Abstract

The amount of reflected light fed back in the coupling of semiconductor lasers and tapered hemispherical-end (TH) fiber is estimated. Reflection from incident hemisphere is estimated to be below −50 dB, from the loss in the coupling between the laser and its virtual image. For multimode TH fiber reflection of backward-propagating light from connections can be reduced to below −50 dB by an ∼10-μm lateral displacement parallel to the junction plane; there is a small penalty in forward-coupling efficiency. The reduction of reflection is confirmed by measuring relative intensity noise of coupled laser light.

© 1983 Optical Society of America

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References

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  1. H. Kuwahara, H. Furuta, Proc.IEEE 67, 1456 (1979).
    [CrossRef]
  2. T. Shibagaki, K. Ozeki, Natl. Conv. Record IECE Jpn. 314 (1982),in Japanese.
  3. I. G. A. Davies, T. Bricheno, A. R. Goodwin, R. G. Plumb, in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), p. 199.
  4. H. Nakata, K. Fujino, K. Ichida, Natl. Conv. Record IECE Jpn. 2195 (1982), in Japanese.
  5. H. Kuwahara, M. Sasaki, N. Tokoyo, Appl. Opt. 19, 2578 (1980).
    [CrossRef] [PubMed]
  6. W. Bludau, R. Rossberg, Appl. Opt. 21, 1933 (1982).
    [CrossRef] [PubMed]
  7. A. Yariv, Quantum Electronics (Wiley, New York, 1975).
  8. H. Kogelnik, in Symposium on Quasi Optics, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), p. 333.
  9. K. Shima, K. Hanamitsu, M. Takusagawa, IEEE J. Quantum Electron. QE-18, 1688 (1982).
    [CrossRef]
  10. H. Ishikawa, H. Imai, T. Tanahashi, Y. Nishitani, K. Hori, K. Takahei, IEEE J. Quantum Electron. QE-18, 1704 (1982).
    [CrossRef]

1982 (5)

T. Shibagaki, K. Ozeki, Natl. Conv. Record IECE Jpn. 314 (1982),in Japanese.

H. Nakata, K. Fujino, K. Ichida, Natl. Conv. Record IECE Jpn. 2195 (1982), in Japanese.

W. Bludau, R. Rossberg, Appl. Opt. 21, 1933 (1982).
[CrossRef] [PubMed]

K. Shima, K. Hanamitsu, M. Takusagawa, IEEE J. Quantum Electron. QE-18, 1688 (1982).
[CrossRef]

H. Ishikawa, H. Imai, T. Tanahashi, Y. Nishitani, K. Hori, K. Takahei, IEEE J. Quantum Electron. QE-18, 1704 (1982).
[CrossRef]

1980 (1)

1979 (1)

H. Kuwahara, H. Furuta, Proc.IEEE 67, 1456 (1979).
[CrossRef]

Bludau, W.

Bricheno, T.

I. G. A. Davies, T. Bricheno, A. R. Goodwin, R. G. Plumb, in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), p. 199.

Davies, I. G. A.

I. G. A. Davies, T. Bricheno, A. R. Goodwin, R. G. Plumb, in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), p. 199.

Fujino, K.

H. Nakata, K. Fujino, K. Ichida, Natl. Conv. Record IECE Jpn. 2195 (1982), in Japanese.

Furuta, H.

H. Kuwahara, H. Furuta, Proc.IEEE 67, 1456 (1979).
[CrossRef]

Goodwin, A. R.

I. G. A. Davies, T. Bricheno, A. R. Goodwin, R. G. Plumb, in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), p. 199.

Hanamitsu, K.

K. Shima, K. Hanamitsu, M. Takusagawa, IEEE J. Quantum Electron. QE-18, 1688 (1982).
[CrossRef]

Hori, K.

H. Ishikawa, H. Imai, T. Tanahashi, Y. Nishitani, K. Hori, K. Takahei, IEEE J. Quantum Electron. QE-18, 1704 (1982).
[CrossRef]

Ichida, K.

H. Nakata, K. Fujino, K. Ichida, Natl. Conv. Record IECE Jpn. 2195 (1982), in Japanese.

Imai, H.

H. Ishikawa, H. Imai, T. Tanahashi, Y. Nishitani, K. Hori, K. Takahei, IEEE J. Quantum Electron. QE-18, 1704 (1982).
[CrossRef]

Ishikawa, H.

H. Ishikawa, H. Imai, T. Tanahashi, Y. Nishitani, K. Hori, K. Takahei, IEEE J. Quantum Electron. QE-18, 1704 (1982).
[CrossRef]

Kogelnik, H.

H. Kogelnik, in Symposium on Quasi Optics, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), p. 333.

Kuwahara, H.

Nakata, H.

