Abstract

The theory is given for polarizing beam splitters made from polished-type directional couplers using anisotropic core material. A comparison is made between these beam splitters and those of the fused, biconical type.

© 1986 Optical Society of America

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References

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  1. M. S. Yataki, D. N. Payne, Electron. Lett. 21, 249 (1985).
    [CrossRef]
  2. T. Bricheno, V. Baker, Electron. Lett. 21, 251 (1985).
    [CrossRef]
  3. I. Yokohama, K. Okamoto, J. Noda, Electron. Lett. 21, 415 (1985).
    [CrossRef]
  4. A. W. Snyder, Electron. Lett. 21, 623 (1985); A. W. Snyder, X. Zheng, Electron. Lett.21, 1079 (1985).
    [CrossRef]
  5. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), Chaps. 18 and 19.
  6. A. W. Snyder, A. J. Stevenson, in Digest of Third International Conference on Optical Fiber Sensors (Optical Society of America, Washington, D.C., 1985), paper THCC2.
  7. A. W. Snyder, A. J. Stevenson, Electron. Lett. 21, 75 (1985).
    [CrossRef]
  8. A. W. Snyder, W. R. Young, J. Opt. Soc. Am. 68, 297 (1978).
    [CrossRef]
  9. A. W. Snyder, J. Opt. Soc. Am. 62, 1267 (1972).
    [CrossRef]
  10. A. Ankiewicz, A. W. Snyder, X.-H. Zheng, “Coupling between parallel cores: critical examination,” J. Opt. Soc. Am. A (to be published).

1985 (5)

M. S. Yataki, D. N. Payne, Electron. Lett. 21, 249 (1985).
[CrossRef]

T. Bricheno, V. Baker, Electron. Lett. 21, 251 (1985).
[CrossRef]

I. Yokohama, K. Okamoto, J. Noda, Electron. Lett. 21, 415 (1985).
[CrossRef]

A. W. Snyder, Electron. Lett. 21, 623 (1985); A. W. Snyder, X. Zheng, Electron. Lett.21, 1079 (1985).
[CrossRef]

A. W. Snyder, A. J. Stevenson, Electron. Lett. 21, 75 (1985).
[CrossRef]

1978 (1)

1972 (1)

Ankiewicz, A.

A. Ankiewicz, A. W. Snyder, X.-H. Zheng, “Coupling between parallel cores: critical examination,” J. Opt. Soc. Am. A (to be published).

Baker, V.

T. Bricheno, V. Baker, Electron. Lett. 21, 251 (1985).
[CrossRef]

Bricheno, T.

T. Bricheno, V. Baker, Electron. Lett. 21, 251 (1985).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), Chaps. 18 and 19.

Noda, J.

I. Yokohama, K. Okamoto, J. Noda, Electron. Lett. 21, 415 (1985).
[CrossRef]

Okamoto, K.

I. Yokohama, K. Okamoto, J. Noda, Electron. Lett. 21, 415 (1985).
[CrossRef]

Payne, D. N.

M. S. Yataki, D. N. Payne, Electron. Lett. 21, 249 (1985).
[CrossRef]

Snyder, A. W.

A. W. Snyder, Electron. Lett. 21, 623 (1985); A. W. Snyder, X. Zheng, Electron. Lett.21, 1079 (1985).
[CrossRef]

A. W. Snyder, A. J. Stevenson, Electron. Lett. 21, 75 (1985).
[CrossRef]

A. W. Snyder, W. R. Young, J. Opt. Soc. Am. 68, 297 (1978).
[CrossRef]

A. W. Snyder, J. Opt. Soc. Am. 62, 1267 (1972).
[CrossRef]

A. Ankiewicz, A. W. Snyder, X.-H. Zheng, “Coupling between parallel cores: critical examination,” J. Opt. Soc. Am. A (to be published).

A. W. Snyder, A. J. Stevenson, in Digest of Third International Conference on Optical Fiber Sensors (Optical Society of America, Washington, D.C., 1985), paper THCC2.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), Chaps. 18 and 19.

Stevenson, A. J.

