Abstract

The excitation efficiencies of the dominant and low-order modes in an optical fiber are theoretically determined for an incident Gaussian beam that is offset with respect to the fiber axis. The excitation efficiencies are shown to be strongly influenced by both the numerical aperture of the fiber and the wavefront curvature of the incident beam.

© 1975 Optical Society of America

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References

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  1. A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1138 (1969).
    [CrossRef]
  2. P. J. B. Clarricoats, K. B. Chan, Electron. Lett. 6, 750 (1970).
    [CrossRef]
  3. D. Marcuse, Bell Syst. Tech. J. 49, 1695 (1970).
  4. J. R. Stern, R. B. Dyott, Electron. Lett. 7, 52 (1971).
    [CrossRef]
  5. H. J. Heyke, Arch. Elektron. Ubertragung. 26, 455 (1972).
  6. L. G. Cohen, Bell Syst. Tech. J. 51, 573 (1972).
  7. M. Imai, E. H. Hara, Appl. Opt. 13, 1893 (1974).
    [CrossRef] [PubMed]
  8. D. Gloge, Appl. Opt. 10, 2252 (1971).
    [CrossRef] [PubMed]

1974 (1)

1972 (2)

H. J. Heyke, Arch. Elektron. Ubertragung. 26, 455 (1972).

L. G. Cohen, Bell Syst. Tech. J. 51, 573 (1972).

1971 (2)

D. Gloge, Appl. Opt. 10, 2252 (1971).
[CrossRef] [PubMed]

J. R. Stern, R. B. Dyott, Electron. Lett. 7, 52 (1971).
[CrossRef]

1970 (2)

P. J. B. Clarricoats, K. B. Chan, Electron. Lett. 6, 750 (1970).
[CrossRef]

D. Marcuse, Bell Syst. Tech. J. 49, 1695 (1970).

1969 (1)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1138 (1969).
[CrossRef]

Chan, K. B.

P. J. B. Clarricoats, K. B. Chan, Electron. Lett. 6, 750 (1970).
[CrossRef]

Clarricoats, P. J. B.

P. J. B. Clarricoats, K. B. Chan, Electron. Lett. 6, 750 (1970).
[CrossRef]

Cohen, L. G.

L. G. Cohen, Bell Syst. Tech. J. 51, 573 (1972).

Dyott, R. B.

J. R. Stern, R. B. Dyott, Electron. Lett. 7, 52 (1971).
[CrossRef]

Gloge, D.

Hara, E. H.

Heyke, H. J.

H. J. Heyke, Arch. Elektron. Ubertragung. 26, 455 (1972).

Imai, M.

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 49, 1695 (1970).

Snyder, A. W.

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1138 (1969).
[CrossRef]

Stern, J. R.

J. R. Stern, R. B. Dyott, Electron. Lett. 7, 52 (1971).
[CrossRef]

Appl. Opt. (2)

Arch. Elektron. Ubertragung. (1)

H. J. Heyke, Arch. Elektron. Ubertragung. 26, 455 (1972).

Bell Syst. Tech. J. (2)

L. G. Cohen, Bell Syst. Tech. J. 51, 573 (1972).

D. Marcuse, Bell Syst. Tech. J. 49, 1695 (1970).

Electron. Lett. (2)

J. R. Stern, R. B. Dyott, Electron. Lett. 7, 52 (1971).
[CrossRef]

P. J. B. Clarricoats, K. B. Chan, Electron. Lett. 6, 750 (1970).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1138 (1969).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Geometrical configuration of the optical-fiber waveguide and the off-axis Gaussian beam.

Fig. 2
Fig. 2

Excitation efficiencies of the HE11 mode as a function of a·k for an offset beam with a plane wavefront (R/a = ∞; solid curves) and a curved wavefront (R/a = 10.0; dashed curves) with the beam spot size equal to the core diameter (s/a = 0.5).

