Abstract

The coupling characteristics of gradient-index lenses when used as devices to couple a light source to a fiber are analyzed by the imaging condition.

© 1984 Optical Society of America

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References

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  1. W. J. Tomlinson, “Aberrations of GRIN-Rod Lenses in Multimode Optical Fiber Devices,” Appl. Opt. 19, 1117 (1980).
    [CrossRef] [PubMed]
  2. K. Thyagarajan, A. Rohra, A. K. Ghatak, “Aberration Losses of the Microoptic Directional Coupler: Errata,” Appl. Opt. 19, 1061 (1980).
    [CrossRef] [PubMed]

1980 (2)

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Figures (9)

Fig. 1
Fig. 1

Model of coupling loss between light source and fiber caused by the optical setup.

Fig. 2
Fig. 2

Imaging rule of SML.

Fig. 3
Fig. 3

Effective N.A. of SML.

Fig. 4
Fig. 4

Effective N.A. of SML varies with the normalized object–lens distance.

Fig. 5
Fig. 5

Incident power distribution emitted by the LD.

Fig. 6
Fig. 6

Coupling loss and the normalized object–lens distance.

Fig. 7
Fig. 7

Object–lens distance which gives no excess coupling loss and its lens pitch.

Fig. 8
Fig. 8

Estimation of coupling loss and the object–lens distance.

Fig. 9
Fig. 9

Coupling loss and the normalized object–lens distance.

Equations (16)

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sin 2 θ s - max = N . A . 2 ( r i ) = N . A . 0 2 [ 1 - ( r i r 0 ) 2 ] ,
sin 2 θ s - max = r i 2 / ( η i 2 + r i 2 ) ,
N . A . eff 2 = N . A . 0 2 2 [ η 1 2 + 1 + 1 N . A . 0 2 - ( η 1 2 - 1 + 1 N . A . 0 2 ) + 4 n 1 2 ] ,
r i = N . A . eff / 1 - N . A . eff 2 .
P ( x , y ) = A exp ( - 2 x 2 x 0 2 - 2 y 2 y 0 2 ) .
P ( r i , x 0 , y 0 ) = 2 π 0 π / 2 x 0 y 0 [ 1 - exp 2 r i 2 ( - cos 2 θ x 0 2 - sin 2 θ y 0 2 ) ] y 0 2 cos 2 θ + x 0 2 sin 2 θ d θ ,
N . A . 0 = n 0 g r 0 ,             η 1 = l 1 / r 0 , and η 2 = l 2 / r 0 , N . A . 0 · η 2 = N . A . 0 · η 1 cos g z 0 + sin g z 0 N . A . 0 · η 1 sin g z 0 - cos g z 0 ,
m 2 = ( N . A . 0 · η 2 ) 2 + 1 ( N . A . 0 · η 1 ) 2 + 1 .
η 1 = ( cos g z 0 + 1 m ) / N . A . 0 · sin g z 0 .
N . A . f 2 = sin 2 θ f - max = N . A . 0 2 ( 1 - r out 2 r 0 2 ) ,
N . A . f r out / r 0 η 2 ,
η 2 2 = 1 N . A . f 2 - 1 N . A . 0 2 .
η 1 = 1 N . A . 0 ( N . A . 0 2 N . A . f 2 - 1 ) 1 / 2 cos g z 0 + sin g z 0 ( N . A . 0 2 N . A . f 2 - 1 ) 1 / 2 sin g z 0 - cos g z 0 .
a = 0.64 λ / sin θ ,
η 1 = 0.0622 + cos g z 0 0.46 sin g z 0 .
η 1 = 2.07 cos g z 0 + sin g z 0 0.46 ( 2.07 sin g z 0 - cos g z 0 ) .

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