Abstract

Promising results of various coupling experiments between laser diodes and single-mode fibers to determine the optimum coupling method are reported. The cylindrical lens method is shown to be most efficient, with a coupling loss of 1.8 dB under optimum alignment conditions. More than −2 dB coupling efficiency is attained with a cylindrical lens whose radius is less than 8 μm. The laser to fiber coupling characteristics are estimated by Gaussian beam approximation. The optimum radius of a cylindrical lens, which gives maximum coupling efficiency, is derived by theoretical calculation, using the ray matrix method. The cylindrical lens alignment tolerance is also shown theoretically and experimentally.

© 1979 Optical Society of America

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  1. M. Kawachi, A. Kawana, T. Miyashita, Electron. Lett. 13, 442 (1977).
    [CrossRef]
  2. T. Kimura, M. Saruwatari, J. Yamada, S. Uehara, T. Miyashita, Appl. Opt. 17, 2420 (1978).
    [CrossRef] [PubMed]
  3. D. E. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
    [CrossRef]
  4. A. Kawana, M. Kawachi, T. Miyashita, M. Saruwatari, K. Asatani, J. Yamada, K. Oe, Opt. Lett. 2, 106 (1978).
  5. M. Saruwatari, K. Asatani, J. Yamada, I. Hatakeyama, K. Sugiyama, T. Kimura, Electron. Lett. 14, 187 (1978).
    [CrossRef]
  6. J. Yamada, M. Saruwatari, K. Asatani, H. Tsuchiya, A. Kawana, K. Sugiyama, T. Kimura, IEEE J. Quantum Electron. QE-14, 791 (1978).
    [CrossRef]
  7. L. G. Cohen, Bell. Syst. Tech. J. 51, 573 (1972).
  8. E. Weidel, Electron. Lett. 11, 436 (1975).
    [CrossRef]
  9. E. Weidel, Opt. Commun. 12, 93 (1974).
    [CrossRef]
  10. L. G. Cohen, M. V. Schneider, Appl. Opt. 13, 89 (1974).
    [CrossRef] [PubMed]
  11. Y. Odagiri, M. Shikada, K. Kobayashi, Electron. Lett. 13, 395 (1977).
    [CrossRef]
  12. D. Marcuse, Bell. Syst. Tech. J. 56, 703 (1977).
  13. H. Kogelnik, in Microwave Research Institute Symposia Series, Vol. 14, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), p. 333.

1978 (4)

A. Kawana, M. Kawachi, T. Miyashita, M. Saruwatari, K. Asatani, J. Yamada, K. Oe, Opt. Lett. 2, 106 (1978).

M. Saruwatari, K. Asatani, J. Yamada, I. Hatakeyama, K. Sugiyama, T. Kimura, Electron. Lett. 14, 187 (1978).
[CrossRef]

J. Yamada, M. Saruwatari, K. Asatani, H. Tsuchiya, A. Kawana, K. Sugiyama, T. Kimura, IEEE J. Quantum Electron. QE-14, 791 (1978).
[CrossRef]

T. Kimura, M. Saruwatari, J. Yamada, S. Uehara, T. Miyashita, Appl. Opt. 17, 2420 (1978).
[CrossRef] [PubMed]

1977 (3)

Y. Odagiri, M. Shikada, K. Kobayashi, Electron. Lett. 13, 395 (1977).
[CrossRef]

D. Marcuse, Bell. Syst. Tech. J. 56, 703 (1977).

M. Kawachi, A. Kawana, T. Miyashita, Electron. Lett. 13, 442 (1977).
[CrossRef]

1975 (2)

D. E. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
[CrossRef]

E. Weidel, Electron. Lett. 11, 436 (1975).
[CrossRef]

1974 (2)

1972 (1)

L. G. Cohen, Bell. Syst. Tech. J. 51, 573 (1972).

Asatani, K.

A. Kawana, M. Kawachi, T. Miyashita, M. Saruwatari, K. Asatani, J. Yamada, K. Oe, Opt. Lett. 2, 106 (1978).

M. Saruwatari, K. Asatani, J. Yamada, I. Hatakeyama, K. Sugiyama, T. Kimura, Electron. Lett. 14, 187 (1978).
[CrossRef]

J. Yamada, M. Saruwatari, K. Asatani, H. Tsuchiya, A. Kawana, K. Sugiyama, T. Kimura, IEEE J. Quantum Electron. QE-14, 791 (1978).
[CrossRef]

Cohen, L. G.

L. G. Cohen, M. V. Schneider, Appl. Opt. 13, 89 (1974).
[CrossRef] [PubMed]

L. G. Cohen, Bell. Syst. Tech. J. 51, 573 (1972).

Gambling, W. A.

D. E. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
[CrossRef]

Hatakeyama, I.

