Abstract

Two modes have been launched into a conventional 10-m long multimode graded-index optical fiber using spatial filtering techniques. The measured cross talk between the two modes in the baseband is −20 dB at the output end of the fiber. Modal multiplexing thus appears to be possible over short fiber lengths.

© 1982 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. N. S. Kapany, J. J. Burke, T. Sawatari, Opt J. Soc. Am. 60, 1178 (1970).
    [Crossref]
  3. P. Facq, P. Fournet, J. Arnaud, Electron. Lett. 16, 648 (1980).
    [Crossref]
  4. P. Facq, J. Arnaud, “Tubular Mode Excitation in Graded-Index Multimode Fibres,” in Proceedings, Photon 80, Paris, Oct. 21-23 1980 (Quartz et Silice, Pithiviers, France, 1981).
  5. P. Facq et al., unpublished work.
  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. L. Jeunhomme, P. Lamouler, Opt. Quantum Electron. 12, 57 (1980).
    [Crossref]
  9. J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976), pp. 104–106.
  10. For power-law index profiles with 0.5 < κ < + ∞, the mode filter design is almost independent of the κ value. Only the tubular mode mean radius is significantly affected by the profile.
  11. F. de Fornel, P. Facq, in Colloque Monomode 80, Limoges, June1980.

1980 (2)

P. Facq, P. Fournet, J. Arnaud, Electron. Lett. 16, 648 (1980).
[Crossref]

L. Jeunhomme, P. Lamouler, Opt. Quantum Electron. 12, 57 (1980).
[Crossref]

1978 (1)

1974 (1)

1973 (1)

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

1970 (1)

N. S. Kapany, J. J. Burke, T. Sawatari, Opt J. Soc. Am. 60, 1178 (1970).
[Crossref]

Arnaud, J.

P. Facq, P. Fournet, J. Arnaud, Electron. Lett. 16, 648 (1980).
[Crossref]

P. Facq, J. Arnaud, “Tubular Mode Excitation in Graded-Index Multimode Fibres,” in Proceedings, Photon 80, Paris, Oct. 21-23 1980 (Quartz et Silice, Pithiviers, France, 1981).

Arnaud, J. A.

J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976), pp. 104–106.

Burke, J. J.

N. S. Kapany, J. J. Burke, T. Sawatari, Opt J. Soc. Am. 60, 1178 (1970).
[Crossref]

de Fornel, F.

F. de Fornel, P. Facq, in Colloque Monomode 80, Limoges, June1980.

Facq, P.

P. Facq, P. Fournet, J. Arnaud, Electron. Lett. 16, 648 (1980).
[Crossref]

F. de Fornel, P. Facq, in Colloque Monomode 80, Limoges, June1980.

P. Facq, J. Arnaud, “Tubular Mode Excitation in Graded-Index Multimode Fibres,” in Proceedings, Photon 80, Paris, Oct. 21-23 1980 (Quartz et Silice, Pithiviers, France, 1981).

Fournet, P.

P. Facq, P. Fournet, J. Arnaud, Electron. Lett. 16, 648 (1980).
[Crossref]

Gambling, W. A.

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

Jeunhomme, L.

L. Jeunhomme, P. Lamouler, Opt. Quantum Electron. 12, 57 (1980).
[Crossref]

Kapany, N. S.

N. S. Kapany, J. J. Burke, T. Sawatari, Opt J. Soc. Am. 60, 1178 (1970).
[Crossref]

Keck, D. B.

Lamouler, P.

L. Jeunhomme, P. Lamouler, Opt. Quantum Electron. 12, 57 (1980).
[Crossref]

Matsumura, H.

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

Oaks, S. M.

Olshansky, R.

Payne, D. N.

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

Sawatari, T.

N. S. Kapany, J. J. Burke, T. Sawatari, Opt J. Soc. Am. 60, 1178 (1970).
[Crossref]

Appl. Opt. (2)

Electron. Lett. (2)

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

P. Facq, P. Fournet, J. Arnaud, Electron. Lett. 16, 648 (1980).
[Crossref]

Opt J. Soc. Am. (1)

N. S. Kapany, J. J. Burke, T. Sawatari, Opt J. Soc. Am. 60, 1178 (1970).
[Crossref]

Opt. Quantum Electron. (1)

L. Jeunhomme, P. Lamouler, Opt. Quantum Electron. 12, 57 (1980).
[Crossref]

Other (5)

J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976), pp. 104–106.

For power-law index profiles with 0.5 < κ < + ∞, the mode filter design is almost independent of the κ value. Only the tubular mode mean radius is significantly affected by the profile.

F. de Fornel, P. Facq, in Colloque Monomode 80, Limoges, June1980.

P. Facq, J. Arnaud, “Tubular Mode Excitation in Graded-Index Multimode Fibres,” in Proceedings, Photon 80, Paris, Oct. 21-23 1980 (Quartz et Silice, Pithiviers, France, 1981).

