Abstract

Losses are calculated for the single-mode graded-index- (GRIN-) lens coupler. The main advantage of this coupling system is large separation between fibers with small power loss. The excess loss of the GRIN-lens coupler is due primarily to the misalignments of the GRIN lenses and is most sensitive to angular tilt rather than lateral offset or end separation. The excess loss is calculated from the overlap of two differently sized or misaligned Gaussian beams. Experimental results show that this method is adequate for predicting losses that are due to misalignments of the GRIN lenses.

© 1994 Optical Society of America

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References

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  1. D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
  2. W. J. Tomlinson, “Applications of GRIN-rod lenses in optical fiber communication systems,” Appl. Opt. 19, 1127–1138(1980).
    [CrossRef] [PubMed]
  3. Y. C. Shi, L. Klafter, E. E. Harstead, “A dual-fiber optical rotary joint,” J. Lightwave Technol. LT-3, 999–1004 (1985).
    [CrossRef]
  4. N. Ito, T. Numazaki, “Optical two-way communication system using a rotary coupler,” Appl. Opt. 24, 2221–2224 (1985).
    [CrossRef] [PubMed]
  5. J. C. Palais, “Fiber coupling using graded-index rod lenses,” Appl. Opt. 19, 2011–2018 (1980).
    [CrossRef] [PubMed]
  6. A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart & Winston, New York, 1985), Chap. 2, pp. 23–24.
  7. E. G. Rawson, D. R. Herriott, J. McKenna, “Analysis of refractive index distributions in cylindrical, graded-index glass rods (GRIN rods) used as image relays,” Appl. Opt. 9, 753–759 (1970).
    [CrossRef] [PubMed]
  8. NSG America, Inc., a subsidiary of Nippon Sheet Glass Co., Ltd., Selfoc Product Guide, manufacturer’s literature on fiber collimators.

1985

Y. C. Shi, L. Klafter, E. E. Harstead, “A dual-fiber optical rotary joint,” J. Lightwave Technol. LT-3, 999–1004 (1985).
[CrossRef]

N. Ito, T. Numazaki, “Optical two-way communication system using a rotary coupler,” Appl. Opt. 24, 2221–2224 (1985).
[CrossRef] [PubMed]

1980

1977

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).

1970

Harstead, E. E.

Y. C. Shi, L. Klafter, E. E. Harstead, “A dual-fiber optical rotary joint,” J. Lightwave Technol. LT-3, 999–1004 (1985).
[CrossRef]

Herriott, D. R.

Ito, N.

Klafter, L.

Y. C. Shi, L. Klafter, E. E. Harstead, “A dual-fiber optical rotary joint,” J. Lightwave Technol. LT-3, 999–1004 (1985).
[CrossRef]

Marcuse, D.

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).

McKenna, J.

Numazaki, T.

Palais, J. C.

Rawson, E. G.

Shi, Y. C.

Y. C. Shi, L. Klafter, E. E. Harstead, “A dual-fiber optical rotary joint,” J. Lightwave Technol. LT-3, 999–1004 (1985).
[CrossRef]

Tomlinson, W. J.

Yariv, A.

A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart & Winston, New York, 1985), Chap. 2, pp. 23–24.

Appl. Opt.

Bell Syst. Tech. J.

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).

J. Lightwave Technol.

Y. C. Shi, L. Klafter, E. E. Harstead, “A dual-fiber optical rotary joint,” J. Lightwave Technol. LT-3, 999–1004 (1985).
[CrossRef]

Other

A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart & Winston, New York, 1985), Chap. 2, pp. 23–24.

NSG America, Inc., a subsidiary of Nippon Sheet Glass Co., Ltd., Selfoc Product Guide, manufacturer’s literature on fiber collimators.

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Figures (11)

Fig. 1
Fig. 1

Fiber GRIN lens system.

Fig. 2
Fig. 2

Critical alignment factors are (a) lateral offset, (b) separation, and (c) angular tilt.

Fig. 3
Fig. 3

Position coordinate r and the slope coordinate r ˙ in the GRIN lens.

Fig. 4
Fig. 4

Sinusoidal ray paths through a GRIN lens.

Fig. 5
Fig. 5

Lateral displacement of a ray entering the GRIN lens increases the angle at which the ray emerges.

Fig. 6
Fig. 6

Rays incident upon the GRIN lens at the angle θ cause a displacement Dθ on the image on the fiber.

Fig. 7
Fig. 7

Output beam from the first GRIN lens expands in the air gap, producing an enlarged image on the receiving fiber.

Fig. 8
Fig. 8

Offset and separation misalignments were in the X and the Z directions, respectively.

Fig. 9
Fig. 9

Excess loss that is due to lateral offset.

Fig. 10
Fig. 10

Excess loss that is due to separation.

Fig. 11
Fig. 11

Excess loss that is due to angular tilt.

Equations (17)

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n ( r ) = n 0 ( 1 - A r 2 2 )
| r 2 r ˙ 2 | = | cos ( A Z ) 1 n 0 A sin ( A Z ) - n 0 A sin A z cos A Z | | r 1 r ˙ 1 | ,
w = NA n 0 A
r 2 = r ˙ 1 e n 0 A ,
r ˙ 2 = - A r 1 e .
D θ = tan θ n 0 A .
w 2 ( Z ) = w 1 [ 1 + ( λ Z π n w 1 2 ) 2 ] 1 / 2
w 3 = w 2 w 0 w 1 ,
E ( X 0 ) = - + - + exp [ - ( x + X 0 ) 2 + y 2 w 1 2 ] × exp ( - x 2 + y 2 w 1 2 ) d x d y
E ( Z ) = - + - + exp { - x 2 + y 2 [ w 3 ( Z ) ] 2 } × exp [ - x 2 + y 2 w 0 2 ] [ 1 w 3 ( Z ) ] 2 d x d y
E ( θ ) = - + - + exp [ - ( x + D θ ) 2 + y 2 w 0 2 ] × exp ( - x 2 + y 2 w 0 2 ) d x d y
L = - 10 log [ E ( X 0 , Z , θ ) E ( 0 , 0 , 0 ) ] 2 ,
- + exp [ - ( A X 2 + B X + C ) ] d X = π A exp [ ( B 2 - 4 A C ) 4 A ] .
L = 4.343 X 0 2 w 1 2
L = 8.686 ln [ 1 + 1 2 ( λ Z π n w 1 2 ) 2 ]
L = 4.343 D θ 2 w 0 2
L = - 10 log ( P m P 0 ) .

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