Abstract

Eigenstates of a given elliptical birefringent are determined at 1.530 and 1.580 μm by generating sequences of polarization states that converge to the eigenstates. The principal states of polarization of the device for the two considered wavelengths are shown to be eigenstates of the succession of two birefringents at 1.530 and 1.580 μm; they are produced by applying the previous iterative process. Experimental results are compared to theoretical estimates.

© 2012 Optical Society of America

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References

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  1. C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization mode dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
    [CrossRef]
  2. C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
    [CrossRef]
  3. J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
    [CrossRef]
  4. J. N. Damask, Polarization Optics in Telecommunications (Springer, 2005).
  5. N. Friedman, A. Eyal, and M. Tur, “The use of the principal sates of polarization to describe tunability in a fiber laser,” IEEE J. Quantum Electron. 33, 642–648 (1997).
    [CrossRef]
  6. T. Merker, A. Schwarzbeck, and P. Meissner, “PMD compensation up to second order by tracking the principal states of polarization using a two-section compensator,” Opt. Commun. 198, 41–47 (2001).
    [CrossRef]
  7. G. N. Ramachandran and S. Rameseshan, Crystal Optics, Vol. 25/1 of Handbuch der Physik, S. Flügge ed. (Springer, 1961).
  8. P. Pellat-Finet, “Geometrical approach to polarization optics. I—Geometrical structure of polarized light,” Optik 87, 27–33 (1991).
  9. P. Pellat-Finet, “Geometrical approach to polarization optics. II—Quaternionic representation of polarized light,” Optik 87, 68–76 (1991).
  10. P. Pellat-Finet and M. Bausset, “What is common to both polarization optics and relativistic kinematics?,” Optik 90, 101–106 (1992).
  11. P. Pellat-Finet, “An introduction to a vectorial calculus for polarization optics,” Optik 84, 169–175 (1990).

2001 (1)

T. Merker, A. Schwarzbeck, and P. Meissner, “PMD compensation up to second order by tracking the principal states of polarization using a two-section compensator,” Opt. Commun. 198, 41–47 (2001).
[CrossRef]

2000 (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
[CrossRef]

1997 (1)

N. Friedman, A. Eyal, and M. Tur, “The use of the principal sates of polarization to describe tunability in a fiber laser,” IEEE J. Quantum Electron. 33, 642–648 (1997).
[CrossRef]

1992 (1)

P. Pellat-Finet and M. Bausset, “What is common to both polarization optics and relativistic kinematics?,” Optik 90, 101–106 (1992).

1991 (2)

P. Pellat-Finet, “Geometrical approach to polarization optics. I—Geometrical structure of polarized light,” Optik 87, 27–33 (1991).

P. Pellat-Finet, “Geometrical approach to polarization optics. II—Quaternionic representation of polarized light,” Optik 87, 68–76 (1991).

1990 (1)

P. Pellat-Finet, “An introduction to a vectorial calculus for polarization optics,” Optik 84, 169–175 (1990).

1988 (1)

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

1986 (1)

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization mode dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
[CrossRef]

Bausset, M.

P. Pellat-Finet and M. Bausset, “What is common to both polarization optics and relativistic kinematics?,” Optik 90, 101–106 (1992).

Bergano, N. S.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Damask, J. N.

J. N. Damask, Polarization Optics in Telecommunications (Springer, 2005).

Eyal, A.

N. Friedman, A. Eyal, and M. Tur, “The use of the principal sates of polarization to describe tunability in a fiber laser,” IEEE J. Quantum Electron. 33, 642–648 (1997).
[CrossRef]

Friedman, N.

N. Friedman, A. Eyal, and M. Tur, “The use of the principal sates of polarization to describe tunability in a fiber laser,” IEEE J. Quantum Electron. 33, 642–648 (1997).
[CrossRef]

Gordon, J. P.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
[CrossRef]

Kogelnik, H.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
[CrossRef]

Meissner, P.

T. Merker, A. Schwarzbeck, and P. Meissner, “PMD compensation up to second order by tracking the principal states of polarization using a two-section compensator,” Opt. Commun. 198, 41–47 (2001).
[CrossRef]

Merker, T.

T. Merker, A. Schwarzbeck, and P. Meissner, “PMD compensation up to second order by tracking the principal states of polarization using a two-section compensator,” Opt. Commun. 198, 41–47 (2001).
[CrossRef]

Pellat-Finet, P.

P. Pellat-Finet and M. Bausset, “What is common to both polarization optics and relativistic kinematics?,” Optik 90, 101–106 (1992).

P. Pellat-Finet, “Geometrical approach to polarization optics. I—Geometrical structure of polarized light,” Optik 87, 27–33 (1991).

P. Pellat-Finet, “Geometrical approach to polarization optics. II—Quaternionic representation of polarized light,” Optik 87, 68–76 (1991).

P. Pellat-Finet, “An introduction to a vectorial calculus for polarization optics,” Optik 84, 169–175 (1990).

Poole, C. D.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization mode dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
[CrossRef]

Ramachandran, G. N.

