Abstract

A geometric optics model for evaluating end separation and transverse offset losses at a graded-index (GRIN) rod lens to lens coupler is extended to the case of angular tilt misalignment loss. Two different fiber–lens combinations are examined, and the model is verified by comparison to experimental measurements, which show close agreement to the theoretical predictions. In addition, invariance of the angular tilt loss to differing optical launch and receive conditions is shown, and a possible explanation for this phenomenon is provided. Finally, the theoretical model is used to predict fiber–lens combinations which minimize possible angular tilt losses.

© 1986 Optical Society of America

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References

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  1. G. A. Gasparian, “Expanded Beam Directional Couplers for LAN,” Proc. Soc. Photo-Opt. Instrum. Eng. 434, 15 (1983).
  2. T. Miki, H. Ishio, “Viabilities of Wavelength-Division-Multiplexed Transmission System over an Optical Fiber Cable,” IEEE Trans. Commun. COM-26, 1082 (1978).
    [CrossRef]
  3. W. J. Tomlinson, “Applications of GRIN Rod Lenses in Optical Fiber Communication Systems,” Appl. Opt. 19, 1127 (1980).
    [CrossRef] [PubMed]
  4. J. M. Senior, S. D. Cusworth, N. G. Burrow, A. D. Muirhead, “Misalignment Losses at Multimode Graded-index Fiber Splices and GRIN Rod Lens Couplers,” Appl. Opt. 24, 977 (1985).
    [CrossRef] [PubMed]
  5. J. C. Palais, “Fiber Coupling Using Graded-index Rod Lenses,” Appl. Opt. 15, 2011 (1980).
    [CrossRef]
  6. A. Nicia, “Lens Coupling in Fiber Optic Devices: Efficiency Limits,” Appl. Opt. 20, 3136 (1981).
    [CrossRef] [PubMed]
  7. K. Sono, T. Yamasaki, T. Kishimoto, “Graded Index Rod Lenses,” Laser Focus70 (Feb.1981).
  8. D. Gloge, “Multimode Theory of Graded Core Fibers,” Bell Syst. Tec. J. 9, 1563 (1973).
  9. C. M. Miller, S. C. Mettler, “A Loss Model for Parabolic Profile Fiber Splices,” Bell Syst. Tech. J. 57, 3167 (1978).
  10. D. Gloge, “Offset and Tilt Loss in Optical Fiber Splices,” Bell Syst. Tech. J. 55, 905 (1976).

1985 (1)

1983 (1)

G. A. Gasparian, “Expanded Beam Directional Couplers for LAN,” Proc. Soc. Photo-Opt. Instrum. Eng. 434, 15 (1983).

1981 (2)

A. Nicia, “Lens Coupling in Fiber Optic Devices: Efficiency Limits,” Appl. Opt. 20, 3136 (1981).
[CrossRef] [PubMed]

K. Sono, T. Yamasaki, T. Kishimoto, “Graded Index Rod Lenses,” Laser Focus70 (Feb.1981).

1980 (2)

1978 (2)

T. Miki, H. Ishio, “Viabilities of Wavelength-Division-Multiplexed Transmission System over an Optical Fiber Cable,” IEEE Trans. Commun. COM-26, 1082 (1978).
[CrossRef]

C. M. Miller, S. C. Mettler, “A Loss Model for Parabolic Profile Fiber Splices,” Bell Syst. Tech. J. 57, 3167 (1978).

1976 (1)

D. Gloge, “Offset and Tilt Loss in Optical Fiber Splices,” Bell Syst. Tech. J. 55, 905 (1976).

1973 (1)

D. Gloge, “Multimode Theory of Graded Core Fibers,” Bell Syst. Tec. J. 9, 1563 (1973).

Burrow, N. G.

Cusworth, S. D.

Gasparian, G. A.

G. A. Gasparian, “Expanded Beam Directional Couplers for LAN,” Proc. Soc. Photo-Opt. Instrum. Eng. 434, 15 (1983).

Gloge, D.

D. Gloge, “Offset and Tilt Loss in Optical Fiber Splices,” Bell Syst. Tech. J. 55, 905 (1976).

D. Gloge, “Multimode Theory of Graded Core Fibers,” Bell Syst. Tec. J. 9, 1563 (1973).

Ishio, H.

T. Miki, H. Ishio, “Viabilities of Wavelength-Division-Multiplexed Transmission System over an Optical Fiber Cable,” IEEE Trans. Commun. COM-26, 1082 (1978).
[CrossRef]

Kishimoto, T.

K. Sono, T. Yamasaki, T. Kishimoto, “Graded Index Rod Lenses,” Laser Focus70 (Feb.1981).

Mettler, S. C.

C. M. Miller, S. C. Mettler, “A Loss Model for Parabolic Profile Fiber Splices,” Bell Syst. Tech. J. 57, 3167 (1978).

Miki, T.

T. Miki, H. Ishio, “Viabilities of Wavelength-Division-Multiplexed Transmission System over an Optical Fiber Cable,” IEEE Trans. Commun. COM-26, 1082 (1978).
[CrossRef]

Miller, C. M.

