Abstract

Single or close to single tunneling leaky modes have been prism coupled into nominally parabolic index SEL-FOC fibers with effective efficiencies on the order of 10%. The mode parameters fit fairly well to an analytical continuation of the solutions to Gloge and Marcatili’s equations for parabolic index fibers. The data can also be used in conjunction with the Gloge and Marcatili equations to obtain information about the index profile.

© 1976 Optical Society of America

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References

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  1. E. Snitzer, Advances in Quantum Electronics (Columbia U.P., New York, 1961).
  2. A. W. Snyder, Appl. Phys. 4, 273 (1974) and references therein.
    [CrossRef]
  3. M. J. Adams, D. N. Payne, F. M. E. Sladen, Electron. Lett. 11, 238 (1975); W. J. Stewart, Electron. Lett. 11, 321 (1975).
    [CrossRef]
  4. M. J. Adams, D. N. Payne, F. M. E. Sladen, Electron, Lett. 11, 389 (1975).
    [CrossRef]
  5. D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).
  6. Prism coupling techniques reported in the literature include: J. E. Midwinter, Opt. Quant. Elec. 7, 297 (1975) and P. J. R. Lay-bourn, C. A. Millar, G. Stewart, C. D. W. Wilkinson, Electron. Lett. 11, 2 (1975).
    [CrossRef]
  7. D. Gloge, Appl. Opt. 10, 2252 (1971).
    [CrossRef] [PubMed]
  8. S. Zemon, D. Fellows, Opt. Commun. 13, 198 (1975).
    [CrossRef]
  9. D. Gloge, Appl. Opt. 11, 2506 (1972).
    [CrossRef] [PubMed]
  10. D. Gloge, IEEE Trans. Microwave Theory Tech. MTT-23, 106 (1975).
    [CrossRef]

1975 (5)

M. J. Adams, D. N. Payne, F. M. E. Sladen, Electron. Lett. 11, 238 (1975); W. J. Stewart, Electron. Lett. 11, 321 (1975).
[CrossRef]

M. J. Adams, D. N. Payne, F. M. E. Sladen, Electron, Lett. 11, 389 (1975).
[CrossRef]

Prism coupling techniques reported in the literature include: J. E. Midwinter, Opt. Quant. Elec. 7, 297 (1975) and P. J. R. Lay-bourn, C. A. Millar, G. Stewart, C. D. W. Wilkinson, Electron. Lett. 11, 2 (1975).
[CrossRef]

S. Zemon, D. Fellows, Opt. Commun. 13, 198 (1975).
[CrossRef]

D. Gloge, IEEE Trans. Microwave Theory Tech. MTT-23, 106 (1975).
[CrossRef]

1974 (1)

A. W. Snyder, Appl. Phys. 4, 273 (1974) and references therein.
[CrossRef]

1973 (1)

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

1972 (1)

1971 (1)

Adams, M. J.

M. J. Adams, D. N. Payne, F. M. E. Sladen, Electron. Lett. 11, 238 (1975); W. J. Stewart, Electron. Lett. 11, 321 (1975).
[CrossRef]

M. J. Adams, D. N. Payne, F. M. E. Sladen, Electron, Lett. 11, 389 (1975).
[CrossRef]

Fellows, D.

S. Zemon, D. Fellows, Opt. Commun. 13, 198 (1975).
[CrossRef]

Gloge, D.

D. Gloge, IEEE Trans. Microwave Theory Tech. MTT-23, 106 (1975).
[CrossRef]

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

D. Gloge, Appl. Opt. 11, 2506 (1972).
[CrossRef] [PubMed]

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

Marcatili, E. A. J.

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

Midwinter, J. E.

Prism coupling techniques reported in the literature include: J. E. Midwinter, Opt. Quant. Elec. 7, 297 (1975) and P. J. R. Lay-bourn, C. A. Millar, G. Stewart, C. D. W. Wilkinson, Electron. Lett. 11, 2 (1975).
[CrossRef]

Payne, D. N.

M. J. Adams, D. N. Payne, F. M. E. Sladen, Electron, Lett. 11, 389 (1975).
[CrossRef]

M. J. Adams, D. N. Payne, F. M. E. Sladen, Electron. Lett. 11, 238 (1975); W. J. Stewart, Electron. Lett. 11, 321 (1975).
[CrossRef]

Sladen, F. M. E.

M. J. Adams, D. N. Payne, F. M. E. Sladen, Electron. Lett. 11, 238 (1975); W. J. Stewart, Electron. Lett. 11, 321 (1975).
[CrossRef]

M. J. Adams, D. N. Payne, F. M. E. Sladen, Electron, Lett. 11, 389 (1975).
[CrossRef]

Snitzer, E.

