Abstract

In this paper, we theoretically analyze the loss and branching ratio of multimode optical branching waveguides by using a ray tracing method to obtain less mode-dependent branching characteristics. First, a 2 × 2 optical mixing and branching waveguide with a step-index profile are considered. It is found that an optimum length to achieve a low loss and stable branching ratio exists. Second, a waveguide with mode scrambler is investigated. By sacrificing some amount of insertion loss, the mode dependence can be minimized.

© 1985 Optical Society of America

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References

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  1. M. Oikawa, K. Iga, “Stacked Array Components with Distributed-Index Planar Microlens,” at Fourth Topical Meeting on Graded-Index Optical Imaging Systems (Kobe, 1983), paper H2.
  2. E. G. Rawson, M. D. Bailey, “Bitaper Star Couplers with up to 100 Fiber Channels,” Electron. Lett. 15, 432 (1979).
    [CrossRef]
  3. K. Nosu, R. Watanabe, “Slab Waveguide Star Coupler for Multimode Optical Fibers,” Electron. Lett. 16, 608 (1980).
    [CrossRef]
  4. N. Takato, T. Kurokawa, “Polymer Waveguide Star Coupler,” Appl. Opt. 21, 1940 (1982).
    [CrossRef] [PubMed]
  5. E. Okuda, I. Tanaka, T. Yamasaki, “Planar Gradient-Index Glass Waveguide and its Applications to a 4-port Branched Circuit and Star Coupler,” Appl. Opt. 23, 1745 (1984).
    [CrossRef] [PubMed]
  6. Y. Yamada, M. Kawachi, M. Yasu, M. Kobayashi, “Fabrication of a High Silica Glass Waveguide Optical Accessor,” Electron. Lett. 20, 589 (1984).
    [CrossRef]
  7. Y. Kokubun, S. Suzuki, T. Fuse, H. Uehara, K. Iga, M. Oikawa, S. Misawa, “A Novel Mode Scrambler for Reducing Mode Dependence in Multimode Optical Waveguide,” Electron. Lett. 19, 1009 (1983).
    [CrossRef]
  8. M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452 (1981).
    [CrossRef]

1984 (2)

E. Okuda, I. Tanaka, T. Yamasaki, “Planar Gradient-Index Glass Waveguide and its Applications to a 4-port Branched Circuit and Star Coupler,” Appl. Opt. 23, 1745 (1984).
[CrossRef] [PubMed]

Y. Yamada, M. Kawachi, M. Yasu, M. Kobayashi, “Fabrication of a High Silica Glass Waveguide Optical Accessor,” Electron. Lett. 20, 589 (1984).
[CrossRef]

1983 (1)

Y. Kokubun, S. Suzuki, T. Fuse, H. Uehara, K. Iga, M. Oikawa, S. Misawa, “A Novel Mode Scrambler for Reducing Mode Dependence in Multimode Optical Waveguide,” Electron. Lett. 19, 1009 (1983).
[CrossRef]

1982 (1)

1981 (1)

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452 (1981).
[CrossRef]

1980 (1)

K. Nosu, R. Watanabe, “Slab Waveguide Star Coupler for Multimode Optical Fibers,” Electron. Lett. 16, 608 (1980).
[CrossRef]

1979 (1)

E. G. Rawson, M. D. Bailey, “Bitaper Star Couplers with up to 100 Fiber Channels,” Electron. Lett. 15, 432 (1979).
[CrossRef]

Bailey, M. D.

E. G. Rawson, M. D. Bailey, “Bitaper Star Couplers with up to 100 Fiber Channels,” Electron. Lett. 15, 432 (1979).
[CrossRef]

Fuse, T.

Y. Kokubun, S. Suzuki, T. Fuse, H. Uehara, K. Iga, M. Oikawa, S. Misawa, “A Novel Mode Scrambler for Reducing Mode Dependence in Multimode Optical Waveguide,” Electron. Lett. 19, 1009 (1983).
[CrossRef]

Iga, K.

Y. Kokubun, S. Suzuki, T. Fuse, H. Uehara, K. Iga, M. Oikawa, S. Misawa, “A Novel Mode Scrambler for Reducing Mode Dependence in Multimode Optical Waveguide,” Electron. Lett. 19, 1009 (1983).
[CrossRef]

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452 (1981).
[CrossRef]

M. Oikawa, K. Iga, “Stacked Array Components with Distributed-Index Planar Microlens,” at Fourth Topical Meeting on Graded-Index Optical Imaging Systems (Kobe, 1983), paper H2.

