Abstract

The modal noise and distortion caused by a longitudinal gap between two multimode parabolic-index fibers are discussed and quantified by means of modal analysis. It is found that, for coherent illumination and a given loss, the modal noise and distortion due to a gap are generally as severe as or worse than those due to an axial offset between two fibers. It is also shown that, when a partially coherent source is used, the transmission characteristics of a gap can be improved by increasing the operating wavelength. Experimental results have been obtained for modal distortion and are shown to be in close agreement with the theory.

© 1984 Optical Society of America

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  1. R. E. Epworth, in Technical Digest, Fourth European Conference on Optical Communications, Genoa (1978).
  2. K. Petermann, Electron. Lett. 15, 706 (1979).
    [CrossRef]
  3. K. Petermann, IEEE J. Quantum Electron. QE-16, 761 (1980).
    [CrossRef]
  4. H. Olesen, Electron. Lett. 16, 217 (1980).
    [CrossRef]
  5. H. Olesen, E. Nicolaisen, M. Danielsen, in Technical Digest, Seventh Duropean Conferences on Optical Communications, Copenhagen (1981).
  6. C. Pask, in Proc. Inst. Electr. Eng. 127, 282 (1980).
  7. J. Saijonmaa, S. J. Halme, in Technical Digest, Eighth European Conference on Optical Communication, Cannes (1982).
  8. B. Daino, G. De Marchis, S. Piazzolla, Electron. Lett. 15, 755 (1979).
    [CrossRef]
  9. G. De Marchis, S. Piazzolla, B. Daino, in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981).
  10. K. O. Hill, Y. Tremblay, B. S. Kawasaki, Opt. Lett. 5, 270 (1980).
    [CrossRef] [PubMed]
  11. Y. Tremblay, B. S. Kawasaki, K. O. Hill, Appl. Opt. 20, 1652 (1981).
    [CrossRef] [PubMed]
  12. E. G. Rawson, J. W. Goodman, R. E. Norton, J. Opt. Soc. Am. 70, 968 (1980).
    [CrossRef]
  13. J. W. Goodman, E. G. Rawson, Opt. Lett. 6, 324 (1981).
    [CrossRef] [PubMed]
  14. S. Das, P. A. Goud, C. G. Englefield, in Proc. Soc. Photo-Opt. Instrum. Eng. 380, 364 (1983).
  15. D. Marcuse, Bell Syst. Tech. J. 54, 1507 (1975).
  16. R. E. Wagner, C. R. Sandahl, Appl. Opt. 21, 1381 (1982).
    [CrossRef] [PubMed]
  17. H. Kogelnik, in Proceedings, Symposium on Quasi-Optics, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), p. 338.
  18. K. Petermann, G. Arnold, IEEE J. Quantum Electron. QE-18, 550 (1982).
  19. D. Gloge, Bell Syst. Tech. J. 55, 905 (1976).
  20. A. Weierholt, A. Mickelson, D. Thingbo, A. Berg, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper THFF5.
  21. R. Olshansky, D. B. Keck, Appl. Opt. 15, 486 (1976).
  22. R. E. Epworth, Laser Focus 17, 112 (1981).
  23. General Optronics Corp., Application Notes (1981).
  24. H. Kuwahara, M. Goto, Electron. Lett. 17, 626 (1981).
    [CrossRef]
  25. K. Kikushima, O. Hirota, M. Shindo, V. Stoykov, Y. Suematsu, J. Opt. Commun. 3, 129 (1982).
  26. A. H. Cherin, in An Introduction to Optical Fibers (McGraw-Hill, New York, 1983, p. 260.

1983

S. Das, P. A. Goud, C. G. Englefield, in Proc. Soc. Photo-Opt. Instrum. Eng. 380, 364 (1983).

1982

K. Kikushima, O. Hirota, M. Shindo, V. Stoykov, Y. Suematsu, J. Opt. Commun. 3, 129 (1982).

R. E. Wagner, C. R. Sandahl, Appl. Opt. 21, 1381 (1982).
[CrossRef] [PubMed]

K. Petermann, G. Arnold, IEEE J. Quantum Electron. QE-18, 550 (1982).

1981

R. E. Epworth, Laser Focus 17, 112 (1981).

General Optronics Corp., Application Notes (1981).

