. E. Epworth, in Digest, Fourth ECOC, Genoa, 1978, pp. 492–501.
  16. M. Tateda, M. Ikeda, Appl. Opt. 15, 2308 (1976).
    [CrossRef] [PubMed]

1978

1977

S. Kawakami, Electron. Lett. 13, 706 (1977).
[CrossRef]

1976

1975

1974

S. Kawakami, S. Nishida, IEEE J. Quantum Electron. QE-10, 879 (1974).
[CrossRef]

D. B. Keck, Appl. Opt. 13, 1882 (1974).
[CrossRef] [PubMed]

1972

D. Marcuse, Bell Syst. Tech. J. 51, 1199 (1972).

D. Marcuse, Bell Syst. Tech. J. 51, 1199 (1972).

1971

S. D. Personik, Bell Syst. Tech. J. 50, 843 (1971).

Epworth, R. E.

R. E. Epworth, in Digest, Fourth ECOC, Genoa, 1978, pp. 492–501.

Gambling, W. A.

Ikeda, M.

S. Kawakami, M. Ikeda, IEEE J. Quantum Electron. QE-14, 608 (1978).
[CrossRef]

M. Tateda, M. Ikeda, Appl. Opt. 15, 2308 (1976).
[CrossRef] [PubMed]

Jeunhomme, L.

L. Jeunhomme, J. P. Pocholle, Electron. Lett. 11, 425 (1975).
[CrossRef]

Kawakami, S.

S. Kawakami, M. Ikeda, IEEE J. Quantum Electron. QE-14, 608 (1978).
[CrossRef]

M. Miyagi, S. Kawakami, M. Ohashi, S. Nishida, Appl. Opt. 17, 3238 (1978).
[CrossRef] [PubMed]

S. Kawakami, Electron. Lett. 13, 706 (1977).
[CrossRef]

S. Kawakami, S. Nishida, IEEE J. Quantum Electron. QE-10, 879 (1974).
[CrossRef]

S. Kawakami, Optical Waveguides (Asakura, Tokyo, 1980), Chap. 8 (in Japanese).

Keck, D. B.

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 51, 1199 (1972).

D. Marcuse, Bell Syst. Tech. J. 51, 1199 (1972).

Matsumura, H.

Miyagi, M.

Nishida, S.

M. Miyagi, S. Kawakami, M. Ohashi, S. Nishida, Appl. Opt. 17, 3238 (1978).
[CrossRef] [PubMed]

S. Kawakami, S. Nishida, IEEE J. Quantum Electron. QE-10, 879 (1974).
[CrossRef]

Oaks, S. M.

Ohashi, M.

Olshansky, R.

Payne, D. N.

Personik, S. D.

S. D. Personik, Bell Syst. Tech. J. 50, 843 (1971).

Pocholle, J. P.

L. Jeunhomme, J. P. Pocholle, Electron. Lett. 11, 425 (1975).
[CrossRef]

Tateda, M.

Appl. Opt.

Bell Syst. Tech. J.

S. D. Personik, Bell Syst. Tech. J. 50, 843 (1971).

D. Marcuse, Bell Syst. Tech. J. 51, 1199 (1972).

D. Marcuse, Bell Syst. Tech. J. 51, 1199 (1972).

Electron. Lett.

L. Jeunhomme, J. P. Pocholle, Electron. Lett. 11, 425 (1975).
[CrossRef]

S. Kawakami, Electron. Lett. 13, 706 (1977).
[CrossRef]

IEEE J. Quantum Electron.

S. Kawakami, S. Nishida, IEEE J. Quantum Electron. QE-10, 879 (1974).
[CrossRef]

S. Kawakami, M. Ikeda, IEEE J. Quantum Electron. QE-14, 608 (1978).
[CrossRef]

Other

S. Kawakami, Optical Waveguides (Asakura, Tokyo, 1980), Chap. 8 (in Japanese).

R. E. Epworth, in Digest, Fourth ECOC, Genoa, 1978, pp. 492–501.

M. Ohashi, M.S. Thesis, Tohoku U., Sendai, Japan (1979).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Measured mode mixing effects due to the butt-coupling: (a) amplitude (modal power) and (b) phase distributions of the modulated light before (dotted) and after (solid) the splicing.

Fig. 3
Fig. 3

Measured amplitude and phase distributions for fiber B at z = 4 m (dotted) and z = 1250 m (solid). Fiber A is used as a launching fiber.

Fig. 4
Fig. 4

Measured amplitude and phase distributions for fiber C at z = 4 m (dotted) and z = 1000 m (solid). Fiber B is used as a launching fiber.

Fig. 5
Fig. 5

Mode conversion coefficients: (a) in fiber A; (b) in fiber B; and (c) in fiber C. Solid and dashed lines correspond to frequency and time domain measurements, respectively. Dotted lines are obtained under the assumption of m(z)/dz = 0.

Fig. 6
Fig. 6

Mode dependent losses: (a) in fiber A; (b) in fiber B; and (c) in fiber C. Solid and dashed lines correspond to frequency domain and time domain measurements, respectively.

Fig. 7
Fig. 7

Simulated phase differences between modes and lowest order mode as a function of the propagation distance in fiber A.

Tables (2)

Tables Icon

Table I Parameters of Three Fibers Used in the Measurement

Tables Icon

Table II Estimated Coupling Lengths and Parameters

Equations (13)

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P m z + 1 v m P m t = - 2 α m P m + h m ( m + 1 ( P m + 1 - P m ) + m - 1 m h m ( m - 1 ) ( P m - 1 - P m ) ,
P m ( z , t ) = A m ( z ) exp { j [ ω t - ϕ m ( z ) ] } ,
d A m d z = - 2 α m A m + h m ( m + 1 ) [ A m + 1 cos ( ϕ m - ϕ m + 1 ) - A m ] + m - 1 m h m ( m - 1 ) [ A m - 1 cos ( ϕ m - ϕ m - 1 ) - A m ] ,
d ϕ m d z = ω v m - A m + 1 A m h m ( m + 1 ) sin ( ϕ m - ϕ m + 1 ) - m - 1 m A m - 1 A m h m ( m - 1 ) sin ( ϕ m - ϕ m - 1 ) .
h n ( n + 1 ) = m = 1 n m A m 2 ( d ϕ m d z - ω v m ) m = 1 n m A m 2 - m = n + 1 M m A m 2 ( d ϕ m d z - ω v m ) m = n + 1 M m A m 2 n A n A n + 1 sin ( ϕ n + 1 - ϕ n ) [ ( m = 1 n m A m 2 ) 2 - ( m = n + 1 M m A m 2 ) - 1 ] .
v m - 1 v m - 1 + constant ,
ϕ m ( z ) ϕ m ( z ) + g ( z ) .
d A m ( z ) / d z = - 2 α av A m ( z ) ,
d ϕ m ( z ) / d z = 0 ,
2 ( α m - α av ) = h m ( m + 1 ) [ A m + 1 A m cos ( ϕ m - ϕ m + 1 ) - 1 ] + m - 1 m h m ( m - 1 ) [ A m - 1 A m cos ( ϕ m - ϕ m - 1 ) - 1 ] .
h m = h 0 ( m / M ) - 2 q ,
2 α m = { constant ( m M ) , ( m > M )
L c ~ M 2 h 0 ( 1 + q ) 2 λ 1 2 ,

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