Abstract

An analysis was made of the modal properties of the step-index concentric-core fiberguide of circular cross section, which has found application in duplex (two-channel) transmission and in secure communications. The total number of modes capable of propagating in the guide and their longitudinal propagation constants were evaluated for a variety of geometrical parameters and operating conditions. The intensity variation across the guide’s cross section was also determined, and a criterion, the core-to-ring intensity ratio, was established to designate whether any mode is confined exclusively to the core region, to the ring region, or spread out significantly over both regions. Information about the distribution of each mode’s energy across a cross section is essential in determining the amount of cross talk present in a guide. It was also demonstrated that when the propagation constants for a core and a ring mode coincide a resonant transfer of energy takes place between the core and ring regions. This resonance condition is extremely sensitive to changes in normalized frequency and the radii.

© 1983 Optical Society of America

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References

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  1. A. Bender, G. Salisbury, F. Akers, R. Christian, P. Steensma, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1979), paper ThC4.
  2. C. Chan, P. Steensma, “Crosstalk Analysis in Multi-Layered Fibers,” in Physics of Fiber Optics, Vol. 2, B. Bendow, S. S. Mitra, Eds. (American Ceramic Society, Columbus, Ohio (1981), pp. 297–312.
  3. R. DeVore, J. F. Toth, R. Caldecott, J. Appl. Phys. 44, 4488 (1973).
    [CrossRef]
  4. H. Kajioka, Trans. IECE Jpn. E-63, 414 (1980).
  5. L. Eyges, P. Wintersteiner, J. Opt. Soc. Am. 72, 1597 (1982).
    [CrossRef]
  6. D. Gloge, Appl. Opt. 10, 2252 (1971).
    [CrossRef] [PubMed]
  7. A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1130 (1969).
    [CrossRef]

1982 (1)

1980 (1)

H. Kajioka, Trans. IECE Jpn. E-63, 414 (1980).

1973 (1)

R. DeVore, J. F. Toth, R. Caldecott, J. Appl. Phys. 44, 4488 (1973).
[CrossRef]

1971 (1)

1969 (1)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1130 (1969).
[CrossRef]

Akers, F.

A. Bender, G. Salisbury, F. Akers, R. Christian, P. Steensma, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1979), paper ThC4.

Bender, A.

A. Bender, G. Salisbury, F. Akers, R. Christian, P. Steensma, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1979), paper ThC4.

Caldecott, R.

R. DeVore, J. F. Toth, R. Caldecott, J. Appl. Phys. 44, 4488 (1973).
[CrossRef]

Chan, C.

C. Chan, P. Steensma, “Crosstalk Analysis in Multi-Layered Fibers,” in Physics of Fiber Optics, Vol. 2, B. Bendow, S. S. Mitra, Eds. (American Ceramic Society, Columbus, Ohio (1981), pp. 297–312.

Christian, R.

A. Bender, G. Salisbury, F. Akers, R. Christian, P. Steensma, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1979), paper ThC4.

DeVore, R.

R. DeVore, J. F. Toth, R. Caldecott, J. Appl. Phys. 44, 4488 (1973).
[CrossRef]

Eyges, L.

Gloge, D.

Kajioka, H.

H. Kajioka, Trans. IECE Jpn. E-63, 414 (1980).

Salisbury, G.

A. Bender, G. Salisbury, F. Akers, R. Christian, P. Steensma, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1979), paper ThC4.

Snyder, A. W.

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1130 (1969).
[CrossRef]

Steensma, P.

C. Chan, P. Steensma, “Crosstalk Analysis in Multi-Layered Fibers,” in Physics of Fiber Optics, Vol. 2, B. Bendow, S. S. Mitra, Eds. (American Ceramic Society, Columbus, Ohio (1981), pp. 297–312.

A. Bender, G. Salisbury, F. Akers, R. Christian, P. Steensma, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1979), paper ThC4.

Toth, J. F.

R. DeVore, J. F. Toth, R. Caldecott, J. Appl. Phys. 44, 4488 (1973).
[CrossRef]

Wintersteiner, P.