H. Kuwahara, M. Goto, Electron. Lett. 17, 626 (1981).
[CrossRef]

J. W. Goodman, E. G. Rawson, Opt. Lett. 6, 324 (1981).
[CrossRef] [PubMed]

Y. Tremblay, B. S. Kawasaki, K. O. Hill, Appl. Opt. 20, 1652 (1981).
[CrossRef] [PubMed]

1980

E. G. Rawson, J. W. Goodman, R. E. Norton, J. Opt. Soc. Am. 70, 968 (1980).
[CrossRef]

K. Petermann, IEEE J. Quantum Electron. QE-16, 761 (1980).
[CrossRef]

H. Olesen, Electron. Lett. 16, 217 (1980).
[CrossRef]

C. Pask, in Proc. Inst. Electr. Eng. 127, 282 (1980).

K. O. Hill, Y. Tremblay, B. S. Kawasaki, Opt. Lett. 5, 270 (1980).
[CrossRef] [PubMed]

1979

B. Daino, G. De Marchis, S. Piazzolla, Electron. Lett. 15, 755 (1979).
[CrossRef]

K. Petermann, Electron. Lett. 15, 706 (1979).
[CrossRef]

1976

D. Gloge, Bell Syst. Tech. J. 55, 905 (1976).

R. Olshansky, D. B. Keck, Appl. Opt. 15, 486 (1976).

1975

D. Marcuse, Bell Syst. Tech. J. 54, 1507 (1975).

Arnold, G.

K. Petermann, G. Arnold, IEEE J. Quantum Electron. QE-18, 550 (1982).

Berg, A.

A. Weierholt, A. Mickelson, D. Thingbo, A. Berg, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper THFF5.

Cherin, A. H.

A. H. Cherin, in An Introduction to Optical Fibers (McGraw-Hill, New York, 1983, p. 260.

Daino, B.

B. Daino, G. De Marchis, S. Piazzolla, Electron. Lett. 15, 755 (1979).
[CrossRef]

G. De Marchis, S. Piazzolla, B. Daino, in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981).

Danielsen, M.

H. Olesen, E. Nicolaisen, M. Danielsen, in Technical Digest, Seventh Duropean Conferences on Optical Communications, Copenhagen (1981).

Das, S.

S. Das, P. A. Goud, C. G. Englefield, in Proc. Soc. Photo-Opt. Instrum. Eng. 380, 364 (1983).

De Marchis, G.

B. Daino, G. De Marchis, S. Piazzolla, Electron. Lett. 15, 755 (1979).
[CrossRef]

G. De Marchis, S. Piazzolla, B. Daino, in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981).

Englefield, C. G.

S. Das, P. A. Goud, C. G. Englefield, in Proc. Soc. Photo-Opt. Instrum. Eng. 380, 364 (1983).

Epworth, R. E.

R. E. Epworth, Laser Focus 17, 112 (1981).

R. E. Epworth, in Technical Digest, Fourth European Conference on Optical Communications, Genoa (1978).

Gloge, D.

D. Gloge, Bell Syst. Tech. J. 55, 905 (1976).

Goodman, J. W.

Goto, M.

H. Kuwahara, M. Goto, Electron. Lett. 17, 626 (1981).
[CrossRef]

Goud, P. A.

S. Das, P. A. Goud, C. G. Englefield, in Proc. Soc. Photo-Opt. Instrum. Eng. 380, 364 (1983).

Halme, S. J.

J. Saijonmaa, S. J. Halme, in Technical Digest, Eighth European Conference on Optical Communication, Cannes (1982).

Hill, K. O.

Hirota, O.

K. Kikushima, O. Hirota, M. Shindo, V. Stoykov, Y. Suematsu, J. Opt. Commun. 3, 129 (1982).

Kawasaki, B. S.

Keck, D. B.

R. Olshansky, D. B. Keck, Appl. Opt. 15, 486 (1976).

Kikushima, K.

K. Kikushima, O. Hirota, M. Shindo, V. Stoykov, Y. Suematsu, J. Opt. Commun. 3, 129 (1982).

Kogelnik, H.

H. Kogelnik, in Proceedings, Symposium on Quasi-Optics, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), p. 338.

Kuwahara, H.

H. Kuwahara, M. Goto, Electron. Lett. 17, 626 (1981).
[CrossRef]

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 54, 1507 (1975).

Mickelson, A.

A. Weierholt, A. Mickelson, D. Thingbo, A. Berg, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper THFF5.

Nicolaisen, E.

H. Olesen, E. Nicolaisen, M. Danielsen, in Technical Digest, Seventh Duropean Conferences on Optical Communications, Copenhagen (1981).