Kawachi, M.

Y. Yamada, M. Kawachi, M. Yasu, M. Kobayashi, “Fabrication of a High Silica Glass Waveguide Optical Accessor,” Electron. Lett. 20, 589 (1984).
[CrossRef]

Kobayashi, M.

Y. Yamada, M. Kawachi, M. Yasu, M. Kobayashi, “Fabrication of a High Silica Glass Waveguide Optical Accessor,” Electron. Lett. 20, 589 (1984).
[CrossRef]

Kokubun, Y.

Y. Kokubun, S. Suzuki, T. Fuse, H. Uehara, K. Iga, M. Oikawa, S. Misawa, “A Novel Mode Scrambler for Reducing Mode Dependence in Multimode Optical Waveguide,” Electron. Lett. 19, 1009 (1983).
[CrossRef]

Kurokawa, T.

Misawa, S.

Y. Kokubun, S. Suzuki, T. Fuse, H. Uehara, K. Iga, M. Oikawa, S. Misawa, “A Novel Mode Scrambler for Reducing Mode Dependence in Multimode Optical Waveguide,” Electron. Lett. 19, 1009 (1983).
[CrossRef]

Nosu, K.

K. Nosu, R. Watanabe, “Slab Waveguide Star Coupler for Multimode Optical Fibers,” Electron. Lett. 16, 608 (1980).
[CrossRef]

Oikawa, M.

Y. Kokubun, S. Suzuki, T. Fuse, H. Uehara, K. Iga, M. Oikawa, S. Misawa, “A Novel Mode Scrambler for Reducing Mode Dependence in Multimode Optical Waveguide,” Electron. Lett. 19, 1009 (1983).
[CrossRef]

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452 (1981).
[CrossRef]

M. Oikawa, K. Iga, “Stacked Array Components with Distributed-Index Planar Microlens,” at Fourth Topical Meeting on Graded-Index Optical Imaging Systems (Kobe, 1983), paper H2.

Okuda, E.

Rawson, E. G.

E. G. Rawson, M. D. Bailey, “Bitaper Star Couplers with up to 100 Fiber Channels,” Electron. Lett. 15, 432 (1979).
[CrossRef]

Sanada, T.

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452 (1981).
[CrossRef]

Suzuki, S.

Y. Kokubun, S. Suzuki, T. Fuse, H. Uehara, K. Iga, M. Oikawa, S. Misawa, “A Novel Mode Scrambler for Reducing Mode Dependence in Multimode Optical Waveguide,” Electron. Lett. 19, 1009 (1983).
[CrossRef]

Takato, N.

Tanaka, I.

Uehara, H.

Y. Kokubun, S. Suzuki, T. Fuse, H. Uehara, K. Iga, M. Oikawa, S. Misawa, “A Novel Mode Scrambler for Reducing Mode Dependence in Multimode Optical Waveguide,” Electron. Lett. 19, 1009 (1983).
[CrossRef]

Watanabe, R.

K. Nosu, R. Watanabe, “Slab Waveguide Star Coupler for Multimode Optical Fibers,” Electron. Lett. 16, 608 (1980).
[CrossRef]

Yamada, Y.

Y. Yamada, M. Kawachi, M. Yasu, M. Kobayashi, “Fabrication of a High Silica Glass Waveguide Optical Accessor,” Electron. Lett. 20, 589 (1984).
[CrossRef]

Yamasaki, T.

Yasu, M.

Y. Yamada, M. Kawachi, M. Yasu, M. Kobayashi, “Fabrication of a High Silica Glass Waveguide Optical Accessor,” Electron. Lett. 20, 589 (1984).
[CrossRef]

Appl. Opt. (2)

Electron. Lett. (5)

E. G. Rawson, M. D. Bailey, “Bitaper Star Couplers with up to 100 Fiber Channels,” Electron. Lett. 15, 432 (1979).
[CrossRef]

K. Nosu, R. Watanabe, “Slab Waveguide Star Coupler for Multimode Optical Fibers,” Electron. Lett. 16, 608 (1980).
[CrossRef]

Y. Yamada, M. Kawachi, M. Yasu, M. Kobayashi, “Fabrication of a High Silica Glass Waveguide Optical Accessor,” Electron. Lett. 20, 589 (1984).
[CrossRef]

Y. Kokubun, S. Suzuki, T. Fuse, H. Uehara, K. Iga, M. Oikawa, S. Misawa, “A Novel Mode Scrambler for Reducing Mode Dependence in Multimode Optical Waveguide,” Electron. Lett. 19, 1009 (1983).
[CrossRef]

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452 (1981).
[CrossRef]

Other (1)

M. Oikawa, K. Iga, “Stacked Array Components with Distributed-Index Planar Microlens,” at Fourth Topical Meeting on Graded-Index Optical Imaging Systems (Kobe, 1983), paper H2.

