Abstract

A simple method has been devised for the experimental determination of mode conversion coefficients in multimode fibers and involves only the observation of the far-field output as the angle of incidence of a collimated input beam is changed. The normalized mode coupling coefficient in a liquid-core fiber is D = 3 × 10−6 rad2 m−1 and increases by as much as a factor of 10 when transverse pressure is applied. Values some 2 orders of magnitude larger are found in glass-core fibers. There is good agreement between the theory presented and experiment.

© 1975 Optical Society of America

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References

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  1. W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 9, 412 (1973).
    [CrossRef]
  2. W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 10, 148 (1974).
    [CrossRef]
  3. E. L. Chinnock, L. G. Cohen, W. S. Holden, D. R. Standley, D. B. Keck, Proc. IEEE 61, 1499 (1973).
    [CrossRef]
  4. W. A. Gambling, D. N. Payne, H. Matsumura, “Propagation in Curved Multimode Cladded Fibres,” paper presented at AGARD Conference on Electromagnetic Wave Propagation involving Irregular Surfaces and Inhomogeneous Media, The Hague, (1974) (Conference preprint 144).
  5. D. Gloge, Bell Syst. Tech. J. 51, 1767 (1972).
  6. D. N. Payne, W. A. Gambling, Opto-Electron. 5, 297 (1973).
    [CrossRef]
  7. W. A. Gambling, D. N. Payne, H. Matsumura, Radio Electron. Eng. 43, 683 (1973).
    [CrossRef]

1974

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 10, 148 (1974).
[CrossRef]

1973

E. L. Chinnock, L. G. Cohen, W. S. Holden, D. R. Standley, D. B. Keck, Proc. IEEE 61, 1499 (1973).
[CrossRef]

D. N. Payne, W. A. Gambling, Opto-Electron. 5, 297 (1973).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, Radio Electron. Eng. 43, 683 (1973).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 9, 412 (1973).
[CrossRef]

1972

D. Gloge, Bell Syst. Tech. J. 51, 1767 (1972).

Chinnock, E. L.

E. L. Chinnock, L. G. Cohen, W. S. Holden, D. R. Standley, D. B. Keck, Proc. IEEE 61, 1499 (1973).
[CrossRef]

Cohen, L. G.

E. L. Chinnock, L. G. Cohen, W. S. Holden, D. R. Standley, D. B. Keck, Proc. IEEE 61, 1499 (1973).
[CrossRef]

Gambling, W. A.

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 10, 148 (1974).
[CrossRef]

D. N. Payne, W. A. Gambling, Opto-Electron. 5, 297 (1973).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, Radio Electron. Eng. 43, 683 (1973).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 9, 412 (1973).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, “Propagation in Curved Multimode Cladded Fibres,” paper presented at AGARD Conference on Electromagnetic Wave Propagation involving Irregular Surfaces and Inhomogeneous Media, The Hague, (1974) (Conference preprint 144).

Gloge, D.

D. Gloge, Bell Syst. Tech. J. 51, 1767 (1972).

Holden, W. S.

E. L. Chinnock, L. G. Cohen, W. S. Holden, D. R. Standley, D. B. Keck, Proc. IEEE 61, 1499 (1973).
[CrossRef]

Keck, D. B.

E. L. Chinnock, L. G. Cohen, W. S. Holden, D. R. Standley, D. B. Keck, Proc. IEEE 61, 1499 (1973).
[CrossRef]

Matsumura, H.

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 10, 148 (1974).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, Radio Electron. Eng. 43, 683 (1973).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 9, 412 (1973).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, “Propagation in Curved Multimode Cladded Fibres,” paper presented at AGARD Conference on Electromagnetic Wave Propagation involving Irregular Surfaces and Inhomogeneous Media, The Hague, (1974) (Conference preprint 144).

Payne, D. N.

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 10, 148 (1974).
[CrossRef]

D. N. Payne, W. A. Gambling, Opto-Electron. 5, 297 (1973).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, Radio Electron. Eng. 43, 683 (1973).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 9, 412 (1973).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, “Propagation in Curved Multimode Cladded Fibres,” paper presented at AGARD Conference on Electromagnetic Wave Propagation involving Irregular Surfaces and Inhomogeneous Media, The Hague, (1974) (Conference preprint 144).

Standley, D. R.

E. L. Chinnock, L. G. Cohen, W. S. Holden, D. R. Standley, D. B. Keck, Proc. IEEE 61, 1499 (1973).
[CrossRef]

Bell Syst. Tech. J.

