Abstract

We present a detailed analysis of key attributes and performance characteristics of controllably-spun birefringent-fiber-based all-fiber waveplates or “all fiber polarization transformers” (AFPTs), first proposed and demonstrated by Huang [11]; these AFPTs consist essentially of a long carefully-designed “spin-twisted” high-birefringence fiber, fabricated by slowly varying the spin rate of a birefringent fiber preform (either from very fast to very slow or vice versa) while the fiber is being drawn. The evolution of the eigenstate from a linear polarization state to a circular polarization state, induced by slow variation of the intrinsic structure from linear anisotropy at the unspun end to circular anisotropy at the fast-spun end, enables the AFPT to behave like an all-fiber quarter-wave plate independent of the wavelength of operation. Power coupling between local eigenstates causes unique evolution of the polarization state along the fiber, and has been studied to gain insight into – as well as to understand detailed characteristics of -- the polarization transformation behavior. This has been graphically illustrated via plots of the relative power in these local eigenstates as a function of distance along the length of the fiber and plots of the extinction ratio of the output state of polarization (SOP) as a function of distance and the normalized spin rate. Deeper understanding of such polarization transformers has been further elucidated by quantitative calculations related to two crucial requirements for fabricating practical AFPT devices. Our calculations have also indicated that the polarization mode dispersion behaviour of the AFPT is much smaller than that of the original birefringent fiber. Finally, a specific AFPT was experimentally investigated at two widely-separated wavelengths (1310 nm and 1550 nm) of interest in telecommunications systems applications, further demonstrating and elucidating the broadband character of such AFPTs.

© 2006 Optical Society of America

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  1. I. P. Kaminow, "Polarization in optical fibers," IEEE J. Quantum Electron. QE-17, 15-22 (1981).
    [CrossRef]
  2. R. Ulrich, and A. Simon, "Polarization optics of twisted single-mode fibers," Appl. Opt. 18, 2241-2251 (1979).
    [CrossRef] [PubMed]
  3. D. N. Payne, A. J. Barlow, and J. J. Ramskov-Hansen, "Development of low- and high-birefringence optical fibers," J. Quantum Electron. QE-18, 477-488 (1982).
    [CrossRef]
  4. R. H. Stolen, V. Ramaswamy, P. Kaiser, and W. Pleibel, "Linear polarization in birefringenct single-mode fibers," Appl. Phys. Lett. 33, 699-701 (1978).
    [CrossRef]
  5. A. J. Barlow, D. N. Payne, M. R. Hadley, and R. J. Mansfield, "Production of single-mode fibers with negligible intrinsic birefringence and polarization mode dispersion," Electron. Lett. 17, 725-726 (1981).
    [CrossRef]
  6. M. J. Li and D. A. Nolan, "Fiber spin-profile designs for producing fibers with low polarization mode dispersion," Opt. Lett. 23, 1659-1661 (1998).
    [CrossRef]
  7. A. J. Barlow, J. J. Ramskov-Hansen, and D. N. Payne, "Birefringence and polarization mode-dispersion in spun single-mode fibers," Appl. Opt. 20, 2962-2968 (1981).
    [CrossRef] [PubMed]
  8. A. J. Barlow, J. J. Ramskov-Hansen, and D. N. Payne, "Anisotropy in spun single-mode fibers," Electron. Lett. 18, 200-202 (1982).
    [CrossRef]
  9. R. E. Schuh, XK. Shan and A. S. Siddiqui, "Polarization mode dispersion in spun fibers with different linear birefringence and spinning parameters," J. Lightwave Technol. 16, 1583-1588 (1998).
    [CrossRef]
  10. M. Fuochi, J. R. Hayes, K. Furusawa, W. Belardi, J. C. Baggett, T. M. Monro, and D. J. Richardson, "Polarization mode dispersion reduction in spun large mode area silica holey fibers," Opt. Express 12, 1972-1977 (2004).
    [CrossRef] [PubMed]
  11. H. Huang, "Fiber-optic analogs of bulk-optic wave plates," Appl. Opt. 36, 4241-4258 (1997).
    [CrossRef] [PubMed]
  12. H. Huang, Microwave approach to highly irregular fiber optics, (Wiley, New York, 1998).
  13. X. S. Zhu, "All-fiber broadband polarization transformer", Master’s Thesis, Univ. of New Mexico (2004).
  14. H. Sanghvi, "All-fiber broadband waveplates", Master’s Thesis, Virginia Institute of Technology (2004).
  15. A. H. Rose, N. Feat, and S. M. Etzel, "Wavelength and temperature performance of polarization-transforming fibers," Appl. Opt. 42, 6897-6904 (2003).
    [CrossRef] [PubMed]
  16. P. McIntyre and A. W. Snyder, "Light propagating in twisted anisotropic media: Application to photoreceptors," J. Opt. Soc. Am. 68, 149-156 (1978).
    [CrossRef] [PubMed]
  17. M. Monerie and L. Jeunhomme, "Polarization mode coupling in long single-mode fibers," Opt. And Quantum Electron. 12, 449-461 (1980).
    [CrossRef]

