Abstract

The graded-index rod lens (GRIN lens) is useful in coupling between multimode optical fibers. Applications include connectors, switches, multiplexers, and branch couplers. In these devices, one GRIN lens collimates light from an input fiber, and a second lens collects the light and focuses it on an output fiber. This paper presents analyses of power losses in these devices resulting from lateral and angular misalignments and from the spacing between the lenses. It is found that the GRIN lens coupling system is very sensitive to angular alignment but is more tolerant of lateral errors and lens spacing.

© 1980 Optical Society of America

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References

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  1. W. J. Tomlinson, in Digest of Topical Meeting on Gradient Index Optical Imaging Systems (Optical Society of America, Washington, D.C., 1979), paper WC6.
  2. Nippon Sheet Glass Co., Ltd., manufacturer's literature on the Selfoc microlens.
  3. T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
    [CrossRef]
  4. M. Shimizu, Y. Ueno, in CLEOS, 7-9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WAA3.
  5. M. Shimizu, T. Mori, R. Ishikawa, K. Kaede, in CLEOS, 7–9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WFF2.
  6. T. Matsui, N. Tsukada, T. Nakayama, M. Hirano, in CLEOS, 7-9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WAA5.
  7. W. J. Tomlinson, Appl. Opt. 16, 2180 (1977).
    [CrossRef] [PubMed]
  8. E. G. Rawson, D. R. Herriott, J. McKenna, Appl. Opt. 9, 753 (1970).
    [CrossRef] [PubMed]
  9. W. Streifer, K. B. Paxton, Appl. Opt. 10, 769 (1971).
    [CrossRef] [PubMed]
  10. K. B. Paxton, W. Striefer, Appl. Opt. 10, 1164 (1971).
    [CrossRef] [PubMed]
  11. K. B. Paxton, W. Streifer, Appl. Opt. 10, 2090 (1971).
    [CrossRef] [PubMed]
  12. A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1976).
  13. M. K. Barnoski, Fundamentals of Optical Fiber Communications (Academic Press, New York, 1976).
  14. F. L. Thiel, R. M. Hawk, Appl. Opt. 15, 2785 (1976).
    [CrossRef] [PubMed]

1977 (1)

1976 (1)

1971 (3)

1970 (2)

E. G. Rawson, D. R. Herriott, J. McKenna, Appl. Opt. 9, 753 (1970).
[CrossRef] [PubMed]

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Barnoski, M. K.

M. K. Barnoski, Fundamentals of Optical Fiber Communications (Academic Press, New York, 1976).

Furukawa, M.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Hawk, R. M.

Herriott, D. R.

Hirano, M.

T. Matsui, N. Tsukada, T. Nakayama, M. Hirano, in CLEOS, 7-9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WAA5.

Ishikawa, R.

M. Shimizu, T. Mori, R. Ishikawa, K. Kaede, in CLEOS, 7–9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WFF2.

Kaede, K.

M. Shimizu, T. Mori, R. Ishikawa, K. Kaede, in CLEOS, 7–9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WFF2.

Kitano, I.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Koizumi, K.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Matsui, T.

T. Matsui, N. Tsukada, T. Nakayama, M. Hirano, in CLEOS, 7-9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WAA5.

Matsumura, H.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

McKenna, J.

Mori, T.

M. Shimizu, T. Mori, R. Ishikawa, K. Kaede, in CLEOS, 7–9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WFF2.

Nakayama, T.

T. Matsui, N. Tsukada, T. Nakayama, M. Hirano, in CLEOS, 7-9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WAA5.

Paxton, K. B.

Rawson, E. G.

Shimizu, M.

M. Shimizu, T. Mori, R. Ishikawa, K. Kaede, in CLEOS, 7–9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WFF2.

M. Shimizu, Y. Ueno, in CLEOS, 7-9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WAA3.

Streifer, W.

Striefer, W.

Thiel, F. L.

Tomlinson, W. J.

W. J. Tomlinson, Appl. Opt. 16, 2180 (1977).
[CrossRef] [PubMed]

W. J. Tomlinson, in Digest of Topical Meeting on Gradient Index Optical Imaging Systems (Optical Society of America, Washington, D.C., 1979), paper WC6.

Tsukada, N.

T. Matsui, N. Tsukada, T. Nakayama, M. Hirano, in CLEOS, 7-9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WAA5.

Uchida, T.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Ueno, Y.

M. Shimizu, Y. Ueno, in CLEOS, 7-9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WAA3.

Yariv, A.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1976).

Appl. Opt. (6)

IEEE J. Quantum Electron. (1)

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Other (7)

M. Shimizu, Y. Ueno, in CLEOS, 7-9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WAA3.

M. Shimizu, T. Mori, R. Ishikawa, K. Kaede, in CLEOS, 7–9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WFF2.

T. Matsui, N. Tsukada, T. Nakayama, M. Hirano, in CLEOS, 7-9 Feb. 1978, Digest of Technical Papers (Optical Society of America, Washington, D.C., 1978), paper WAA5.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1976).