D. Gloge, Bell Syst. Tech. J. 51, 1767 (1972).

Electron. Lett.

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 9, 412 (1973).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 10, 148 (1974).
[CrossRef]

Opto-Electron.

D. N. Payne, W. A. Gambling, Opto-Electron. 5, 297 (1973).
[CrossRef]

Proc. IEEE

E. L. Chinnock, L. G. Cohen, W. S. Holden, D. R. Standley, D. B. Keck, Proc. IEEE 61, 1499 (1973).
[CrossRef]

Radio Electron. Eng.

W. A. Gambling, D. N. Payne, H. Matsumura, Radio Electron. Eng. 43, 683 (1973).
[CrossRef]

Other

W. A. Gambling, D. N. Payne, H. Matsumura, “Propagation in Curved Multimode Cladded Fibres,” paper presented at AGARD Conference on Electromagnetic Wave Propagation involving Irregular Surfaces and Inhomogeneous Media, The Hague, (1974) (Conference preprint 144).

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Figures (5)

Fig. 1
Fig. 1

Schematic of experimental arrangement. A collimated input beam is launched at an angle of incidence θ0 into a length z of multimode fiber. The far-field output pattern, in general, consists of an annular ring at a mean angle θ′.

Fig. 2
Fig. 2

(a) Normalized output angular power distribution for the normalized input angles (A/D)1/4θ0 × 104 shown on the curves at a normalized fiber length of 4(AD)1/2z = 10−7. (b) Normalized angular power distributions for the various lengths shown on the curves, in units of 4(AD)1/2 × 107, at a fixed input angle of incidence (A/D)1/4θ0 = 4 × 10−4.

Fig. 3
Fig. 3

Input angle corresponding to the transition from ring to disk at the output as a function of fiber length. For the dashed curve the ordinate scale should be multiplied by 105 and the abscissa by 109.

Fig. 4
Fig. 4

Angular intensity distribution at the output of an 82-m length of liquid-core fiber for different transverse pressures. The launching angle of incidence is 6° in air. The double-peaked curve 1 in (a) is for a relatively unstressed fiber and that 2 in (b) is for a moderate pressure. Steadily increasing pressures result in the flat-topped curves 3 and 4 in (a) and (b), respectively (see text).

Fig. 5
Fig. 5

(a) Transition angle (θ0,m) as a function of fiber length for fiber samples 1–5. (b) Transition angle (θ0,m) as a function of fiber length for fiber samples 6–8.

Tables (2)

Tables Icon

Table I Coupling Coefficients for Liquid-Core Fibers

Tables Icon

Table II Coupling Coefficients for Glass Fibers

Equations (16)

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P ( Θ , z ) z = A Θ 2 P + D Θ Θ ( Θ P Θ ) ,
P ( Θ , z ) = Q ( Θ ) exp ( rz )
x = ( A / D ) 1 / 2 Θ 2 ,
Q ( Θ ) = G ( x ) exp ( ½ x ) .
x d 2 G d x 2 + ( 1 x ) dG dx + ½ [ r 2 ( AD ) 1 / 2 1 ] G = 0 .
G ( x ) = L n ( x )
r n = 2 ( 2 n + 1 ) ( AD ) 1 / 2 ,
P = n = 0 K n L n ( x ) exp ( ½ x ) exp ( r n z ) ,
0 L n ( x ) L m ( x ) exp ( x ) dx = { 0 m n , n ! m = n .
K n = 0 P ( t , 0 ) L n ( t ) exp ( ½ t ) dt ,
n = 0 L n ( x ) L n ( y ) z n = ( 1 z ) 1 exp [ z ( x + y ) ( 1 z ) ] I 0 [ 2 ( xyz ) 1 / 2 ( 1 z ) ] ,
P ( x , z ) = exp [ ( x 0 + x 2 ) ( 1 + exp ( bz ) 1 exp ( bz ) ) ] × [ exp ( ½ bz ) 1 exp ( bz ) ] I 0 [ ( 4 x 0 x ) 1 / 2 exp ( ½ bz ) 1 exp ( bz ) ] ,
2 P ( Θ , z ) Θ 2 = 0 at Θ = 0 .
( A / D ) 1 / 4 Θ 0 , m = { 1 exp [ 8 ( AD ) 1 / 2 z ] 2 exp [ 4 ( AD ) 1 / 2 z ] } 1 / 2 .
log ( A / D ) 1 / 4 Θ 0 , m = ½ log [ 4 ( AD ) 1 / 2 z ]
log Θ 0 , m = ½ log z + log 2 D 1 / 2 .

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