M. Saruwatari, K. Asatani, J. Yamada, I. Hatakeyama, K. Sugiyama, T. Kimura, Electron. Lett. 14, 187 (1978).
[CrossRef]

Kawachi, M.

Kawana, A.

A. Kawana, M. Kawachi, T. Miyashita, M. Saruwatari, K. Asatani, J. Yamada, K. Oe, Opt. Lett. 2, 106 (1978).

J. Yamada, M. Saruwatari, K. Asatani, H. Tsuchiya, A. Kawana, K. Sugiyama, T. Kimura, IEEE J. Quantum Electron. QE-14, 791 (1978).
[CrossRef]

M. Kawachi, A. Kawana, T. Miyashita, Electron. Lett. 13, 442 (1977).
[CrossRef]

Kimura, T.

T. Kimura, M. Saruwatari, J. Yamada, S. Uehara, T. Miyashita, Appl. Opt. 17, 2420 (1978).
[CrossRef] [PubMed]

M. Saruwatari, K. Asatani, J. Yamada, I. Hatakeyama, K. Sugiyama, T. Kimura, Electron. Lett. 14, 187 (1978).
[CrossRef]

J. Yamada, M. Saruwatari, K. Asatani, H. Tsuchiya, A. Kawana, K. Sugiyama, T. Kimura, IEEE J. Quantum Electron. QE-14, 791 (1978).
[CrossRef]

Kobayashi, K.

Y. Odagiri, M. Shikada, K. Kobayashi, Electron. Lett. 13, 395 (1977).
[CrossRef]

Kogelnik, H.

H. Kogelnik, in Microwave Research Institute Symposia Series, Vol. 14, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), p. 333.

Marcuse, D.

D. Marcuse, Bell. Syst. Tech. J. 56, 703 (1977).

Miyashita, T.

Odagiri, Y.

Y. Odagiri, M. Shikada, K. Kobayashi, Electron. Lett. 13, 395 (1977).
[CrossRef]

Oe, K.

Payne, D. E.

D. E. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
[CrossRef]

Saruwatari, M.

T. Kimura, M. Saruwatari, J. Yamada, S. Uehara, T. Miyashita, Appl. Opt. 17, 2420 (1978).
[CrossRef] [PubMed]

M. Saruwatari, K. Asatani, J. Yamada, I. Hatakeyama, K. Sugiyama, T. Kimura, Electron. Lett. 14, 187 (1978).
[CrossRef]

A. Kawana, M. Kawachi, T. Miyashita, M. Saruwatari, K. Asatani, J. Yamada, K. Oe, Opt. Lett. 2, 106 (1978).

J. Yamada, M. Saruwatari, K. Asatani, H. Tsuchiya, A. Kawana, K. Sugiyama, T. Kimura, IEEE J. Quantum Electron. QE-14, 791 (1978).
[CrossRef]

Schneider, M. V.

Shikada, M.

Y. Odagiri, M. Shikada, K. Kobayashi, Electron. Lett. 13, 395 (1977).
[CrossRef]

Sugiyama, K.

J. Yamada, M. Saruwatari, K. Asatani, H. Tsuchiya, A. Kawana, K. Sugiyama, T. Kimura, IEEE J. Quantum Electron. QE-14, 791 (1978).
[CrossRef]

M. Saruwatari, K. Asatani, J. Yamada, I. Hatakeyama, K. Sugiyama, T. Kimura, Electron. Lett. 14, 187 (1978).
[CrossRef]

Tsuchiya, H.

J. Yamada, M. Saruwatari, K. Asatani, H. Tsuchiya, A. Kawana, K. Sugiyama, T. Kimura, IEEE J. Quantum Electron. QE-14, 791 (1978).
[CrossRef]

Uehara, S.

Weidel, E.

E. Weidel, Electron. Lett. 11, 436 (1975).
[CrossRef]

E. Weidel, Opt. Commun. 12, 93 (1974).
[CrossRef]

Yamada, J.

J. Yamada, M. Saruwatari, K. Asatani, H. Tsuchiya, A. Kawana, K. Sugiyama, T. Kimura, IEEE J. Quantum Electron. QE-14, 791 (1978).
[CrossRef]

A. Kawana, M. Kawachi, T. Miyashita, M. Saruwatari, K. Asatani, J. Yamada, K. Oe, Opt. Lett. 2, 106 (1978).

M. Saruwatari, K. Asatani, J. Yamada, I. Hatakeyama, K. Sugiyama, T. Kimura, Electron. Lett. 14, 187 (1978).
[CrossRef]

T. Kimura, M. Saruwatari, J. Yamada, S. Uehara, T. Miyashita, Appl. Opt. 17, 2420 (1978).
[CrossRef] [PubMed]

Appl. Opt. (2)