2004 (1)

2003 (1)

1998 (2)

1997 (1)

1982 (2)

A. J. Barlow, J. J. Ramskov-Hansen, and D. N. Payne, "Anisotropy in spun single-mode fibers," Electron. Lett. 18, 200-202 (1982).
[CrossRef]

D. N. Payne, A. J. Barlow, and J. J. Ramskov-Hansen, "Development of low- and high-birefringence optical fibers," J. Quantum Electron. QE-18, 477-488 (1982).
[CrossRef]

1981 (3)

A. J. Barlow, D. N. Payne, M. R. Hadley, and R. J. Mansfield, "Production of single-mode fibers with negligible intrinsic birefringence and polarization mode dispersion," Electron. Lett. 17, 725-726 (1981).
[CrossRef]

I. P. Kaminow, "Polarization in optical fibers," IEEE J. Quantum Electron. QE-17, 15-22 (1981).
[CrossRef]

A. J. Barlow, J. J. Ramskov-Hansen, and D. N. Payne, "Birefringence and polarization mode-dispersion in spun single-mode fibers," Appl. Opt. 20, 2962-2968 (1981).
[CrossRef] [PubMed]

1980 (1)

M. Monerie and L. Jeunhomme, "Polarization mode coupling in long single-mode fibers," Opt. And Quantum Electron. 12, 449-461 (1980).
[CrossRef]

1979 (1)

1978 (2)

P. McIntyre and A. W. Snyder, "Light propagating in twisted anisotropic media: Application to photoreceptors," J. Opt. Soc. Am. 68, 149-156 (1978).
[CrossRef] [PubMed]

R. H. Stolen, V. Ramaswamy, P. Kaiser, and W. Pleibel, "Linear polarization in birefringenct single-mode fibers," Appl. Phys. Lett. 33, 699-701 (1978).
[CrossRef]

Baggett, J. C.

Barlow, A. J.

D. N. Payne, A. J. Barlow, and J. J. Ramskov-Hansen, "Development of low- and high-birefringence optical fibers," J. Quantum Electron. QE-18, 477-488 (1982).
[CrossRef]

A. J. Barlow, J. J. Ramskov-Hansen, and D. N. Payne, "Anisotropy in spun single-mode fibers," Electron. Lett. 18, 200-202 (1982).
[CrossRef]

A. J. Barlow, D. N. Payne, M. R. Hadley, and R. J. Mansfield, "Production of single-mode fibers with negligible intrinsic birefringence and polarization mode dispersion," Electron. Lett. 17, 725-726 (1981).
[CrossRef]

A. J. Barlow, J. J. Ramskov-Hansen, and D. N. Payne, "Birefringence and polarization mode-dispersion in spun single-mode fibers," Appl. Opt. 20, 2962-2968 (1981).
[CrossRef] [PubMed]

Belardi, W.

Etzel, S. M.

Feat, N.

Fuochi, M.

Furusawa, K.

Hadley, M. R.

A. J. Barlow, D. N. Payne, M. R. Hadley, and R. J. Mansfield, "Production of single-mode fibers with negligible intrinsic birefringence and polarization mode dispersion," Electron. Lett. 17, 725-726 (1981).
[CrossRef]

Hayes, J. R.

Huang, H.

Jeunhomme, L.