H. Nakata, K. Fujino, K. Ichida, Natl. Conv. Record IECE Jpn. 2195 (1982), in Japanese.

Nishitani, Y.

H. Ishikawa, H. Imai, T. Tanahashi, Y. Nishitani, K. Hori, K. Takahei, IEEE J. Quantum Electron. QE-18, 1704 (1982).
[CrossRef]

Ozeki, K.

T. Shibagaki, K. Ozeki, Natl. Conv. Record IECE Jpn. 314 (1982),in Japanese.

Plumb, R. G.

I. G. A. Davies, T. Bricheno, A. R. Goodwin, R. G. Plumb, in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), p. 199.

Rossberg, R.

Sasaki, M.

Shibagaki, T.

T. Shibagaki, K. Ozeki, Natl. Conv. Record IECE Jpn. 314 (1982),in Japanese.

Shima, K.

K. Shima, K. Hanamitsu, M. Takusagawa, IEEE J. Quantum Electron. QE-18, 1688 (1982).
[CrossRef]

Takahei, K.

H. Ishikawa, H. Imai, T. Tanahashi, Y. Nishitani, K. Hori, K. Takahei, IEEE J. Quantum Electron. QE-18, 1704 (1982).
[CrossRef]

Takusagawa, M.

K. Shima, K. Hanamitsu, M. Takusagawa, IEEE J. Quantum Electron. QE-18, 1688 (1982).
[CrossRef]

Tanahashi, T.

H. Ishikawa, H. Imai, T. Tanahashi, Y. Nishitani, K. Hori, K. Takahei, IEEE J. Quantum Electron. QE-18, 1704 (1982).
[CrossRef]

Tokoyo, N.

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

Appl. Opt. (2)

IEEE J. Quantum Electron. (2)

K. Shima, K. Hanamitsu, M. Takusagawa, IEEE J. Quantum Electron. QE-18, 1688 (1982).
[CrossRef]

H. Ishikawa, H. Imai, T. Tanahashi, Y. Nishitani, K. Hori, K. Takahei, IEEE J. Quantum Electron. QE-18, 1704 (1982).
[CrossRef]

Natl. Conv. Record IECE Jpn. (2)

T. Shibagaki, K. Ozeki, Natl. Conv. Record IECE Jpn. 314 (1982),in Japanese.

H. Nakata, K. Fujino, K. Ichida, Natl. Conv. Record IECE Jpn. 2195 (1982), in Japanese.

Proc.IEEE (1)

H. Kuwahara, H. Furuta, Proc.IEEE 67, 1456 (1979).
[CrossRef]

Other (3)

I. G. A. Davies, T. Bricheno, A. R. Goodwin, R. G. Plumb, in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), p. 199.

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

H. Kogelnik, in Symposium on Quasi Optics, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), p. 333.

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of coupling section in the coupling of a semiconductor laser and a tapered hemispherical-end (TH) fiber, located at distance d and having a curvature radius R.

Fig. 2
Fig. 2

Dependence of feedback efficiency on distance d1 and curvature radius R of the TH fiber. The emitting angle from the laser (λ = 0.85 μm) is assumed to be 2θ = 16°, 2θ = 37° (FWHM). The reflectivity of the incident surface is calculated by Fresnel's formula.

Fig. 3
Fig. 3

Another example of calculated feedback efficiency. The emitting pattern from the laser (λ = 1.3 μm) is more circular. The values of curvature radius R of the end hemisphere are selected for TH single-mode fiber.

Fig. 4
Fig. 4

Angular deflection of reflection point H with laterally displaced coupling; S is the source point; O is the center of hemisphere.

Fig. 5
Fig. 5

Integrated distribution of the beam emerging from TH multimode fiber vs the position of the knife-edge. The curvature radius of the TH fiber is 38 μm and distance d1 is 45 μm. Measured data (solid line) and theoretical curve (dashed line) assuming a Gaussian beam (error function) coincide quite well. The beam radius W0 is 10.6 μm.

Fig. 6
Fig. 6

Integrated distribution of the beam emerging from flat-MMF, TH-MMF, flat-SMF, TH-SMF. In the flat fibers, the distance between fiber and laser is ∼10 μm or less to maximize the forward-coupling efficiency.

Fig. 7
Fig. 7

Measured beam radius W0 is shown for curvature radius R. Open and closed circles correspond to multimode and single-mode fibers, respectively. R = ∞ indicate the flat-end fiber. In each coupling, distance d1 is determined to maximize the forward-coupling efficiency.

Fig. 8
Fig. 8

Dependence of backward- and forward-coupling efficiences of multimode fiber on lateral displacement. The curvature radius R of the incident hemisphere is 38 μm, 55 μm, and ∞ (flat end). Tolerated lateral displacement for forward coupling is greater than for backward coupling.

