Abstract

The author’s discovery of an unusual fiber element that is simply a variably spun birefringent fiber with a spin rate that varies from fast to zero or vice versa is revealed. The novel fiber element can be readily made by the existing fabrication technique, with fairly loose tolerances of the structural parameters. Analytic theory predicts that such a nonuniform fiber element can function as a bulk-optic quarter-wave plate, but with the advantage of being inherently wide band. Experimental evidence confirms the theoretical prediction. With such a fiber-optic analog of a quarter-wave plate as a building block, wide-band half-wave plates and full wave plates can likewise be made in the form of variably spun birefringent fibers.

© 1997 Optical Society of America

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References

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  1. H. C. LeFevre, “Fiber optic polarization controller,” U.S. patent4,389,090 (21June1983).
  2. T. Matsumoto, H. Kano, “Fiber optic polarization controller,” U.S. patent4,793,678 (27December1988).
  3. H. J. Shaw, R. C. Youngquist, J. L. Brooks, “Birefringent fiber narrow-band polarization coupler and method of coupling using same,” U.S. patent4,801,189 (31January1989).
  4. Hung-chia Huang, “Passive fiber-optic polarization control,” U.S. patent4,943,132 (24July1990).
  5. Hung-chia Huang, “Passive fiber-optic polarization control element,” U.S. patent5,096,312 (17March1992).
  6. Hung-chia Huang, “Practical circular-polarization maintaining optical fiber,” U.S. patent5,452,394 (19September1995).
  7. Hung-chia Huang, Microwave Approach to Highly Irregular Fiber Optics (Wiley, New York), to be published.
  8. P. McIntyre, A. W. Snyder, “Light propagation in twisted anisotropic media: application to photoreceptors,” J. Opt. Soc. Am. 68, 149–157 (1978).
    [Crossref] [PubMed]
  9. F. P. Kapron, N. F. Borrelli, D. B. Keck, “Birefringence in dielectric optical waveguides,” IEEE J. Quantum Electronics QE-8, 222–225 (1972).
    [Crossref]
  10. A. J. Barlow, J. J. Ramskov-Hansen, D. N. Payne, “Birefringence and polarization mode dispersion in spun single-mode fibers,” Appl. Opt. 20, 2962–2968 (1981).
    [Crossref] [PubMed]
  11. J. S. Cook, “Tapered velocity coupler,” Bell Syst. Tech. J. 34, 807–822 (1955).
    [Crossref]
  12. A. G. Fox, “Wave coupling by warped normal modes,” Bell Syst. Tech. J. 34, 823–852 (1955).
    [Crossref]
  13. W. H. Louisell, “Analysis of the single tapered mode coupler,” Bell Syst. Tech. J. 34, 853–870 (1955).
    [Crossref]
  14. Hung-chia Huang, “Generalized theory of coupled local normal modes in multi-wave guides,” Sci. Sin. 9, 142–154 (1960).
  15. Hung-chia Huang, “Method of slowly varying parameters,” Acta Math. Sin. 11, 238–247 (1961).
  16. H. B. Keller, J. B. Keller, “Exponential-like solutions of system of ordinary differential equations,” J. Soc. Ind. Appl. Math. 10, 246–259 (1962).
    [Crossref]

1981 (1)

1978 (1)

1972 (1)

F. P. Kapron, N. F. Borrelli, D. B. Keck, “Birefringence in dielectric optical waveguides,” IEEE J. Quantum Electronics QE-8, 222–225 (1972).
[Crossref]

1962 (1)

H. B. Keller, J. B. Keller, “Exponential-like solutions of system of ordinary differential equations,” J. Soc. Ind. Appl. Math. 10, 246–259 (1962).
[Crossref]

1961 (1)

Hung-chia Huang, “Method of slowly varying parameters,” Acta Math. Sin. 11, 238–247 (1961).

1960 (1)

Hung-chia Huang, “Generalized theory of coupled local normal modes in multi-wave guides,” Sci. Sin. 9, 142–154 (1960).