C. M. Miller, S. C. Mettler, “A Loss Model for Parabolic Profile Fiber Splices,” Bell Syst. Tech. J. 57, 3167 (1978).

Muirhead, A. D.

Nicia, A.

Palais, J. C.

J. C. Palais, “Fiber Coupling Using Graded-index Rod Lenses,” Appl. Opt. 15, 2011 (1980).
[CrossRef]

Senior, J. M.

Sono, K.

K. Sono, T. Yamasaki, T. Kishimoto, “Graded Index Rod Lenses,” Laser Focus70 (Feb.1981).

Tomlinson, W. J.

Yamasaki, T.

K. Sono, T. Yamasaki, T. Kishimoto, “Graded Index Rod Lenses,” Laser Focus70 (Feb.1981).

Appl. Opt. (4)

Bell Syst. Tec. J. (1)

D. Gloge, “Multimode Theory of Graded Core Fibers,” Bell Syst. Tec. J. 9, 1563 (1973).

Bell Syst. Tech. J. (2)

C. M. Miller, S. C. Mettler, “A Loss Model for Parabolic Profile Fiber Splices,” Bell Syst. Tech. J. 57, 3167 (1978).

D. Gloge, “Offset and Tilt Loss in Optical Fiber Splices,” Bell Syst. Tech. J. 55, 905 (1976).

IEEE Trans. Commun. (1)

T. Miki, H. Ishio, “Viabilities of Wavelength-Division-Multiplexed Transmission System over an Optical Fiber Cable,” IEEE Trans. Commun. COM-26, 1082 (1978).
[CrossRef]

Laser Focus (1)

K. Sono, T. Yamasaki, T. Kishimoto, “Graded Index Rod Lenses,” Laser Focus70 (Feb.1981).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

G. A. Gasparian, “Expanded Beam Directional Couplers for LAN,” Proc. Soc. Photo-Opt. Instrum. Eng. 434, 15 (1983).

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Figures (7)

Fig. 1
Fig. 1

Coordinate geometry of a light cone transmitted between two GRIN rod lenses separated by a distance z.

Fig. 2
Fig. 2

Coordinate geometry of a light cone incident on the receiving GRIN rod lens face for an angular tilt τ between the two lenses.

Fig. 3
Fig. 3

Experimental arrangement for the angular tilt misalignment loss measurements.

Fig. 4
Fig. 4

Optical power loss vs angular misalignment for 50/125-μm graded-index fiber (N.A. = 0.24) attached to SLS-1.0-0.25P lenses. Measured loss with 10 m of launch and receive fiber × and 1 km of launch and receive fiber □. The solid line depicts the theoretically derived loss curve.

Fig. 5
Fig. 5

Optical power loss vs angular misalignment for 200/250-μm step-index fiber (N.A. = 0.5) attached to SLW-1.8-0.25P lenses. Measured loss with 10 m of launch and receive fiber × and 1 km of launch and receive fiber □. The solid line depicts the theoretically derived loss curve.

Fig. 6
Fig. 6

Percentage of lost rays vs normalized emitted ray angle for 50/125-μm graded-index fiber and SLS-1.0-0.25P lens —, 200/250- μm step-index fiber and SLW-1.8-0.25P lens– – –.

Fig. 7
Fig. 7

Comparison of theoretically derived loss curves for 50/125- μm graded-index fiber (N.A. = 0.24) with SLS-1.0-0.25P lens …, SLW-1.8-0.25P lens +++ and 200/250-μm step-index fiber (N.A. = 0.5) with SLS-1.0-0.25P lens —, SLW-1.8-0.25P lens – – – –.

Tables (1)

Tables Icon

Table I Maximum Output Beam Divergence for Four Different Fiber–Lens Combinations

Equations (14)

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p ( r ) = p ( 0 ) [ 1 ( r / a ) α ] ,
P ( θ ) = P ( 0 ) exp [ 2 ( θ / θ m ) 2 ] ,
N . A . ( r ) = n ( r ) sin θ m = n 1 2 Δ [ 1 ( r / a ) α ] 1 / 2 ,
( r 2 a 2 ) = [ cos ( A 1 / 2 L ) n a 1 A 1 / 2 sin ( A 1 / 2 L ) n a A 1 / 2 sin ( A 1 / 2 L ) cos ( A 1 / 2 L ) ] ( r 1 a 1 ) ,
P E α β = 0 2 π r = a a θ = θ m θ m P ( θ + δ θ 2 ) p ( r + δ r 2 ) r δ θ δ r δ β .
( r 4 a 4 ) = [ cos ( A 1 / 2 L ) n a 1 A 1 / 2 sin ( A 1 / 2 L ) n a A 1 / 2 sin ( A 1 / 2 L ) cos ( A 1 / 2 L ) ] ( r 3 a 3 ) ,
r 3 r 2 .
a 3 = a 2 cos β .
a 3 = a 2 cos β ± τ for a 2 0 , a 3 = a 2 cos β τ for a 2 < 0 ,
| r 3 | > R ,
| r 4 | > a ,
| a 4 | > N . A . ( r 4 ) ,
P L α β r θ P ( θ + δ θ 2 ) p ( r + δ r 2 ) r δ θ δ r δ β ,
loss = 10 log [ 1 ( P L / P E ) ] dB .

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