Norton, R. E.

Olesen, H.

H. Olesen, Electron. Lett. 16, 217 (1980).
[CrossRef]

H. Olesen, E. Nicolaisen, M. Danielsen, in Technical Digest, Seventh Duropean Conferences on Optical Communications, Copenhagen (1981).

Olshansky, R.

R. Olshansky, D. B. Keck, Appl. Opt. 15, 486 (1976).

Pask, C.

C. Pask, in Proc. Inst. Electr. Eng. 127, 282 (1980).

Petermann, K.

K. Petermann, G. Arnold, IEEE J. Quantum Electron. QE-18, 550 (1982).

K. Petermann, IEEE J. Quantum Electron. QE-16, 761 (1980).
[CrossRef]

K. Petermann, Electron. Lett. 15, 706 (1979).
[CrossRef]

Piazzolla, S.

B. Daino, G. De Marchis, S. Piazzolla, Electron. Lett. 15, 755 (1979).
[CrossRef]

G. De Marchis, S. Piazzolla, B. Daino, in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981).

Rawson, E. G.

Saijonmaa, J.

J. Saijonmaa, S. J. Halme, in Technical Digest, Eighth European Conference on Optical Communication, Cannes (1982).

Sandahl, C. R.

Shindo, M.

K. Kikushima, O. Hirota, M. Shindo, V. Stoykov, Y. Suematsu, J. Opt. Commun. 3, 129 (1982).

Stoykov, V.

K. Kikushima, O. Hirota, M. Shindo, V. Stoykov, Y. Suematsu, J. Opt. Commun. 3, 129 (1982).

Suematsu, Y.

K. Kikushima, O. Hirota, M. Shindo, V. Stoykov, Y. Suematsu, J. Opt. Commun. 3, 129 (1982).

Thingbo, D.

A. Weierholt, A. Mickelson, D. Thingbo, A. Berg, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper THFF5.

Tremblay, Y.

Wagner, R. E.

Weierholt, A.

A. Weierholt, A. Mickelson, D. Thingbo, A. Berg, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper THFF5.

Appl. Opt.

Application Notes

General Optronics Corp., Application Notes (1981).

Bell Syst. Tech. J.

D. Gloge, Bell Syst. Tech. J. 55, 905 (1976).

D. Marcuse, Bell Syst. Tech. J. 54, 1507 (1975).

Electron. Lett.

H. Kuwahara, M. Goto, Electron. Lett. 17, 626 (1981).
[CrossRef]

K. Petermann, Electron. Lett. 15, 706 (1979).
[CrossRef]

H. Olesen, Electron. Lett. 16, 217 (1980).
[CrossRef]

B. Daino, G. De Marchis, S. Piazzolla, Electron. Lett. 15, 755 (1979).
[CrossRef]

IEEE J. Quantum Electron.

K. Petermann, IEEE J. Quantum Electron. QE-16, 761 (1980).
[CrossRef]

K. Petermann, G. Arnold, IEEE J. Quantum Electron. QE-18, 550 (1982).

J. Opt. Commun.

K. Kikushima, O. Hirota, M. Shindo, V. Stoykov, Y. Suematsu, J. Opt. Commun. 3, 129 (1982).

J. Opt. Soc. Am.

Laser Focus

R. E. Epworth, Laser Focus 17, 112 (1981).

Opt. Lett.

Proc. Inst. Electr. Eng.

C. Pask, in Proc. Inst. Electr. Eng. 127, 282 (1980).

Proc. Soc. Photo-Opt. Instrum. Eng.

S. Das, P. A. Goud, C. G. Englefield, in Proc. Soc. Photo-Opt. Instrum. Eng. 380, 364 (1983).

Other

J. Saijonmaa, S. J. Halme, in Technical Digest, Eighth European Conference on Optical Communication, Cannes (1982).

G. De Marchis, S. Piazzolla, B. Daino, in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981).

H. Kogelnik, in Proceedings, Symposium on Quasi-Optics, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), p. 338.

H. Olesen, E. Nicolaisen, M. Danielsen, in Technical Digest, Seventh Duropean Conferences on Optical Communications, Copenhagen (1981).

A. H. Cherin, in An Introduction to Optical Fibers (McGraw-Hill, New York, 1983, p. 260.

R. E. Epworth, in Technical Digest, Fourth European Conference on Optical Communications, Genoa (1978).

A. Weierholt, A. Mickelson, D. Thingbo, A. Berg, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper THFF5.

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Figures (9)

Fig. 1
Fig. 1

Two fibers separated by a longitudinal gap d. At z = d, the free-space LG beam radius is w d .