Fig. 3
Fig. 3

Same as Fig. 2, with the spot size equal to the core diameter (s/a = 1.0).

Fig. 4
Fig. 4

Maximum excitation efficiencies of the HE11 mode plotted as a function of the beam size (s/a) for an offset Gaussian beam with a plane wavefront (R/a = ∞; solid curves) and a curved wavefront (R/a = 10.0; dashed curves).

Fig. 5
Fig. 5

Maximum excitation efficiencies of the HE11 mode plotted as a function of the beam size (s/a) for offset Gaussian beams. The numerical aperture of the fiber is chosen to be (n12n22)1/2 = 0.40 (dotted curves) and (n12− n22)1/2 = 0.20 (dashed curves).

Fig. 6
Fig. 6

Excitation efficiencies of the HE12 mode as a function of a·k for various spot sizes of a Gaussian beam at normal incidence.

Fig. 7
Fig. 7

Excitation efficiencies of the HE21 mode as a function of a·k for offset Gaussian beams.

Equations (6)

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E x = ( 2 Z 0 π s 2 ) 1 / 2 exp [ 1 2 ( 1 s 2 + j k R ) × ( r 2 2 r ρ sin ϕ + ρ 2 ) ] ,
P l m = Re ( C l m · D l m ) ,
C l m = 1 2 0 0 2 π ( E r h ϕ * E ϕ h r * ) r d r d ϕ , D l m = 1 2 0 0 2 π ( e r H ϕ * e ϕ H r * ) r d r d ϕ .
P l m = exp ( ρ 2 / s 2 ) ( a s ) 2 n 2 { K l + 1 ( w ) K l 1 ( w ) K l 2 ( w ) 1 + n 1 n 2 [ 1 J l + 1 ( u ) J l 1 ( u ) J l 2 ( u ) ] } × [ 0 r d r exp ( r 2 2 s 2 ) A l ( r ) L l ( r ) × 0 r d r exp ( r 2 2 s 2 ) A l ( r ) M l ( r ) + 0 r d r exp ( r 2 2 s 2 ) B l ( r ) L l ( r ) × 0 r d r exp ( r 2 2 s 2 ) B l ( r ) M l ( r ) ] ,
A l ( r ) = F l cos [ ( r 2 + ρ 2 ) / 2 R ] k + G l sin [ ( r 2 + ρ 2 ) / 2 R ] k , B l ( r ) = F l sin [ ( r 2 + ρ 2 ) / 2 R ] k G l cos [ ( r 2 + ρ 2 ) / 2 R ] k , L l ( r ) = { n 1 J l ( u r / a ) / J l ( u ) ; r a , n 2 K l ( w r / a ) / K l ( w ) ; r a , M l ( r ) = { J l ( u r / a ) / J l ( u ) ; r a , K l ( w r / a ) / K l ( w ) ; r a ,
F 0 = n n ( 1 ) n J 2 n ( k ρ r R ) I 2 n ( ρ r s 2 ) , G 0 = 2 n ( 1 ) n J 2 n + 1 ( k ρ r R ) I 2 n + 1 ( ρ r s 2 ) , F 1 = 2 n ( 1 ) n J 2 n ( k ρ r R ) I 2 n + 1 ( ρ r s 2 ) , G 1 = J 1 ( k ρ r R ) I 0 ( ρ r s 2 ) 2 n ( 1 ) n + 1 J 2 n + 1 ( k ρ r R ) I 2 ( n + 1 ) ( ρ r s 2 ) , F 2 = J 2 ( k ρ r R ) I 0 ( ρ r s 2 ) + 2 n ( 1 ) n + 1 J 2 n ( k ρ r R ) I 2 ( n + 1 ) ( ρ r s 2 ) , G 2 = 2 J 1 ( k ρ r R ) I 1 ( ρ r s 2 ) + 2 n ( 1 ) n + 1 J 2 n + 1 ( k ρ r R ) I 2 n + 3 ( ρ r s 2 ) ,

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