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Figures (14)

Fig. 1
Fig. 1

Projection from 3-D ray trajectory to 2-D ray trajectory. GI fiber is butt-jointed to the branching waveguide with a square cross section.

Fig. 2
Fig. 2

Light emittance profile at the end of a GI multimode fiber.

Fig. 3
Fig. 3

Ray propagation in a straight waveguide (step-index type).

Fig. 4
Fig. 4

Saw function S(X).

Fig. 5
Fig. 5

Ray propagation in a bent waveguide.

Fig. 6
Fig. 6

Ray propagation in a tapered waveguide.

Fig. 7
Fig. 7

Loss vs normalized tapered (branching) angle of tapered waveguide.

Fig. 8
Fig. 8

Ray trajectories in 2 × 2 mixing and branching waveguide with a straight waveguide (projected on the X-Z plane).

Fig. 9
Fig. 9

Branching characteristics against normalized mixing length (2 × 2 mixing and branching waveguide with a straight waveguide): (a) calculation; (b) lmax, lmin, lo and ΔR are defined in this figure.

Fig. 10
Fig. 10

lmax, lmin, and lopt vs normalized branching angle.

Fig. 11
Fig. 11

Branching characteristics against input position (2 × 2 mixing and branching waveguide with a straight waveguide).

Fig. 12
Fig. 12

Structure of the 2 × 2 branching waveguide with a mode scrambler.

Fig. 13
Fig. 13

Branching characteristics against bend number (2 × 2 mixing and branching waveguide with a mode scrambler).

Fig. 14
Fig. 14

Cross section of the elliptical cone.

Equations (18)

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{ X = x / a , X ˙ = tan θ / tan θ c
X 2 + X ˙ 2 1 .
W ( X , X ˙ ) = 1 X 2 1 X 2 Y ˙ Y ˙ + F ( X , Y , X ˙ , Y ˙ ) d Y ˙ d Y ,
W ( X , X ˙ ) = π ( 1 X 2 X ˙ 2 ) 1 / 2 .
{ X o = S ( X l ) , X ˙ o = X ˙ i ( 1 ) [ | X l + 1 | / 2 ] , X l = X i + X ˙ i ( l / a ) tan θ c ,
{ X ( + ) = X ( 1 ) , X ˙ ( + ) = X ˙ ( ) + δ X ˙ , δ X ˙ = tan θ s / tan θ c ,
tan ( θ ± θ s ) tan θ ± tan θ s .
{ X o = S ( X l ) , X ˙ o = { X ˙ i + sgn ( X i ) · tan ( θ t · [ | X l + 1 | / 2 ] ) / tan θ c } · ( 1 ) [ | X l + 1 | / 2 ] , X ˙ l = X i + X ˙ i ( l / a ) tan θ c ,
R b = I l / I r ,
α = I r a d / I t = 10 log [ ( I r + I l ) / I t ] [ dB ] ,
n 2 ( r ) = n 2 ( 0 ) [ 1 ( g r ) 2 ] ,
{ x = x i cos ( g z ) + ( x ˙ i / g ) sin ( g z ) , x ˙ = g x i sin ( g z ) + x ˙ i cos ( g z ) ,
{ X = X i cos ( g z ) + X i sin ( g z ) , X = X i sin ( g z ) + X i cos ( g z ) ,
a g = sin θ max tan θ max .
{ X = X i 2 + X i 2 cos ( g z α ) , X = X i 2 + X i 2 sin ( g z α ) , α = cos 1 ( X i / X i 2 + X i 2 ) .
X 2 + X ˙ 2 = X i 2 + X ˙ i 2 1 .
( I Y 2 ) X ˙ 2 + ( 1 X 2 ) Y ˙ 2 + 2 X Y X ˙ Y ˙ + X 2 + Y 2 1 = 0 .
( 1 X 2 ) Y ˙ 2 + 2 X Y X ˙ Y ˙ + X 2 ( 1 Y 2 ) + X ˙ 2 + Y 2 1 = 0 .

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