1955 (3)

J. S. Cook, “Tapered velocity coupler,” Bell Syst. Tech. J. 34, 807–822 (1955).
[Crossref]

A. G. Fox, “Wave coupling by warped normal modes,” Bell Syst. Tech. J. 34, 823–852 (1955).
[Crossref]

W. H. Louisell, “Analysis of the single tapered mode coupler,” Bell Syst. Tech. J. 34, 853–870 (1955).
[Crossref]

Barlow, A. J.

Borrelli, N. F.

F. P. Kapron, N. F. Borrelli, D. B. Keck, “Birefringence in dielectric optical waveguides,” IEEE J. Quantum Electronics QE-8, 222–225 (1972).
[Crossref]

Brooks, J. L.

H. J. Shaw, R. C. Youngquist, J. L. Brooks, “Birefringent fiber narrow-band polarization coupler and method of coupling using same,” U.S. patent4,801,189 (31January1989).

Cook, J. S.

J. S. Cook, “Tapered velocity coupler,” Bell Syst. Tech. J. 34, 807–822 (1955).
[Crossref]

Fox, A. G.

A. G. Fox, “Wave coupling by warped normal modes,” Bell Syst. Tech. J. 34, 823–852 (1955).
[Crossref]

Huang, Hung-chia

Hung-chia Huang, “Method of slowly varying parameters,” Acta Math. Sin. 11, 238–247 (1961).

Hung-chia Huang, “Generalized theory of coupled local normal modes in multi-wave guides,” Sci. Sin. 9, 142–154 (1960).

Hung-chia Huang, “Passive fiber-optic polarization control,” U.S. patent4,943,132 (24July1990).

Hung-chia Huang, “Passive fiber-optic polarization control element,” U.S. patent5,096,312 (17March1992).

Hung-chia Huang, “Practical circular-polarization maintaining optical fiber,” U.S. patent5,452,394 (19September1995).

Hung-chia Huang, Microwave Approach to Highly Irregular Fiber Optics (Wiley, New York), to be published.

Kano, H.

T. Matsumoto, H. Kano, “Fiber optic polarization controller,” U.S. patent4,793,678 (27December1988).

Kapron, F. P.

F. P. Kapron, N. F. Borrelli, D. B. Keck, “Birefringence in dielectric optical waveguides,” IEEE J. Quantum Electronics QE-8, 222–225 (1972).
[Crossref]

Keck, D. B.

F. P. Kapron, N. F. Borrelli, D. B. Keck, “Birefringence in dielectric optical waveguides,” IEEE J. Quantum Electronics QE-8, 222–225 (1972).
[Crossref]

Keller, H. B.

H. B. Keller, J. B. Keller, “Exponential-like solutions of system of ordinary differential equations,” J. Soc. Ind. Appl. Math. 10, 246–259 (1962).
[Crossref]

Keller, J. B.

H. B. Keller, J. B. Keller, “Exponential-like solutions of system of ordinary differential equations,” J. Soc. Ind. Appl. Math. 10, 246–259 (1962).
[Crossref]

LeFevre, H. C.

H. C. LeFevre, “Fiber optic polarization controller,” U.S. patent4,389,090 (21June1983).

Louisell, W. H.

W. H. Louisell, “Analysis of the single tapered mode coupler,” Bell Syst. Tech. J. 34, 853–870 (1955).
[Crossref]

Matsumoto, T.

T. Matsumoto, H. Kano, “Fiber optic polarization controller,” U.S. patent4,793,678 (27December1988).

McIntyre, P.

Payne, D. N.

Ramskov-Hansen, J. J.

Shaw, H. J.

H. J. Shaw, R. C. Youngquist, J. L. Brooks, “Birefringent fiber narrow-band polarization coupler and method of coupling using same,” U.S. patent4,801,189 (31January1989).

Snyder, A. W.

Youngquist, R. C.

H. J. Shaw, R. C. Youngquist, J. L. Brooks, “Birefringent fiber narrow-band polarization coupler and method of coupling using same,” U.S. patent4,801,189 (31January1989).

Acta Math. Sin. (1)

Hung-chia Huang, “Method of slowly varying parameters,” Acta Math. Sin. 11, 238–247 (1961).

