Abstract

A new method of measuring mode conversion coefficients in multimode fibers is proposed. The principle is based on the phenomenon that modal power propagating along a fiber undergoes a gradual change due to mode coupling and mode-dependent losses. Application of the principle has made it possible to measure mode conversion coefficients of a graded-index fiber that, to the authors' belief, had not been reported before. In the experiment, it was found that the mode conversion coefficient is roughly independent of the mode order. A resolution limit of the mode analyzing technique is also discussed for graded-index fibers.

© 1980 Optical Society of America

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References

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  1. S. Kawakami, J. Nishizawa, IEEE Trans. Microwave Theory Tech. MTT-16, 814 (1968).
    [CrossRef]
  2. A. H. Cherin, P. J. Rich, Appl. Opt. 16, 497 (1977).
    [CrossRef] [PubMed]
  3. M. Eve, A. Hartog, R. Kashyap, D. N. Payne, paper presented at Fourth European Conference on Optical Communication, Genoa, Sept. 1978, paper II-58.
  4. M. Eve, Opt. Quantum Electron. 10, 41 (1978).
    [CrossRef]
  5. T. Matsumoto, K. Nakagawa, Appl. Opt. 18, 1449 (1979).
    [CrossRef] [PubMed]
  6. R. Olshansky, S. M. Oaks, Appl. Opt. 17, 1830 (1978).
    [CrossRef] [PubMed]
  7. R. Olshansky, S. M. Oaks, paper presented at Fourth European Conference on Optical Communication, Genoa, Sept. 1978, paper III-128.
  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. K. Kitayama, M. Ikeda, Appl. Opt. 17, 3979 (1978).
    [CrossRef] [PubMed]
  13. D. Marcuse, Bell Syst. Tech. J. 51, 229 (1972).
  14. R. Olshansky, Appl. Opt. 14, 935 (1975).
    [PubMed]
  15. P. Kaiser, Trans. IECE Jpn. E61, 225 (1978).
  16. R. Olshansky, S. M. Oaks, D. B. Keck, in Digest of Topical Meeting on Optical Fiber Transmission II (Optical Society of America, Washington, D.C., 1977), paper TuE5.
  17. M. Ohashi, M. Eng. Thesis, Tohoku U., Sendai, Japan (1979).

1979

1978

1977

1975

1972

D. Marcuse, Bell Syst. Tech. J. 51, 229 (1972).

1968

S. Kawakami, J. Nishizawa, IEEE Trans. Microwave Theory Tech. MTT-16, 814 (1968).
[CrossRef]

Cherin, A. H.

Eve, M.

M. Eve, Opt. Quantum Electron. 10, 41 (1978).
[CrossRef]

M. Eve, A. Hartog, R. Kashyap, D. N. Payne, paper presented at Fourth European Conference on Optical Communication, Genoa, Sept. 1978, paper II-58.

Gambling, W. A.

Hartog, A.

M. Eve, A. Hartog, R. Kashyap, D. N. Payne, paper presented at Fourth European Conference on Optical Communication, Genoa, Sept. 1978, paper II-58.

Ikeda, M.

Jeunhomme, L.

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

Kaiser, P.

P. Kaiser, Trans. IECE Jpn. E61, 225 (1978).

Kashyap, R.

M. Eve, A. Hartog, R. Kashyap, D. N. Payne, paper presented at Fourth European Conference on Optical Communication, Genoa, Sept. 1978, paper II-58.

Kawakami, S.

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, J. Nishizawa, IEEE Trans. Microwave Theory Tech. MTT-16, 814 (1968).
[CrossRef]

Keck, D. B.

R. Olshansky, S. M. Oaks, D. B. Keck, in Digest of Topical Meeting on Optical Fiber Transmission II (Optical Society of America, Washington, D.C., 1977), paper TuE5.

Kitayama, K.

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 51, 229 (1972).

Matsumoto, T.

Matsumura, H.

Miyagi, M.

Nakagawa, K.

Nishida, S.

Nishizawa, J.

S. Kawakami, J. Nishizawa, IEEE Trans. Microwave Theory Tech. MTT-16, 814 (1968).
[CrossRef]

Oaks, S. M.

R. Olshansky, S. M. Oaks, Appl. Opt. 17, 1830 (1978).
[CrossRef] [PubMed]

R. Olshansky, S. M. Oaks, paper presented at Fourth European Conference on Optical Communication, Genoa, Sept. 1978, paper III-128.

R. Olshansky, S. M. Oaks, D. B. Keck, in Digest of Topical Meeting on Optical Fiber Transmission II (Optical Society of America, Washington, D.C., 1977), paper TuE5.

