Abstract

A spectrometer-polarimeter is described for the measurement of the wavelength-dependent general birefringence of single-mode optical fibers and fiber-optic devices. The polarizer rotates, the analyzer is stepped, and a Fourier transform yields the principal axes and retardation. The Poincaré representation of polarization is used throughout.

© 1981 Optical Society of America

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References

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  1. R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978);J. D. Love, R. A. Sammut, A. W. Snyder, Electron. Lett. 15, 615 (1979).
  2. I. P. Kaminow, V. Ramaswamy, Appl. Phys. Lett. 34, 268 (1979).
  3. Y. Namihira, M. Kudo, Y. Mushiako, Trans. Inst. Chem. Eng. 60C, 391 (1977);M. Johnson, Appl. Opt. 18, 1288 (1979).
  4. R. Ulrich, A. Simon, Appl. Opt. 13, 2241 (1979).
  5. R. Ulrich, S. C. Rashleigh, W. Eickhoff, Opt. Lett. 5, 273 (1980).
  6. R. Ulrich, M. Johnson, Appl. Opt. 11, 1857 (1979).
  7. H. C. Lefevre, Electron. Lett. 16, 778 (1980).
  8. M. Johnson, Opt. Lett. 5, 142 (1980).
  9. Y. Yen, R. Ulrich, Opt. Lett. 6, 278 (1981).
  10. R. H. Stolen, in Digest of Topical Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1980), paper MB2.
  11. S. C. Rashleigh, Opt. Lett. 5, 392 (1980);W. Eickhoff, Opt. Lett. 6, 204 (1981).
  12. G. N. Ramachandra, S. Ramaseshan, in Handbuch der Physik, Vol 25/1, S. Flügge, Ed. (Springer, Berlin, 1962), p. 1;R. Ulrich, Opt. Lett. 1, 109 (1977).
  13. At either end of the fiber a pair of fixed orthogonal reference axes is required normal to the direction of light propagation. One axis of either pair is arbitrarily assigned to mark horizontal H linear polarization, the other axes vertical V. Circular polarization states are called left-(L) or right-(R) handed when the electric vector is seen (facing the source of light) to rotate in the mathematically positive (ccw) or negative (cw) sense, respectively. All azimuths are counted then in the positive sense (ccw) from the H direction.
  14. The factor 2 has been included here in the definition of the angle in accordance with the usual notation of the Poincaré formalism.

1981 (1)

1980 (4)

1979 (3)

R. Ulrich, M. Johnson, Appl. Opt. 11, 1857 (1979).

I. P. Kaminow, V. Ramaswamy, Appl. Phys. Lett. 34, 268 (1979).

R. Ulrich, A. Simon, Appl. Opt. 13, 2241 (1979).

1978 (1)

R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978);J. D. Love, R. A. Sammut, A. W. Snyder, Electron. Lett. 15, 615 (1979).

1977 (1)

Y. Namihira, M. Kudo, Y. Mushiako, Trans. Inst. Chem. Eng. 60C, 391 (1977);M. Johnson, Appl. Opt. 18, 1288 (1979).

Eickhoff, W.

Johnson, M.

Kaiser, P.

R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978);J. D. Love, R. A. Sammut, A. W. Snyder, Electron. Lett. 15, 615 (1979).

Kaminow, I. P.

I. P. Kaminow, V. Ramaswamy, Appl. Phys. Lett. 34, 268 (1979).

Kudo, M.

Y. Namihira, M. Kudo, Y. Mushiako, Trans. Inst. Chem. Eng. 60C, 391 (1977);M. Johnson, Appl. Opt. 18, 1288 (1979).

Lefevre, H. C.

H. C. Lefevre, Electron. Lett. 16, 778 (1980).

Mushiako, Y.

Y. Namihira, M. Kudo, Y. Mushiako, Trans. Inst. Chem. Eng. 60C, 391 (1977);M. Johnson, Appl. Opt. 18, 1288 (1979).

Namihira, Y.

Y. Namihira, M. Kudo, Y. Mushiako, Trans. Inst. Chem. Eng. 60C, 391 (1977);M. Johnson, Appl. Opt. 18, 1288 (1979).

Pleibel, W.

R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978);J. D. Love, R. A. Sammut, A. W. Snyder, Electron. Lett. 15, 615 (1979).

Ramachandra, G. N.

G. N. Ramachandra, S. Ramaseshan, in Handbuch der Physik, Vol 25/1, S. Flügge, Ed. (Springer, Berlin, 1962), p. 1;R. Ulrich, Opt. Lett. 1, 109 (1977).

Ramaseshan, S.

G. N. Ramachandra, S. Ramaseshan, in Handbuch der Physik, Vol 25/1, S. Flügge, Ed. (Springer, Berlin, 1962), p. 1;R. Ulrich, Opt. Lett. 1, 109 (1977).