Appl. Opt. (1)

Bell Syst. Tech. J. (3)

J. S. Cook, “Tapered velocity coupler,” Bell Syst. Tech. J. 34, 807–822 (1955).
[Crossref]

A. G. Fox, “Wave coupling by warped normal modes,” Bell Syst. Tech. J. 34, 823–852 (1955).
[Crossref]

W. H. Louisell, “Analysis of the single tapered mode coupler,” Bell Syst. Tech. J. 34, 853–870 (1955).
[Crossref]

IEEE J. Quantum Electronics (1)

F. P. Kapron, N. F. Borrelli, D. B. Keck, “Birefringence in dielectric optical waveguides,” IEEE J. Quantum Electronics QE-8, 222–225 (1972).
[Crossref]

J. Opt. Soc. Am. (1)

J. Soc. Ind. Appl. Math. (1)

H. B. Keller, J. B. Keller, “Exponential-like solutions of system of ordinary differential equations,” J. Soc. Ind. Appl. Math. 10, 246–259 (1962).
[Crossref]

Sci. Sin. (1)

Hung-chia Huang, “Generalized theory of coupled local normal modes in multi-wave guides,” Sci. Sin. 9, 142–154 (1960).

Other (7)

H. C. LeFevre, “Fiber optic polarization controller,” U.S. patent4,389,090 (21June1983).

T. Matsumoto, H. Kano, “Fiber optic polarization controller,” U.S. patent4,793,678 (27December1988).

H. J. Shaw, R. C. Youngquist, J. L. Brooks, “Birefringent fiber narrow-band polarization coupler and method of coupling using same,” U.S. patent4,801,189 (31January1989).

Hung-chia Huang, “Passive fiber-optic polarization control,” U.S. patent4,943,132 (24July1990).

Hung-chia Huang, “Passive fiber-optic polarization control element,” U.S. patent5,096,312 (17March1992).

Hung-chia Huang, “Practical circular-polarization maintaining optical fiber,” U.S. patent5,452,394 (19September1995).

Hung-chia Huang, Microwave Approach to Highly Irregular Fiber Optics (Wiley, New York), to be published.

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Figures (13)

Fig. 1
Fig. 1

Fiber-optic analog of a bulk-optic quarter-wave plate: top, the structure where C is the core and S is the stress element; bottom, spin-rate variation (Q, normalized spin rate).

Fig. 2
Fig. 2

Circular to principal-axis-aligned linear SOP transform in a PPT by the single supermode.

Fig. 3
Fig. 3

Evolution of power in a circular–linear SOP transform by the single supermode.

Fig. 4
Fig. 4

Evolution of powers in a linear–circular SOP transform by the single supermode.

Fig. 5
Fig. 5

Linear light of different orientations incident on the fast-spun end of a PPT and the consequent SOP transforms by the dual supermode process.

Fig. 6
Fig. 6

Evolution of power in the PPT by the dual supermode process.

Fig. 7
Fig. 7

Spin function for fiber-optic analog of a bulk-optic half-wave plate.

Fig. 8
Fig. 8

Spin function for fiber-optic analog of a bulk-optic full wave plate.

Fig. 9
Fig. 9

Microscopic photos of a prototype PPT fiber: top, fast-spun end; bottom, zero-spun end.

Fig. 10
Fig. 10

Experimental curve showing the circular-to-linear SOP transform with a PPT.

Fig. 11
Fig. 11

Experimental data of a linear–circular transform of the PPT (fast-spun input): C R , right circular output that is due to linear input oriented at ρ; C L left circular output that is due to linear input oriented at ρ + π/2.

Fig. 12
Fig. 12

Experimental data that verifies equal power division property of the PPT for random incident orientation.

Fig. 13
Fig. 13

Experimental confirmation of wide-band characteristics of the PPT (basic properties at 0.83 µm are the same as at 0.6328 µm): upper curve, nearly circular input light (light power I max = 2.16 mW, I min = 1.92 mW); lower curve, basically linear output light (I max ≈ 224 µW, I min ≈ 12 µW). The ordinate scale was not calibrated.