Bell. Syst. Tech. J. (2)

L. G. Cohen, Bell. Syst. Tech. J. 51, 573 (1972).

D. Marcuse, Bell. Syst. Tech. J. 56, 703 (1977).

Electron. Lett. (5)

M. Kawachi, A. Kawana, T. Miyashita, Electron. Lett. 13, 442 (1977).
[CrossRef]

E. Weidel, Electron. Lett. 11, 436 (1975).
[CrossRef]

Y. Odagiri, M. Shikada, K. Kobayashi, Electron. Lett. 13, 395 (1977).
[CrossRef]

D. E. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
[CrossRef]

M. Saruwatari, K. Asatani, J. Yamada, I. Hatakeyama, K. Sugiyama, T. Kimura, Electron. Lett. 14, 187 (1978).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Yamada, M. Saruwatari, K. Asatani, H. Tsuchiya, A. Kawana, K. Sugiyama, T. Kimura, IEEE J. Quantum Electron. QE-14, 791 (1978).
[CrossRef]

Opt. Commun. (1)

E. Weidel, Opt. Commun. 12, 93 (1974).
[CrossRef]

Opt. Lett. (1)

Other (1)

H. Kogelnik, in Microwave Research Institute Symposia Series, Vol. 14, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), p. 333.

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Figures (20)

Fig. 1
Fig. 1

Far-field power distribution of the laser diode in the present experiment. θ and θ|| correspond to angles perpendicular and parallel to the junction plane, respectively. Drive currents are varied from 65 mA to 80 mA.

Fig. 2
Fig. 2

Coupling between two Gaussian beams. The spot size of the incident beam is w1 and the spot size of the single-mode fiber is w0. Spacing between incident beam waist w1 and fiber end is denoted by z. The fiber axis is tilted from the incident axis by θ rad and is displaced from the incident axis by x0.

Fig. 3
Fig. 3

Excess coupling loss characteristics for lateral and angular misalignments, assuming z = 0. Input beam waists are (a) 1.5 μm and (b) 3.0 μm, respectively. Spot size w0 of the fiber beam is assumed to be 3 μm. Each line corresponds to the equivalent excess loss.

Fig. 4
Fig. 4

Excess coupling loss versus lateral misalignment, assuming z = 0. Input beam radius, denoted by w1, is given.

Fig. 5
Fig. 5

Coupling loss characteristics for lateral and angular misalignments. Solid and broken curves correspond to 0 μm and 30 μm, respectively, values for spacing z between input beam and fiber.

Fig. 6
Fig. 6

Calculated coupling characteristics for butt joint. Spot sizes of the input beam parallel and perpendicular to the junction plane are w 1 = 2.05 μ m and w 1 = 0.55 μ m, respectively. Spot size w0 of the fiber is assumed to be 3 μm.

Fig. 7
Fig. 7

Excess coupling loss characteristics of lateral and angular misalignment for butt joint, assuming w 1 = 2.05 μ m , w 1 = 0.55 μ m, w0 = 3 μm, and z = 0. (a) Misalignment parallel to and (b) perpendicular to the junction plane, respectively.

Fig. 8
Fig. 8

Excess coupling loss characteristics of lateral and angular misalignment for butt joint, as a parameter of the spacing z. (a) misalignment perpendicular to and (b) parallel to the junction plane, respectively. All lines represent 0.2-dB excess loss.

Fig. 9
Fig. 9

Coupling method for laser diode to single-mode fiber.

Fig. 10
Fig. 10

Coupling efficiency versus lateral misalignment for cylindrical lens method. Solid and broken curves correspond to radius values of 6.25 μm and 11 μm, respectively.

Fig. 11
Fig. 11

Excess loss versus axial misalignment for cylindrical lens method.

Fig. 12
Fig. 12

Coupling power into single-mode fiber versus laser diode drive current. Solid and broken curves represent laser output and coupling power, respectively.

Fig. 13
Fig. 13

Gaussian beam transformation by cylindrical lens. R is lens radius; n2 and n1 are refractive indices for lens and air, respectively.

Fig. 14
Fig. 14

Coupling loss versus cylindrical lens radius (refractive index n2 = 1.58). Solid and broken curves represent coupling loss (η)1/2 for a one-dimensional beam and that [(η)1/2 · (η||)1/2] for a two-dimensional beam.

Fig. 15
Fig. 15

Coupling loss versus cylindrical lens radius (refractive index n2 = 1.45). Solid and broken curves represent coupling loss (η)1/2 for a one-dimensional beam and that [(η)1/2 · (η||)1/2] for a two-dimensional beam.

Fig. 16
Fig. 16

Coupling loss (η)1/2 versus LD-to-cylindrical lens distance, assuming optimum radius R0 is used (refractive index n2 = 1.58).