M. Monerie and L. Jeunhomme, "Polarization mode coupling in long single-mode fibers," Opt. And Quantum Electron. 12, 449-461 (1980).
[CrossRef]

Kaiser, P.

R. H. Stolen, V. Ramaswamy, P. Kaiser, and W. Pleibel, "Linear polarization in birefringenct single-mode fibers," Appl. Phys. Lett. 33, 699-701 (1978).
[CrossRef]

Kaminow, I. P.

I. P. Kaminow, "Polarization in optical fibers," IEEE J. Quantum Electron. QE-17, 15-22 (1981).
[CrossRef]

Li, M. J.

Mansfield, R. J.

A. J. Barlow, D. N. Payne, M. R. Hadley, and R. J. Mansfield, "Production of single-mode fibers with negligible intrinsic birefringence and polarization mode dispersion," Electron. Lett. 17, 725-726 (1981).
[CrossRef]

McIntyre, P.

Monerie, M.

M. Monerie and L. Jeunhomme, "Polarization mode coupling in long single-mode fibers," Opt. And Quantum Electron. 12, 449-461 (1980).
[CrossRef]

Monro, T. M.

Nolan, D. A.

Payne, D. N.

A. J. Barlow, J. J. Ramskov-Hansen, and D. N. Payne, "Anisotropy in spun single-mode fibers," Electron. Lett. 18, 200-202 (1982).
[CrossRef]

D. N. Payne, A. J. Barlow, and J. J. Ramskov-Hansen, "Development of low- and high-birefringence optical fibers," J. Quantum Electron. QE-18, 477-488 (1982).
[CrossRef]

A. J. Barlow, D. N. Payne, M. R. Hadley, and R. J. Mansfield, "Production of single-mode fibers with negligible intrinsic birefringence and polarization mode dispersion," Electron. Lett. 17, 725-726 (1981).
[CrossRef]

A. J. Barlow, J. J. Ramskov-Hansen, and D. N. Payne, "Birefringence and polarization mode-dispersion in spun single-mode fibers," Appl. Opt. 20, 2962-2968 (1981).
[CrossRef] [PubMed]

Pleibel, W.

R. H. Stolen, V. Ramaswamy, P. Kaiser, and W. Pleibel, "Linear polarization in birefringenct single-mode fibers," Appl. Phys. Lett. 33, 699-701 (1978).
[CrossRef]

Ramaswamy, V.

R. H. Stolen, V. Ramaswamy, P. Kaiser, and W. Pleibel, "Linear polarization in birefringenct single-mode fibers," Appl. Phys. Lett. 33, 699-701 (1978).
[CrossRef]

Ramskov-Hansen, J. J.

A. J. Barlow, J. J. Ramskov-Hansen, and D. N. Payne, "Anisotropy in spun single-mode fibers," Electron. Lett. 18, 200-202 (1982).
[CrossRef]

D. N. Payne, A. J. Barlow, and J. J. Ramskov-Hansen, "Development of low- and high-birefringence optical fibers," J. Quantum Electron. QE-18, 477-488 (1982).
[CrossRef]

A. J. Barlow, J. J. Ramskov-Hansen, and D. N. Payne, "Birefringence and polarization mode-dispersion in spun single-mode fibers," Appl. Opt. 20, 2962-2968 (1981).
[CrossRef] [PubMed]

Richardson, D. J.

Rose, A. H.

Schuh, R. E.

Shan, XK.

Siddiqui, A. S.

Simon, A.

Snyder, A. W.

Stolen, R. H.

R. H. Stolen, V. Ramaswamy, P. Kaiser, and W. Pleibel, "Linear polarization in birefringenct single-mode fibers," Appl. Phys. Lett. 33, 699-701 (1978).
[CrossRef]

Ulrich, R.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

R. H. Stolen, V. Ramaswamy, P. Kaiser, and W. Pleibel, "Linear polarization in birefringenct single-mode fibers," Appl. Phys. Lett. 33, 699-701 (1978).
[CrossRef]

Electron. Lett. (2)

A. J. Barlow, D. N. Payne, M. R. Hadley, and R. J. Mansfield, "Production of single-mode fibers with negligible intrinsic birefringence and polarization mode dispersion," Electron. Lett. 17, 725-726 (1981).
[CrossRef]