P. Facq et al., unpublished work.

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Figures (10)

Fig. 1
Fig. 1

Tubular-mode geometry: rc, core radius; rm, tubular-mode radius; f(r), radial dependence of the field amplitude.

Fig. 2
Fig. 2

Normalized radial dependence f(ρ)/fmax = (e/μ)μ/2ρμ exp(−ρ2/2) of a Gaussian tubular mode with azimuthal number μ. = 8. ρ is the normalized variable r / ξ 0 ; ξ 0 = r c / V, where ξ0 is the 1/e power radius of the fundamental Gaussian mode (μ = 0).

Fig. 3
Fig. 3

Contour line | ψ µ ( ρ , ϕ ) | = 0.3 ψ μ max of a Gaussian tubular mode with azimuthal number μ = 8.

Fig. 4
Fig. 4

Normalized radial dependence for two Gaussian tubular modes of azimuthal orders μ1 = 2 and μ2 = 12.

Fig. 5
Fig. 5

Equal level lines | ψ μ i ( ρ , ϕ ) | = 0.4 ψ μ i max for a pair of Gaussian tubular modes of azimuthal numbers μ1 = 2 and μ2 = 12.

Fig. 6
Fig. 6

Set of diaphragms performing the mode selection at the fiber ends: (a) selection of the inner mode; (b) selection of the outer mode; (c) no mode selection.

Fig. 7
Fig. 7

Hole contour geometry of the two tubular-mode input filters. Inner mode μ1 = 2; outer mode μ2 = 12. For the ease of mechanical implementation the contour of the μ2 = 12 mode holes departs slightly from the ideal contour | ψ μ 2 ( ρ , ϕ ) | = K ψ μ 2 max.

Fig. 8
Fig. 8

Experimental arrangement: L, laser; P, polarizer; M1,M2, microscope objectives; H, pinhole; O1,O2,O3, objectives; F, spatial-mode filter; D1,,D2, input and output diaphragms; D, photodiode; and M3,M4, couple of microscope objectives to obtain ×700 magnification.

Fig. 9
Fig. 9

Near-field pattern at the input end of the fiber. The diameter of the outer ring is ∼20 μm (core diam, 50 μm).

Fig. 10
Fig. 10

Near-field patterns observable at output end of a 10-m fiber under the following injection conditions: (a) inner tubular mode μ1 = 2 at input; (b) outer tubular mode μ2 = 12 at input; (c) both μ1 and μ2 at input.

Tables (3)

Tables Icon

Table I Launching Filter and Discrimination Filter Combinations Leading to Cross Talk Coefficients

Tables Icon

Table II Measurement of Cross Talk Coefficients for Various Positions of the Fiber on the Drum and Adjustments of the Launching Mode Filter: μ1 = 2; μ2 = 12; λ = 633 nm

Tables Icon

Table III C ̅ i j Mean Value of Cijand σ Standard Deviation of Table II Measurements

Equations (22)

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ψ μ ( r , ϕ , z ) = ½ f ( r ) exp ( j β z ) [ exp ( j μ ϕ ) + exp ( j μ ϕ ) ] ,
ψ μ ( ρ , ϕ , z ) = ρ μ exp ( ρ 2 / 2 ) cos μ ϕ exp ( j β z ) ,
ψ μ , α ( ρ , ϕ , z ) = ρ μ exp ( ρ 2 / 2 ) L α μ ( ρ 2 ) cos ( μ ϕ ) exp ( j β z ) ,
L α μ ( ρ 2 ) = s = 0 α ( α + μ ) ! ( 1 ) s ρ 2 s ( μ + s ) ! ( α s ) ! s !
C i j = 10 log 10 ( P i j P j j · P j P i ) , i , j { 0 , 1 } , i j ,
d d r [ 1 n ( r ) n ( 0 ) + 1 2 μ 2 k 0 2 r 2 ] = 0 ,
r m = r c ( μ / V ) 1 / ( κ + 1 ) κ 1 / ( 2 κ + 2 ) .
C 21 = 10 log 10 ( P 21 P 11 P 1 P 2 ) ,
C 12 = 10 log 10 ( P 12 P 22 P 2 P 1 ) ,
P i i = D i | ψ μ i | 2 d s ,
P j i = D i | ψ μ j | 2 d s , i , j { 0 , 1 } ; i j .
P i | ψ μ i | 2 d s = π 2 μ i ! ; i = 1 , 2 .
P i i + P i j = P i , i , j { 0 , 1 } ; i j .
C 21 = 18.8 dB ,
C 12 = 12.9 dB .
P 1
P 11
P 11 + P 12
P 2
P 22
P 22 + P 12
C ̅ i j

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