Fig. 9
Fig. 9

Dependence of backward- and forward-coupling efficiencies of single-mode fiber on lateral displacement. The curvature radius R is 16 μm and ∞ (flat end). Forward- and backward-coupling efficiencies do not differ much.

Fig. 10
Fig. 10

Dependence of relative intensity noise (RIN) and forward- and backward-coupling efficiencies on the lateral displacement. The curvature radius of the multimode TH fiber is 40 μm. Displacement dependence of backward-coupling efficiency coincides with the RIN characteristics, which again increases when the displacement is >11 μm.

Fig. 11
Fig. 11

Dependence of RIN characteristics on the bias current: for the laser itself (○), for maximum coupled fiber (×), and for displaced TH fiber (△).

Tables (1)

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Table I Feedback Efficiency from the Incident Surface of Optical Fiber

Equations (31)

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( A , B C , D ) = ( 1 , d 0 , 1 ) .
( A , B C , D ) = ( 1 , 0 2 / R , 1 ) .
r 2 = ( 1 , d 1 0 , 1 ) r 1 ,
r 3 = ( 1 , 0 2 / R , 1 ) r 2 ,
r 4 = ( 1 , d 2 0 , 1 ) 1 r 3 = ( 1 2 d 2 / R , d 1 d 2 2 d 1 d 2 / R 2 / R , 1 + 2 d 1 / R ) r 1 .
1 q j = 1 R j i λ π W j 2 , ( j = 1 , 2 ) ,
q 2 = ( 1 2 d 2 R ) q 1 + d 1 d 2 2 d 1 d 2 R 2 R q 1 + 1 + 2 d 1 R .
1 q 1 = i λ π W 1 2 = i P , ( P λ π W 1 2 ) .
1 q 2 = 2 i P ( R + 2 d 1 ) R 2 d 2 i P ( d 1 R d 2 R 2 d 1 d 2 ) ,
d 2 = 2 R + P 2 ( R + 2 d 1 ) d 1 R 4 + P 2 ( R + 2 d 1 ) 2 .
W 2 2 = λ [ ( R 2 d 2 ) 2 + P 2 ( d 1 R d 2 R 2 d 1 d 2 ) 2 ] π P R 2 .
C S Q = 4 W 1 2 W 2 2 ( W 1 2 + W 2 2 ) 2 + λ 2 ( d 1 + d 2 ) 2 / π 2 .
C S Q = ( C S Q C S Q ) 1 / 2 ,
I = I 0 exp ( 2 r 2 W 0 2 ) ,
F = x 1 I 0 exp [ 2 ( x 2 + y 2 ) W 0 2 ] dxdy 0 2 π 0 I 0 exp ( 2 r 2 W 0 2 ) rdrd θ = x 1 exp ( 2 x 2 W 0 2 ) d x exp ( 2 x 2 W 0 2 ) d x ( F x ) .
W 1 / 2 = ( ln 2 2 ) 1 / 2 W 0 = 0.5887 W 0 .
C x 0 = C 00 exp ( x 0 2 a b q ) ,
a = ( 1 W ̅ 2 + i k 2 R ̅ ) ,
b = ( 1 W 2 + i k 2 R ) ,
q = a + b ,
C 00 = ( 2 W W ̅ q ) 1 / 2 ;
| C x 0 | 2 = | C 00 | 2 exp [ 2 x 0 2 Re ( a b q ) ] = | C 00 | 2 exp [ x 0 2 K 2 ( 1 W ̅ 2 + 1 W 2 + k 2 W ̅ 2 4 R ̅ 2 + k 2 W 2 4 R 2 ) ] ,
K = 4 W ̅ 2 W 2 q q * = | C 00 | 4 .
K x 0 = | C x 0 | 2 | C 00 | 2 K x 0 2 K 2 2 ( 1 W ̅ 2 + 1 W 2 + k 2 W ̅ 2 4 R ̅ 2 + k 2 W 2 4 R 2 ) .
K x 0 = K x 0 2 K 2 2 ( 1 W ̅ 0 2 + 1 W 0 2 ) .
K x y = | C x y | 2 = | C x 0 | 2 | C y | 2 ,
| C x 0 | 2 = K x 0 | C 00 | 2 = K x 0 K x 1 / 2 ,
| C y | 2 = K y 1 / 2 ,
K x = 4 ( W ̅ 0 W + W W ̅ 0 ) 2 ,
K y = 4 ( W ̅ 0 W + W W ̅ 0 ) 2 .
K x y K x K y [ 1 x 0 2 2 4 W 2 W ̅ 0 2 ( 1 W ̅ 0 2 + 1 W 2 ) ] K x K y ( 1 2 x 0 2 W ̅ 0 2 ) , ( W ̅ 0 W ) .

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