G. N. Ramachandran and S. Rameseshan, Crystal Optics, Vol. 25/1 of Handbuch der Physik, S. Flügge ed. (Springer, 1961).

Rameseshan, S.

G. N. Ramachandran and S. Rameseshan, Crystal Optics, Vol. 25/1 of Handbuch der Physik, S. Flügge ed. (Springer, 1961).

Schulte, H. J.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Schwarzbeck, A.

T. Merker, A. Schwarzbeck, and P. Meissner, “PMD compensation up to second order by tracking the principal states of polarization using a two-section compensator,” Opt. Commun. 198, 41–47 (2001).
[CrossRef]

Tur, M.

N. Friedman, A. Eyal, and M. Tur, “The use of the principal sates of polarization to describe tunability in a fiber laser,” IEEE J. Quantum Electron. 33, 642–648 (1997).
[CrossRef]

Wagner, R. E.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization mode dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
[CrossRef]

Electron. Lett. (1)

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization mode dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
[CrossRef]

IEEE J. Quantum Electron. (1)

N. Friedman, A. Eyal, and M. Tur, “The use of the principal sates of polarization to describe tunability in a fiber laser,” IEEE J. Quantum Electron. 33, 642–648 (1997).
[CrossRef]

J. Lightwave Technol. (1)

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Opt. Commun. (1)

T. Merker, A. Schwarzbeck, and P. Meissner, “PMD compensation up to second order by tracking the principal states of polarization using a two-section compensator,” Opt. Commun. 198, 41–47 (2001).
[CrossRef]

Optik (4)

P. Pellat-Finet, “Geometrical approach to polarization optics. I—Geometrical structure of polarized light,” Optik 87, 27–33 (1991).

P. Pellat-Finet, “Geometrical approach to polarization optics. II—Quaternionic representation of polarized light,” Optik 87, 68–76 (1991).

P. Pellat-Finet and M. Bausset, “What is common to both polarization optics and relativistic kinematics?,” Optik 90, 101–106 (1992).

P. Pellat-Finet, “An introduction to a vectorial calculus for polarization optics,” Optik 84, 169–175 (1990).

Proc. Natl. Acad. Sci. USA (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
[CrossRef]

Other (2)

J. N. Damask, Polarization Optics in Telecommunications (Springer, 2005).

G. N. Ramachandran and S. Rameseshan, Crystal Optics, Vol. 25/1 of Handbuch der Physik, S. Flügge ed. (Springer, 1961).

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Figures (2)

Fig. 1.
Fig. 1.

On the Poincaré sphere, the effect of the birefringent whose eigenstates are represented by E and E is a rotation whose axis is the straight line passing by E and E. The image of Pi is Pi, and we define Pi+1=(Pi+Pi)/2. The sequence P1,P2,P3, converges to E (or to E).

Fig. 2.
Fig. 2.

Schematic experimental setup. The light source is a tunable laser diode. The polarimeter is Thorlabs PX 510 IR. P, linear polarizer; L1 and L2, rotatable achromatic quarter-wave (L1) and half-wave (L2) plates; B, removable birefringent under study.

Tables (3)

Tables Icon

Table 1. Iterations for Obtaining One Eigenstate of Birefringent B at λ1=1.530μma

Tables Icon

Table 2. Iterations for Obtaining the Other Eigenstate of Birefringent B at λ1=1.530μm

Tables Icon

Table 3. Iterations for Obtaining One Principal State of Birefringent B at λ1=1.530μm and λ2=1.580μm

Equations (23)

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Pp=u21u1(Pp),
αi+1=12(αi+αi),χi+1=12(χi+χi),
αE1=3.45°±0.1°,χE1=10.7°±0.1°.
αE1=86.5°±0.1°,χE1=10.5°±0.1°.
P=(0.1184,0.9930,0.0003),
P=(0.2608,0.5299,0.8070),
P=(0.1184,0.9930,0.0004),
P=(0.2349,0.5326,0.8131),
αE2=3.4°±0.1°,χE2=3.95°±0.1°,
αE2=86.4°±0.1°,χE2=3.8°±0.1°,
αa=72.2°±0.5°,χa=0.8°±0.5°.
αb=14.4°±0.5°,χb=4.3°±0.5°.
U=OE1sinφ12cosφ22OE2cosφ12sinφ22+OE1×OE2sinφ12sinφ22.
OPa=UU,
αa=73.5°,χa=2.6°.
αb=16.5°,χb=2.6°.
[(αaαa)2+(χaχa)2]1/2=2.2°,
[(αbαb)2+(χbχb)2]1/2=2.7°,
u=exp(enφ2)=cosφ2+ensinφ2,
u21u1=(cosφ22en2sinφ22)(cosφ12+en1sinφ12)=cosφ22cosφ12+en2·en1sinφ22sinφ12+en1sinφ12cosφ22en2cosφ12sinφ22+en1×en2sinφ12sinφ22.
u21u1=exp(emψ2)=cosψ2+emsinψ2,
cosψ2=cosφ22cosφ12+en2·en1sinφ22sinφ12.
em=UU,

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