Fig. 17
Fig. 17

Coupling loss (η)1/2 versus LD-to-cylindrical lens distance, assuming optimum radius R0 is used (refractive index n2 = 1.45).

Fig. 18
Fig. 18

Laser diode to single-mode fiber coupler.

Fig. 19
Fig. 19

Magnified photograph of the coupling section in the laser diode coupler.

Fig. 20
Fig. 20

Output power characteristics from a pigtail of the laser diode to single-mode fiber coupler.

Tables (2)

Tables Icon

Table I Single-Mode Fiber

Tables Icon

Table II Coupling Efficiency and Tolerance

Equations (19)

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w 0 / a = 0.65 + 1.619 / V 3 / 2 + 2.879 / V 6 ,
η = κ exp ( - κ { x 0 2 2 ( 1 / w 1 2 + 1 / w 0 2 ) + π 2 θ 2 [ w 1 2 ( z ) + w 0 2 ] / 2 λ 2 - x 0 θ z / w 1 2 } ) ,
κ = 4 w 1 2 w 0 2 / [ ( w 1 2 + w 0 2 ) 2 + λ 2 z 2 / π 2 ] ,
w 1 2 ( z ) = w 1 2 [ 1 + ( λ z / π w 1 2 ) 2 ] ,
η 0 = κ 0 exp { - 2 x 0 2 / ( w 1 2 + w 0 2 ) - 2 π 2 θ 2 w 1 2 w 0 2 / [ λ 2 ( w 1 2 + w 0 2 ) ] } ,
κ 0 = 4 / ( w 0 / w 1 + w 1 / w 0 ) 2 .
z ¯ = β 2 R 2 [ 8 n 2 - 8 - n 2 2 n 2 2 d ¯ - 2 ( 2 - n 2 ) n 2 2 + 2 ( n 2 - 1 ) ( 2 - n 2 ) n 2 2 d ¯ 2 + 2 ( n 2 - 1 ) ( 2 - n 2 ) n 2 2 ] 4 ( 1 - 1 / n 2 ) 2 + β 2 [ ( 2 / n 2 - 1 ) R - ( 2 - 2 / n 2 ) R d ¯ ] 2 ,
( w 1 / w ) 2 = [ 2 z ¯ ( 1 / n 2 - 1 ) + 2 / n 2 - 1 ] 2 + β 2 R 2 [ ( 2 / n 2 - 1 ) ( d ¯ + z ¯ ) + 2 / n 2 + ( 2 / n 2 - 2 ) d ¯ z ¯ ] 2 ,
ψ x 0 , θ ( x ) = [ ( 2 π ) 1 / 2 1 w 1 ] 1 / 2 exp [ - ( x - x 0 ) 2 w 1 2 - j k ( x - x 0 ) 2 2 R 1 ] exp ( - j k θ x ) .
C x o , o = C 0 , 0 exp ( - j k θ x 0 2 ) exp [ - x 0 2 q ( 1 w 1 2 + j k 2 R 1 - j k θ 2 x 0 ) × ( 1 w 0 2 - j k 2 R 0 + j k θ 2 x 0 ) ] ,
η = C x o , o 2 C 0 , 0 2 = κ exp ( - κ { x 0 2 2 ( 1 w 1 2 + k 2 w 1 2 2 R 1 2 ) + x 0 2 2 ( 1 w 0 2 + k w 0 2 2 R 0 2 ) + k 2 8 [ ( θ 2 w 1 2 - 2 x 0 θ w 1 2 R 1 ) + ( θ 2 w 0 2 - 2 x 0 θ w 0 2 R 0 ) ] } ) ,
κ = 4 / w 1 2 w 0 2 [ ( 1 / w 1 2 + 1 / w 0 2 ) 2 - k 2 ( 1 / R 1 - 1 / R 0 ) 2 / 4 ] .
M = ( A B C D ) = ( 1 z 0 1 ) M 0 ( 1 d 0 1 ) ,
M 0 = ( 2 n 2 - 1 2 R n 2 1 - n 2 R 2 n 2 2 n 2 - 1 ) .
M = ( 2 - n 2 n 2 + 2 z ( 1 - n 2 ) n 2 R ( 2 - n 2 n 2 ) ( d + z ) + 2 R n 2 + 1 - n 2 R 2 d z n 2 1 - n 2 R · 2 n 2 ( 2 - n 2 n 2 ) + 1 - n 2 R · 2 d n 2 ) .
1 q 2 = C + D / q 1 A + B / q 1 ,
1 q 2 = 1 / R 1 , 2 - j λ / π ω 2 1 , 2 ,
A · C + B · D · ( λ / π w 1 2 ) 2 = 0.
( w 2 / w 1 ) 2 = 1 / [ A 2 + B 2 ( λ / π w 1 2 ) 2 ] .

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