Ohashi, M.

Olshansky, R.

R. Olshansky, S. M. Oaks, Appl. Opt. 17, 1830 (1978).
[CrossRef] [PubMed]

R. Olshansky, Appl. Opt. 14, 935 (1975).
[PubMed]

R. Olshansky, S. M. Oaks, D. B. Keck, in Digest of Topical Meeting on Optical Fiber Transmission II (Optical Society of America, Washington, D.C., 1977), paper TuE5.

R. Olshansky, S. M. Oaks, paper presented at Fourth European Conference on Optical Communication, Genoa, Sept. 1978, paper III-128.

Payne, D. N.

W. A. Gambling, D. N. Payne, H. Matsumura, Appl. Opt. 14, 1538 (1975).
[CrossRef] [PubMed]

M. Eve, A. Hartog, R. Kashyap, D. N. Payne, paper presented at Fourth European Conference on Optical Communication, Genoa, Sept. 1978, paper II-58.

Pocholle, J. P.

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

Rich, P. J.

Appl. Opt.

Bell Syst. Tech. J.

D. Marcuse, Bell Syst. Tech. J. 51, 229 (1972).

Electron. Lett.

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

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

IEEE Trans. Microwave Theory Tech.

S. Kawakami, J. Nishizawa, IEEE Trans. Microwave Theory Tech. MTT-16, 814 (1968).
[CrossRef]

Opt. Quantum Electron.

M. Eve, Opt. Quantum Electron. 10, 41 (1978).
[CrossRef]

Trans. IECE Jpn.

P. Kaiser, Trans. IECE Jpn. E61, 225 (1978).

Other

R. Olshansky, S. M. Oaks, D. B. Keck, in Digest of Topical Meeting on Optical Fiber Transmission II (Optical Society of America, Washington, D.C., 1977), paper TuE5.

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

M. Eve, A. Hartog, R. Kashyap, D. N. Payne, paper presented at Fourth European Conference on Optical Communication, Genoa, Sept. 1978, paper II-58.

R. Olshansky, S. M. Oaks, paper presented at Fourth European Conference on Optical Communication, Genoa, Sept. 1978, paper III-128.

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Figures (13)

Fig. 1
Fig. 1

(a) Schematic diagram of modal power distributions for different launching conditions. Modal power distributions suffer a gradual change along a fiber. (b) Schematic diagram of each quantity appearing in Eq. (3).

Fig. 2
Fig. 2

Refractive-index profile of the fiber and the best-fit α-law profile. The small circles were obtained by the interferometric slab method.

Fig. 3
Fig. 3

Experimental setup.

Fig. 4
Fig. 4

(a) Schematic arrangement of the output end of the fiber. (b) The direction of the motion of the detector viewed from the output end of the fiber.

Fig. 5
Fig. 5

Normalized far-field radiation patterns for different launching conditions and for fiber lengths of 100 m (solid) and 250 m (dashed). The numbers near the curves stand for the radial distance in microns between the fiber axis and the focused laser spot at the input end of the fiber.

Fig. 6
Fig. 6

Mode conversion coefficients in the fiber. Each of the solid and dotted lines corresponds to a particular combination of two farfield patterns.

Fig. 7
Fig. 7

Mode separation by means of a pinhole placed on the center of the fiber core.

Fig. 8
Fig. 8

Effects of pinhole radius on modal resolutions dm and Δm.

Fig. 9
Fig. 9

(a) Resolution limit of the mode analyzer. (b) Normalized optimal pinhole radius.

Fig. 10
Fig. 10

Ratio of modal power passing through the pinhole to the total modal power in the fiber.

Fig. 11
Fig. 11

Schematic diagram of illumination passing through the pinhole.

Fig. 12
Fig. 12

(a) Far-field radiation patterns for different launching conditions. Figures by the curves stand for the offset in microns. (b) Schematic diagram of traces of rays in a fiber when the refractive index has a depression on the axis of the fiber.

Fig. 13
Fig. 13

Mode conversion coefficients in step-index fibers.