A. J. Barlow, J. J. Ramskov-Hansen, and D. N. Payne, "Anisotropy in spun single-mode fibers," Electron. Lett. 18, 200-202 (1982).
[CrossRef]

IEEE J. Quantum Electron. (1)

I. P. Kaminow, "Polarization in optical fibers," IEEE J. Quantum Electron. QE-17, 15-22 (1981).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

J. Quantum Electron. (1)

D. N. Payne, A. J. Barlow, and J. J. Ramskov-Hansen, "Development of low- and high-birefringence optical fibers," J. Quantum Electron. QE-18, 477-488 (1982).
[CrossRef]

Opt. And Quantum Electron. (1)

M. Monerie and L. Jeunhomme, "Polarization mode coupling in long single-mode fibers," Opt. And Quantum Electron. 12, 449-461 (1980).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (3)

H. Huang, Microwave approach to highly irregular fiber optics, (Wiley, New York, 1998).

X. S. Zhu, "All-fiber broadband polarization transformer", Master’s Thesis, Univ. of New Mexico (2004).

H. Sanghvi, "All-fiber broadband waveplates", Master’s Thesis, Virginia Institute of Technology (2004).

Supplementary Material (2)

» Media 1: AVI (521 KB)     
» Media 2: AVI (551 KB)     

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Figures (17)

Fig. 1.
Fig. 1.

“Basics” of our AFPT

Fig. 2.
Fig. 2.

Coordinate systems for the AFPT

Fig. 3.
Fig. 3.

Evolution of pol. eigenstates in an AFPT.

Fig. 4.
Fig. 4.

Effective linear birefringence as a fn. of position in a 20 cm long AFPT with Δβ = 103 rad/m, ξmax = 100Δβ and 1000Δβ respectively.

Fig. 5.
Fig. 5.

Evolution of relative power in two local modes, Px (solid line) and Py (dash-dot line) as a function of the normalized distance, zR (= z/zL), for different values of the normalized final spin rate Qmax [1000 (red), 100 (green), 10 (blue)], assuming single-eigenstate excitation processes. (a) Linearly polarized (along the x axis) light is launched at the unspun end, U (light shading); (b) Circularly polarized light is launched at the fast-spun end, F (dark shading; note that the grayscale in the inset pictorially denotes the spin rate in the AFPT).

Fig. 6.
Fig. 6.

The extinction ratio of the output SOP as a function of the maximum normalized spin rate Qmax when the AFPT operates in the single-eigenstate excitation process. (a) Light linearly polarized along the x-axis is launched at the unspun end; (b) Circularly polarized light is launched at the fast-spun end (the inset shows details for smaller values of Qmax , i.e., it “magnifies” the 0 to 10 range of the horizontal scale).

Fig. 7.
Fig. 7.

Evolution of (a) Px, Py, and (b) ΔΦ (the phase difference between the two local modes) as a function of distance in a 0.2 m long AFPT with Δβ = 103 rad/m when linearly-polarized light (along the x-axis) is launched into the unspun end (U), for maximum spin rates ξmax of 105 (red curves), 5×104 (green curves), and 104 rad/m(blue curves).

Fig. 8.
Fig. 8.

Evolution of (a) Px, Py, and (b) ΔΦ (phase difference between the two local modes) as a function of distance in a 0.02 m long AFPT with Δβ = 103 rad/m when linearly-polarized light (along the x-axis) is launched into the unspun end (U), for maximum spin rates ξmax of 105 (red curves), 5×104 (green curves), and 104 rad/m(blue curves).

Fig. 9.
Fig. 9.

Evolution of (a) Px, Py, and (b) ΔΦ (the phase difference between the two local modes) as a function of distance in a 0.2 m long AFPT with Δβ = 103 rad/m when circularly polarized is launched at the fast-spun end (F) for maximum spin rates ξmax of 105 (red curves), 5×104 (green curves), and 104 rad/m(blue curves).

Fig. 10.
Fig. 10.