Equations (63)

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dA/dz=KA,
A=OW,
dW/dz=ΛW, Λ=O-1KO=jg00-jg,
Wz=expjgz00exp-jgzW0,
Az=TzA0,  Tz=Oexpjgz00exp-jgzO-1,
K=jΔβ/2ξ-ξ-jΔβ/2,
O=cos ϕj sin ϕj sin ϕcos ϕ,  ϕ=1/2arctan2Q,  Q=ξ/Δβ=Lb/LS,
g=π1+4Q21/2.
Rz=cosξz-sinξzsinξzcosξz.
dA/dz=KzA,  Kz=jΔβ/2ξz-ξz-jΔβ/2,
A=OzW,  Oz=cos ϕj sin ϕj sin ϕcos ϕ,
ϕϕz=1/2arctan2Qz,  Qz=ξz/Δβ=Lb/LSz,
dW/dz=NzW,
Nz=O-1KO-O-1dO/dz,
N=jg-jdϕ/dz-jdϕ/dz-jg,
ggz=π1+4Q21/2,  QQz,
dϕ/dz=1+4Q2-1dQ/dz=1/2π1+4Q2-1dξ/dz.
WxzWx0expj 0z gdz, WyzWy0exp-j0z gdz.
WxzexpjρWx0-Wx00zdϕdz×exp-2jρ0zdϕdz exp2jρdzdz-jWy00zdϕdz exp-2jρdz,  Wyzexp-jρWy0-Wy00zdϕdz×exp2jρ0zdϕdz exp-2jρdzdz-jWx00zdϕdz exp2jρdz,
ρρz=0z gdz=0z π1+4Q21/2dz.
Axz=cos ϕ Wxz+j sin ϕ Wyz, Ayz=j sin ϕWxz+cos ϕ Wyz.
Wxz2+Wyz2=1,  Axz2+Ayz2=1.
Qz=Q00.5+0.5 cosπz/Lγ,
QF=Lb/LFS1.
OF  121jj1,
OF-1  121-j-j1.
O0=O0-1=1001,
2g-1|dϕ/dz|=1/4π21+4Q2-3/2dξ/dz1.
WLΛ˜W0,
Λ˜  expjρ00exp-jρ,
ρρL=0L gdz=0L π1+4Lb/LS21/2dz,
AL=OLΛ˜O-10A0,
W0=Wx0Wy0=10.
A0=O0W0=121j,
WL=expjρ00exp-jρW0,  AL=OLWL=10expjρ,
ρρL=0L π1+4Lb/LS21/2dz
A0=121-j,  W0=O-10A0=01,  WL=expjρ00exp-jρW0,  AL=OLWL=01exp-jρ+π/2,
A0=10,  W0=O-10A0=A0,  WL=expjρ00exp-jρW0,  AL=OLWL=121jexpjρ,
A0=01=W0,  Wz=exp-jρW0,  AL=121-jexp-jρ-π/2,
Qz=QL0.5-0.5 cosπz/Lγ,
A0=cos θsin θ,
W0=O-10A0=12exp-jθ-j expjθ,
Wz=expjρ00exp-jρW0,  AL=OLWL=12expjρ-θ-j exp-jρ-θ,
AxL2=AyL2=0.5,
Ψ=90°+2ρ-2θ.
AL=JA0,  A0=cosθsinθ,
J=expjπ/4100j,
Aπ/4L=11-11AL.
Aπ/4L=expjπ/42expjθ-exp-jθ,
AxL2=AyL2=0.5,
Ψ=2θ±π,
Of=121-j-j1,
Of-1=121jj1,
A0=121±j,
AL=±121±jexp±jρ1+ρ2,
A0=cosθ0sinθ0,
AL=cosθLsinθL,
θL=ρ1+ρ2+π/2-θ0.
ΔθL=-Δθ0.
A0=121±j,
AL=121±jexp±jρ1+ρ2,
θL=θ0-ρ1+ρ2,
ΔθL=Δθ0.

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