Fig. 2
Fig. 2

Variation of coupling efficiency 〈η〉 and its standard deviation σ(η) with normalized gap width d/a for an air gap (AG) and an index-matched gap (IM); N.A. = 0.2, a = 25 μm, and V = 21 (λ = 1.55 μm).

Fig. 3
Fig. 3

dc-SNR as a function of coupling loss, for a coherent source; N.A. = 0.2, a = 25 μm, and V = 39 (λ = 0.82 μm) or V = 21 (λ = 1.55 μm).

Fig. 4
Fig. 4

dc-SNR behavior as a function of gap loss as predicted by (1) modal analysis assuming a uniform power distribution and coherent illumination, and (2) speckle theory; N.A. = 0.2, a = 25 μm, and V = 39 (λ = 0.82 μm) or V = 21 (λ = 1.55 μm).

Fig. 5
Fig. 5

dc-SNR for partially coherent sources with coherence time τ c . Coupling loss ≃ 1 dB, a = 25 μm, N.A. = 0.2, τrms = 0.15 nsec, and V = 39 (λ = 0.82 μm), V = 21 (λ = 1.55 μm), or V = 9 (λ = 3.6 μm).

Fig. 6
Fig. 6

Variation of the normalized rms value of the derivative of the coupling efficiency with coupling loss for coherent illumination; N.A. = 0.2, a = 25 μm, τrms = 0.15 nsec, and V = 39 (λ = 0.82 μm), or V = 21 (λ = 1.55 μm).

Fig. 7
Fig. 7

Normalized rms value of the derivative of the coupling efficiency for partially coherent sources with coherence time τ c . Coupling loss ≃ 1 dB, a = 25 μm, N.A. = 0.2, τrms = 0.15 nsec, and V = 39 (λ = 0.82 μm), V = 21 (λ = 21 (λ = 1.55 μm), or V = 9 (λ = 3.6 μm).

Fig. 8
Fig. 8

Experimental setup to measure modal distortion caused by a lossy air gap between two multimode fibers. CMS designates the cladding-mode strippers.

Fig. 9
Fig. 9

Modal distortion R2 f / f as a function of normalized gap width for a partially coherent source; N.A. = 0.2, a = 25 μm, τrms = 0.15 nsec, τ c ≃ 35 psec, V = 39 (λ = 0.82 μm), f = 55 MHz, m = 0.25, and Ω m /2π ≃ 2 GHz.

Equations (15)

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w 0 = a 2 V ,
w d = w 0 [ 1 + ( 2 d k m w 0 2 ) 2 ] 1 / 2 ,
C ν μ = ( 2 w 0 w d w 0 2 + w d 2 ) l + 1 ( q 1 + q 2 + l ) ! [ ( q 1 + l ) ! ( q 2 + l ) ! q 1 ! q 2 ! ] 1 / 2 × ( 1 - 2 w 0 2 w 0 2 + w d 2 ) q 1 ( 1 - ( 1 - 2 w d 2 w 0 2 + w d 2 ) q 2 × H [ - q 1 , - q 2 ; - q 1 - q 2 - l , ( w 0 2 + w d 2 w d 2 - w 0 2 ) 2 ]
H ( a , b ; c , z ) = 1 + a · b c z + a ( a + 1 ) · b ( b + 1 ) c ( c + 1 ) · 2 ! z 2 + .
( 2 q + l + 1 ) max = n 0 k a Δ 2 .
[ F ] = [ C ] [ C ] T .
η = ν = 1 N F ν ν W ν ν = 1 N W ν ,
W ν = m - 3 / 2 ( M - 1 M - m ) 1 / 2             1 m < M
σ ( η ) = [ ν = 1 ν x N x = 1 N G ( τ ν x ) W ν W x ( F ν x ) 2 ] 1 / 2 ν = 1 N W ν ,
dc - SNR = [ η σ ( η ) ] 2 .
dc - SNR = N ( η 1 - η ) .
R 2 f / f 20 log [ ( d η d ω c ) 2 Ω m 2 η ] ,
( d n d ω c ) 2
( d η d ω c ) 2 = [ ν = 1 N x = 1 N G ( τ ν x ) τ ν x 2 W ν W x ( F ν x ) 2 ] 1 / 2 ν = 1 N W ν .
[ ( d η d ω c ) 2 1 τ rms η ]

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