M. K. Barnoski, Fundamentals of Optical Fiber Communications (Academic Press, New York, 1976).

W. J. Tomlinson, in Digest of Topical Meeting on Gradient Index Optical Imaging Systems (Optical Society of America, Washington, D.C., 1979), paper WC6.

Nippon Sheet Glass Co., Ltd., manufacturer's literature on the Selfoc microlens.

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Figures (14)

Fig. 1
Fig. 1

Coupling of fibers using GRIN lenses.

Fig. 2
Fig. 2

Ray path inside a GRIN lens.

Fig. 3
Fig. 3

Ray coordinates of the transmitting GRIN lens.

Fig. 4
Fig. 4

Ray coordinates of the receiving GRIN lens.

Fig. 5
Fig. 5

Path of typical ray.

Fig. 6
Fig. 6

Paths of extreme rays through the transmitting lens.

Fig. 7
Fig. 7

Lateral misalignment of GRIN lenses. (a) Cross-sectional view and (b) end view showing overlapping area.

Fig. 8
Fig. 8

Coupling loss due to lateral misalignment.

Fig. 9
Fig. 9

Angular misalignment. (a) Displacement of the central ray and (b) displacement of the received light spot.

Fig. 10
Fig. 10

Coupling loss due to angular misalignment using GRIN lenses.

Fig. 11
Fig. 11

Effects of a gap between the lenses. The axial rays of the emitted light cones are traced. (a) No gap and (b) gap present.

Fig. 12
Fig. 12

Ray path of cone axis with a lens gap.

Fig. 13
Fig. 13

Universal curve of coupling loss caused by lens spacing.

Fig. 14
Fig. 14

Typical lens spacing coupling loss for fibers of various radii. (a) rf = 200 μm; (b) rf = 100 μm; (c) rf = 50 μm; and (d) rf = 25 μm. The fiber has N.A. = 0.205 and core index of refraction 1.545. The lens is the SLS-10 in Table I.

Tables (1)

Tables Icon

Table I Characteristics of Typical GRIN Lenses2

Equations (36)

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n ( r ) = n 0 ( 1 A r 2 / 2 ) ,
r 1 i = r 0 i cos ( A z ) + ( 1 / A ) r 0 i sin ( A z ) ,
r 1 i = A r 0 i sin ( A z ) + r 0 i cos ( A z ) ,
cos ( A l ) = 0 ,
l = π / 2 A .
r 1 i = r 0 i / A ,
r 1 i = A r 0 i .
r 1 e = r 1 i ,
r 1 e = n 0 r 1 i .
r 1 e = r 0 i / A ,
r 1 e = n 0 A r 0 i .
r 0 i = r 0 e ,
r 0 i = r 0 e / n 0 .
r 1 i = r 0 e / n 0 A ,
r 1 i = A r 0 i = A r 0 e .
( r 3 , r 3 ) = ( r 1 / A , n 0 A r 1 ) .
( r 4 , r 4 ) = ( r 1 / A n 0 d A r 1 , n 0 A r 1 ) ,
( r 6 , r 6 ) = ( r 1 , n 0 d A r 1 r 1 ) .
α l i = tan 1 ( r l A ) .
α f i = sin 1 ( N . A . / n 0 ) .
r l N . A . / n 0 A .
( N . A . ) l = n 0 r l A .
L = 10 log 10 { 2 π sin 1 [ 1 ( z d l ) 2 ] 1 / 2 2 z π d l [ 1 ( z d l ) 2 ] 1 / 2 } , z d l .
z = tan θ / n 0 A .
α n 0 d A r 1 .
P ( r 1 ) = 2 π sin 1 [ 1 ( n 0 d A r 1 2 α f i ) 2 ] 1 / 2 2 π ( n 0 d A r 1 2 α f i ) [ 1 ( n 0 d A r 1 2 α f i ) 2 ] 1 / 2
η = 1 π r f 2 0 r f 0 2 π P ( r 1 ) r 1 d ϕ d r 1 .
L = 10 log 10 ( 2 π ( γ r f ) 2 { π 4 ( 1 2 γ 2 r f 2 ) sin 1 [ 1 ( γ r f ) 2 ] 1 / 2 3 γ r f 4 [ 1 ( γ r f ) 2 ] 1 / 2 + γ r f ( 1 γ 2 r f 2 ) 3 / 2 2 sin 1 ( γ r f ) 4 } ) ,
L = 10 log 10 [ α 2 f i / ( n 0 d A r f ) 2 ] .
L = 10 log 10 ( 1 0.90188 γ r f ) .
L = 3.92 γ r f = 1.96 n 0 A r f / α f i .
r 4 = r 1 / A n 0 d A r 1 ,
r 6 = A r 4 .
r 4 = N . A . / n 0 A .
r 6 = N . A . / n 0 .
η = ( 2 / π ) sin 1 [ 1 ( z / D ) 2 ] 0.5 ( 2 / π ) ( z / D ) [ 1 ( z / D ) 2 ] 0.5 ,

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