E. Snitzer, Advances in Quantum Electronics (Columbia U.P., New York, 1961).

Snyder, A. W.

A. W. Snyder, Appl. Phys. 4, 273 (1974) and references therein.
[CrossRef]

Zemon, S.

S. Zemon, D. Fellows, Opt. Commun. 13, 198 (1975).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. (1)

A. W. Snyder, Appl. Phys. 4, 273 (1974) and references therein.
[CrossRef]

Bell Syst. Tech. J. (1)

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

Electron, Lett. (1)

M. J. Adams, D. N. Payne, F. M. E. Sladen, Electron, Lett. 11, 389 (1975).
[CrossRef]

Electron. Lett. (1)

M. J. Adams, D. N. Payne, F. M. E. Sladen, Electron. Lett. 11, 238 (1975); W. J. Stewart, Electron. Lett. 11, 321 (1975).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

D. Gloge, IEEE Trans. Microwave Theory Tech. MTT-23, 106 (1975).
[CrossRef]

Opt. Commun. (1)

S. Zemon, D. Fellows, Opt. Commun. 13, 198 (1975).
[CrossRef]

Opt. Quant. Elec. (1)

Prism coupling techniques reported in the literature include: J. E. Midwinter, Opt. Quant. Elec. 7, 297 (1975) and P. J. R. Lay-bourn, C. A. Millar, G. Stewart, C. D. W. Wilkinson, Electron. Lett. 11, 2 (1975).
[CrossRef]

Other (1)

E. Snitzer, Advances in Quantum Electronics (Columbia U.P., New York, 1961).

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Figures (8)

Fig. 1
Fig. 1

A classification of LP modes in a parabolic index fiber of radius R0. Each column schematically illustrates representative modes in a degenerate set. (a) and (b) are bound modes, and (c) and (d) are tunneling leaky modes.

Fig. 2
Fig. 2

Near field photographs of tunneling leaky modes in a selfoc fiber.

Fig. 3
Fig. 3

The mode inner radius R in microns vs the azimuthal mode number ν. A line is drawn through the data including the origin.

Fig. 4
Fig. 4

(R+2 + R2) in μm2 vs the mode number m. A line is drawn through the data including the origin.

Fig. 5
Fig. 5

neff2 vs m. A line of predetermined slope is drawn through the data points.

Fig. 6
Fig. 6

neff2 vs ν2. A line is drawn through the data points.

Fig. 7
Fig. 7

log[n02neff2 − (ν/kR±)2] vs log(R±/R0). Two limiting lines are drawn through the data.

Fig. 8
Fig. 8

n2(R±) vs R±2. The line represents the parabolic index profile of Sec. IV, i.e., n02 = 2.370 and NA = 0.26. R0 = 80.0 μm.

Equations (15)

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n ( r ) = n 0 [ 1 - 2 Δ ( r / R 0 ) ] 1 / 2 r < R 0 , n ( r ) = n 0 ( 1 - 2 Δ ) 1 / 2 n b r > R 0 ,
n 0 n eff n b ,
( R ± R 0 ) = 1 2 n 0 2 Δ [ n 0 2 - n eff 2 - ( ν / k R ± ) 2 ] ,
R ± 2 = R 0 2 4 n 0 2 Δ { n 0 2 - n eff 2 ± [ ( n 0 2 - n eff 2 ) 2 - 8 n 0 2 Δ k 2 R 0 2 ν 2 ] 1 / 2 } .
n eff 2 = n 0 2 - { [ 2 n 0 ( 2 Δ ) 1 / 2 ] / R 0 } m ,
R ± 2 = R 0 k 1 n 0 ( 2 Δ ) 1 / 2 [ m ± ( m 2 - ν 2 ) 1 / 2 ] .
ν = ( k / R 0 ) [ n 0 ( 2 Δ ) 1 / 2 ] R + R -
m = ( k / 2 R 0 ) [ n 0 ( 2 Δ ) 1 / 2 ] ( R + 2 + R - 2 ) .
n eff 2 ( ν , R ± ) = - [ 1 / ( k R ± ) 2 ] ν 2 + n 2 ( R ± ) .
n eff 2 ( ν ) ( ) R + = A ν 2 + n 2 ( R + )
n 0 2 = lim R - 0 [ n eff 2 + ( ν / k R - ) 2 ] .
lim R - 0 ( ν / k R - ) 2 = 0.059.
log [ n 0 2 - n eff 2 - ( ν / k R ± ) 2 ] = log ( R ± / R 0 ) + log 2 n 0 2 Δ .
n 2 ( R ± ) = n eff 2 ( R ± ) + ( ν / k R ± ) 2
n 2 ( R ± ) = n eff 2 ( R + )

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