A. W. Snyder, A. J. Stevenson, Electron. Lett. 21, 75 (1985).
[CrossRef]

A. W. Snyder, A. J. Stevenson, in Digest of Third International Conference on Optical Fiber Sensors (Optical Society of America, Washington, D.C., 1985), paper THCC2.

Yataki, M. S.

M. S. Yataki, D. N. Payne, Electron. Lett. 21, 249 (1985).
[CrossRef]

Yokohama, I.

I. Yokohama, K. Okamoto, J. Noda, Electron. Lett. 21, 415 (1985).
[CrossRef]

Young, W. R.

Zheng, X.-H.

A. Ankiewicz, A. W. Snyder, X.-H. Zheng, “Coupling between parallel cores: critical examination,” J. Opt. Soc. Am. A (to be published).

Electron. Lett. (5)

M. S. Yataki, D. N. Payne, Electron. Lett. 21, 249 (1985).
[CrossRef]

T. Bricheno, V. Baker, Electron. Lett. 21, 251 (1985).
[CrossRef]

I. Yokohama, K. Okamoto, J. Noda, Electron. Lett. 21, 415 (1985).
[CrossRef]

A. W. Snyder, Electron. Lett. 21, 623 (1985); A. W. Snyder, X. Zheng, Electron. Lett.21, 1079 (1985).
[CrossRef]

A. W. Snyder, A. J. Stevenson, Electron. Lett. 21, 75 (1985).
[CrossRef]

J. Opt. Soc. Am. (2)

Other (3)

A. Ankiewicz, A. W. Snyder, X.-H. Zheng, “Coupling between parallel cores: critical examination,” J. Opt. Soc. Am. A (to be published).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), Chaps. 18 and 19.

A. W. Snyder, A. J. Stevenson, in Digest of Third International Conference on Optical Fiber Sensors (Optical Society of America, Washington, D.C., 1985), paper THCC2.

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Figures (4)

Fig. 1
Fig. 1

(a), (b) Type I splitters. Typically, Vx can vary from 1.5 to 2.4; core separation d/ρ ranges between 2 and 10; Δx ~ 0.003; and Δy = Δxδ, where δx can take values between 0 and 0.3. (c), (d) Type II splitters. The anisotropic materials are represented by sets of lines parallel to the optical axis of larger refractive index, and isotropic regions are not shaded.

Fig. 2
Fig. 2

Typical parameters for Type I splitters. Given core separation d/ρ and anisotropy δ/Δ, Vx can be varied to determine (a), (b) N, the number of complete coupling cycles for x-polarized light, and (c), (d) L, the length of a polarization splitter, in millimeters, assuming that Δx = 0.003 and ρ = 2.5 μm. Note that only discrete values of Vx can be used to render N an integer or a half-integer, as explained below Eq. (5).

Fig. 3
Fig. 3

(a) Length (left vertical axis) and number of complete coupling cycles (right vertical axis) as a function of anisotropy (δ/Δ for a Type I splitter made from touching fibers with Vx = 2, Δx = 0.003, and ρ = 2.5 μm. (b) Comparison of Type I and Type II splitters, with N = ½, Vx = 2, δ/Δ varying from 0.002 to 0.4, ρ = 2.5 μm, and Δx = 0.003. The length L is given in millimeters on the left vertical axis, and the corresponding core separation d/ρ is given on the right vertical axis.

Fig. 4
Fig. 4

Spectral response of Type I splitters with touching cores, each of radius 2.5 μm. (a) The case δ/Δ = 0.3, N = 4, λ0 = 0.88 μm. (b) The case δ/Δ = 0.1, N = 40, λ0 = 0.79 μm. In both cases, Δx = 0.003, Δy = Δxδ, and the normalized power from the through port is examined for both x polarization (solid curves) and y polarization (dashed curves). Material dispersion is neglected.

Equations (5)

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P i ( λ ) = sin 2 [ L C i ( λ ) ] ,
2 C i = β + i - β - i ,
L = π / [ 2 C x ( λ 0 - C y ( λ 0 ) ] ,
N = C x ( λ 0 ) / [ 2 C x ( λ 0 ) - C y ( λ 0 ) ] .
δ = ( n x - n y ) / n x ,

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