Evolution of (a) Px, Py, and (b) ΔΦ (the phase difference between the two local modes) as a function of distance in a 0.02 m long AFPT with Δβ = 103 rad/m when circularly polarized is launched at the fast-spun end (F) for maximum spin rates ξmax of 105 (red curves), 5× 104 (green curves), and 104 rad/m(blue curves).

Fig. 11.
Fig. 11.

Dual-eigenstate excitation process in an AFPT for the case when light polarized linearly at 45° wrt the birefringence axes is launched at the unspun end. The output polarizations observed correspond to maximum normalized spin rates of 1000 (red), 100 (green) and 10 (blue) respectively.

Fig. 12.
Fig. 12.

Dual-eigenstate excitation process in an AFPT when right circularly-polarized light is launched at the unspun end. The output polarizations observed correspond to maximum normalized spin rates of 1000 (red), 100 (green) and 10 (blue) respectively. [Media 2]

Fig. 13.
Fig. 13.

Generation of circularly polarized light at the unspun end of an AFPT by using a dual-eigenstate excitation process and linearly polarized light at the fast-spun end. The different input polarizations maximum correspond to normalized spin rates of 1000 (red), 100 (green) and 10 (blue), respectively. [Media 1]

Fig. 14.
Fig. 14.

Dual-eigenstate process of the AFPT when linearly polarized light with azimuth of ρ + 45° is launched at the fast-spun end. The maximum normalized spin rates are 1000 (red), 100 (green) and 10 (blue), respectively.

Fig. 15.
Fig. 15.

Schematic experimental setup used to characterize our AFPT.

Fig. 16.
Fig. 16.

Ellipticity of the output SOP at the fast-spun end as a function of the azimuthal angle of the input linear polarization state launched at the unspun end.

Fig. 17.
Fig. 17.

Ellipticity of the output SOP at the unspun end as a function of the orientation of the input linear polarization state launched at the fast-spun end.

Equations (18)

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E x ( z + Δz ) = [ E x ( z ) cos ΔΩ + E y ( z ) sin ΔΩ ] exp ( i β x Δ z )
E y ( z + Δ z ) = [ E x ( z ) cos ΔΩ + E y ( z ) sin ΔΩ ] exp ( i β y Δ z )
d E x dz = i β x E x d Ω dz E y
d E y dz = i β y E y d Ω dz E x
d E x dz = i β x E x + ξ ( z ) E y
d E y dz = i β y E y ξ ( z ) E x
β ± ( z ) = β x + β y 2 ± ξ 2 ( z ) + Δ β 2 4
E ± ( z ) = [ 1 1 + ( Δ β 2 ξ ( z ) ± ( Δ β 2 ξ ( z ) ) 2 ) 2 i Δ β 2 ξ ( z ) ± 1 + ( Δ β 2 ξ ( z ) ) 2 1 + ( Δ β 2 ξ ( z ) ± 1 + ( Δ β 2 ξ ( z ) ) 2 ) 2 ]
Δ β E ( z ) = R ( Δ z ) Δ z = 2 sin 1 ( 1 1 + 4 ξ 2 ( z ) Δ β 2 sin ( Δ β 2 4 ξ 2 ( z ) 2 Δ z ) ) Δ z ,
d E x dz = i Δ β 2 E x + ξ ( z ) E y
d E y dz = i Δ β 2 E y ξ ( z ) E x
E x ( z ) = cos [ tan 1 ( 2 Q ( z ) ) / 2 ] W x ( z ) + i sin [ tan 1 ( 2 Q ( z ) ) / 2 ] W y ( z )
E y ( z ) = i sin [ tan 1 ( 2 Q ( z ) ) / 2 ] W x ( z ) + cos [ tan 1 ( 2 Q ( z ) ) / 2 ] W y ( z ) ,
W x ( z ) W x ( 0 ) exp ( i 0 z π 1 + 4 Q 2 ( z ) )
W y ( z ) W y ( 0 ) exp ( i 0 z π 1 + 4 Q 2 ( z ) )
θ = ρ = 0 z π 1 + 4 Q 2 ( z ) ,
Δ τ = L c d ( Δ β ) dk = L c d dk [ k ( B G + B S ) ] L c B S ,
Δ τ = 0 L B s c 1 1 + 4 Q 2 ( z ) dz ,

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