Equations (37)

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P 1 ( m , z ) z = 2 α ( m ) P 1 ( m , z ) + 1 m m [ mh ( m ) P 1 ( m , z ) m ] ,
P 2 ( m , z ) z = 2 α ( m ) P 2 ( m , z ) + 1 m m [ mh ( m ) P 2 ( m , z ) m ] ,
h ( m ) = 0 m m P 2 2 ( m , z ) z [ P 1 ( m , z ) / P 2 ( m , z ) ] dm m P 2 2 ( m , z ) m [ P 1 ( m , z ) / P 2 ( m , z ) ] .
z [ P 1 ( m , z ) / P 2 ( m , z ) ] P 1 ( m , z + Δ z ) / P 2 ( m , z + Δ z ) P 1 ( m , z ) / P 2 ( m , z ) Δ z ,
m = A 2 ka 2 n 1 2 Δ ϕ 2 ,
n 2 ( r ) = { n 1 2 [ 1 2 Δ ( r / a ) α ] ( 0 r a ) , n 1 2 ( 1 2 Δ ) ( r > a ) ,
m = M [ ( r / a ) α + ( sin θ / sin θ c ) 2 ] ( α + 2 ) / 2 α ,
M = [ α 2 ( α + 2 ) ] 1 / 2 ka sin θ c .
m = M ( sin θ / sin θ c ) ( α + 2 ) / α .
Δ ψ = λ 2 a p ( rad ) ,
d θ = α sin θ c α + 2 ( m M ) 2 / ( α + 2 ) dm M ( rad ) ,
a p / a = [ ( m + Δ m M ) 2 α / ( α + 2 ) ( m M ) 2 α / ( α + 2 ) ] 1 / α .
dm = π a p / a ( α + 2 2 α ) 1 / 2 ( m M ) 2 / ( α + 2 ) .
[ π ( α + 2 2 α ) 1 / 2 m 2 / ( α + 2 ) ] α = δ m α [ ( m + δ m ) 2 α / ( α + 2 ) m 2 α / ( α + 2 ) ] .
δ m = ( π 2 m ) 1 / 3 ,
a p / a = ( δ m / M ) 1 / 2 ,
a p / a = ( π / M ) 1 / 3 ,
δ m = ( π 2 M ) 1 / 3 .
T m ν = r 1 a p [ n 2 ( r ) k 2 β m 2 ν 2 r 2 ] 1 / 2 rdr r 1 r 2 [ n 2 ( r ) k 2 β m 2 ν 2 r 2 ] 1 / 2 rdr ,
β m 2 = n 1 2 k 2 ( 1 2 Δ m M ) .
T m ν = R 1 a p / a x 2 dx [ ( x 2 R 1 2 ) ( R 2 2 x 2 ) ] 1 / 2 R 1 R 2 x 2 dx [ ( x 2 R 1 2 ) ( R 2 2 x 2 ) ] 1 / 2 ,
R 1 2 = ( r 1 a ) 2 = m / M [ ( m / M ) 2 ( ν / M ) 2 ] 1 / 2 2 ,
R 2 2 = ( r 2 a ) 2 = m / M + [ ( m / M ) 2 ( ν / M ) 2 ] 1 / 2 2 .
P pass ( m , z ) = ν = 0 m T m ν P m ν ( z ) = P ( m , z ) ν = 0 m T m ν P ( m , z ) T ( m ) ,
n m = n ( a p )
n m = n 1 ( 1 2 Δ m 0 M ) 1 / 2 .
m 0 / M n 1 n ( a p ) n 1 n ( a ) .
P ( m , z ) Δ m P pass ( m , z ) θ Δ θ .
P ( m , z ) P pass ( m , z ) .
P 1 ( m , z ) P 1 ( m , z ) / T ( m ) P 2 ( m , z ) P 2 ( m , z ) / T ( m ) } .
T ( m ) { m ( m m 0 ) , 1 / m ( m > m 0 ) .
h ( m ) = 0 m m [ P 2 ( m , z ) / T ( m ) ] 2 z [ P 1 ( m , z ) / P 2 ( m , z ) ] dm m [ P 2 ( m , z ) / T ( m ) ] 2 m [ P 1 ( m , z ) / P 2 ( m , z ) ] .
T ( ϕ ) { ϕ 2 ( ϕ ϕ 0 ) , 1 / ϕ ( ϕ > ϕ 0 ) ,
h ( ϕ ) = A 4 ( 2 π a λ n 1 2 Δ ) 2 × 0 ϕ ϕ 3 [ P 2 ( ϕ , z ) / T ( ϕ ) ] 2 z [ P 1 ( ϕ , z ) / P 2 ( ϕ , z ) ] d ϕ ϕ [ P 2 ( ϕ , z ) / T ( ϕ ) ] 2 ϕ [ P 1 ( ϕ , z ) / P 2 ( ϕ , z ) ] .
( θ 1 / θ c ) 2 = Δ 1 / Δ 0.12 ,
Δ 1 n p n dip n 1 , Δ n 1 n ( a ) n 1 .
θ 1 ± 4.0 ( deg ) .

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