Appl. Opt. (1)

IEEE Trans. Microwave Theory Tech. (1)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1130 (1969).
[CrossRef]

J. Appl. Phys. (1)

R. DeVore, J. F. Toth, R. Caldecott, J. Appl. Phys. 44, 4488 (1973).
[CrossRef]

J. Opt. Soc. Am. (1)

Trans. IECE Jpn. (1)

H. Kajioka, Trans. IECE Jpn. E-63, 414 (1980).

Other (2)

A. Bender, G. Salisbury, F. Akers, R. Christian, P. Steensma, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1979), paper ThC4.

C. Chan, P. Steensma, “Crosstalk Analysis in Multi-Layered Fibers,” in Physics of Fiber Optics, Vol. 2, B. Bendow, S. S. Mitra, Eds. (American Ceramic Society, Columbus, Ohio (1981), pp. 297–312.

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic diagram of an arbitrary cross section through a step-index concentric-core fiber showing the various regions of constant refractive index. (b) Wave-number profile through the cross section shown in (a). k i is the transverse propagation wave number of the ith region. k g , the longitudinal propagation constant for a propagating mode, falls between k1 and k2. The distance along any radius is given by ρ.

Fig. 2
Fig. 2

P2 vs B for modes with principal mode number l = 3 in a guide having normalized radii a/d = 0.35 and c/d = 0.7. The dashed curves are for core modes, the solid curves for ring modes.

Fig. 3
Fig. 3

Core-to-ring intensity distribution ratio R vs a limited range of B for the two modes in Fig. 2 which cross at B ≈ 6.75. The upper branch of each curve pertains to the core mode, the lower branches to the ring mode.

Fig. 4
Fig. 4

P2 normalized core radius (a/d) for the set of modes whose l = 1. Binding constant B is fixed at 16.5, while c/d is fixed at 0.7.

Fig. 5
Fig. 5

P2 vs normalized ring radius (c/d) for the set of modes whose l = 0. Binding constant B is fixed at 16, a/d at 0.35. Point G indicates a typical intersection between the core and ring mode graphs.

Fig. 6
Fig. 6

Core-to-ring intensity distribution ratio R vs a limited range of normalized ring radius (c/d) for the two modes which cross at point G in Fig. 5. The upper curve is for the core mode, the lower for the ring mode.

Tables (2)

Tables Icon

Table I Ratio of Number of Spread Modes to Total Number of Propagation Modes for Various Values of Binding Constant B and Combinations of Normalized Radii; the Lower Numbers in Parentheses are the (l,m) Mode Numbers of the Lowest Spread Mode; lmax is the Maximum Allowable Principal Mode Number

Tables Icon

Table II Ratio of Number of Spread Modes to Total Number of Propagation Modes for Changes in Core Radius (a/d) Under the Fixed Conditions: B = 16, c/d = 0.7, 0 ≤ l ≤ 44; the Last Column Gives the (l,m) Mode Numbers for the Lowest Spread Mode

Equations (10)

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Ψ ( ρ , ϕ ) = Φ l ( ρ ) { cos l ϕ sin l ϕ } ,
Φ l = A l J l ( K 1 ρ ) in region 1 ; Φ l = B l I l ( K 2 ρ ) + C l K l ( K 2 ρ ) in region 2 ; Φ l = D l J l ( K 1 ρ ) + F l Y l ( K 1 ρ ) in region 3 ; Φ l = G l K l ( K 2 ρ ) + L l I l ( K 2 ρ ) in region 4 ; Φ l = M l K l ( K 5 ρ ) in region 5 ;
K 1 = ( k 1 2 - k g 2 ) 1 / 2 , K 2 = ( k g 2 - k 2 2 ) 1 / 2 , K 5 = ( k g 2 - k 5 2 ) 1 / 2 .
B = ( k 0 d / π ) ( n 1 2 - n 2 2 ) 1 / 2 = ( d / π ) ( k 1 2 - k 2 2 ) 1 / 2 ,
P 2 = ( k g 2 - k 2 2 ) / ( k 1 2 - k 2 2 ) .
K 1 = π B ( 1 - P 2 ) 1 / 2 / d ;
K 2 = π B ( P 2 ) 1 / 2 / d ;
K 5 = π B ( P 2 + Q ) 1 / 2 d ;
Q = ( n 2 2 - n 5 2 ) / ( n 1 2 - n 2 2 ) .
R = 10 log 10 [ I core ( max ) / I ring ( max ) ] .

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