Ramaswamy, V.

I. P. Kaminow, V. Ramaswamy, Appl. Phys. Lett. 34, 268 (1979).

R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978);J. D. Love, R. A. Sammut, A. W. Snyder, Electron. Lett. 15, 615 (1979).

Rashleigh, S. C.

Simon, A.

R. Ulrich, A. Simon, Appl. Opt. 13, 2241 (1979).

Stolen, R. H.

R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978);J. D. Love, R. A. Sammut, A. W. Snyder, Electron. Lett. 15, 615 (1979).

R. H. Stolen, in Digest of Topical Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1980), paper MB2.

Ulrich, R.

Yen, Y.

Appl. Opt. (2)

R. Ulrich, A. Simon, Appl. Opt. 13, 2241 (1979).

R. Ulrich, M. Johnson, Appl. Opt. 11, 1857 (1979).

Appl. Phys. Lett. (2)

R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978);J. D. Love, R. A. Sammut, A. W. Snyder, Electron. Lett. 15, 615 (1979).

I. P. Kaminow, V. Ramaswamy, Appl. Phys. Lett. 34, 268 (1979).

Electron. Lett. (1)

H. C. Lefevre, Electron. Lett. 16, 778 (1980).

Opt. Lett. (4)

Trans. Inst. Chem. Eng. (1)

Y. Namihira, M. Kudo, Y. Mushiako, Trans. Inst. Chem. Eng. 60C, 391 (1977);M. Johnson, Appl. Opt. 18, 1288 (1979).

Other (4)

R. H. Stolen, in Digest of Topical Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1980), paper MB2.

G. N. Ramachandra, S. Ramaseshan, in Handbuch der Physik, Vol 25/1, S. Flügge, Ed. (Springer, Berlin, 1962), p. 1;R. Ulrich, Opt. Lett. 1, 109 (1977).

At either end of the fiber a pair of fixed orthogonal reference axes is required normal to the direction of light propagation. One axis of either pair is arbitrarily assigned to mark horizontal H linear polarization, the other axes vertical V. Circular polarization states are called left-(L) or right-(R) handed when the electric vector is seen (facing the source of light) to rotate in the mathematically positive (ccw) or negative (cw) sense, respectively. All azimuths are counted then in the positive sense (ccw) from the H direction.

The factor 2 has been included here in the definition of the angle in accordance with the usual notation of the Poincaré formalism.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup of the spectrometer-polarimeter. Explanation of symbols in the text.

Fig. 2
Fig. 2

(a) Representation of the trajectories of the input state of polarization (equator) and output state (circle G) on the Poincaré sphere. (b) Determination of the birefringence vector Ω from the circle G.

Fig. 3
Fig. 3

Measured dispersion of the birefringence of the retarder of a three-stage fiber-optic Solc filter: (a) Azimuth of the birefringence vector, at modulo 180°. At the two positions marked by ao-20-15-2721-i001 the azimuth changes very rapidly by 180°, because Ω passes near the poles of the sphere. (b) Ellipticity of the eigenstates of polarization. (c) Phase retardation shown at modulo 180°.

Fig. 4
Fig. 4

Trajectory of the birefringence vector Ω(ν) of the retarder of Fig. 3 shown on a world map. The parameter along the trajectory is the wave number in units of 100 cm−1.

Fig. 5
Fig. 5

Transmittance of the three-stage Solc filter with bandpass characteristic. -·- measured; ×, calculated from data of Fig. 3.

Equations (18)

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2 ϕ 1 ( t ) = ω t .
2 γ ( t ) = ω t + 2 γ 0 .
T α ( t ) = cos 2 Δ ( t ) = ½ + ½ cos 2 Δ ( t ) .
T α ( t ) = ½ + T α cos ( ω t + χ ) ,
T α 2 = ¼ cos 2 ψ G [ 1 cos 4 ( α ϕ N ) ] ,
tan ( 2 γ 0 χ ) = sin 2 ψ G tan 2 ( α ϕ N ) .
T α , max = ½ , for α = ϕ N or ϕ N + π / 2 ,
T α , max = ½ sin | 2 ψ G | , for α = ϕ N ± π / 4 .
sin | 2 ψ G | = T min / T max .
sin 2 ψ G = d χ / d α | α = ϕ N
2 ϕ Ω = ϕ N γ 0 ,
tan 2 ϕ Ω = sin ( ϕ N + γ 0 ) tan ( ψ G + π / 4 ) .
cos Ω / 2 = cos ( ϕ N + γ 0 ) sin ( ψ G + π / 4 ) .
T α 2 = A 0 + A 4 cos 4 α + B 4 sin 4 α ,
8 A 4 = cos 2 ψ G sin 4 ϕ N , = m = 1 16 T α 2 ( m Δ α ) cos 4 m Δ α ,
8 B 4 = cos 2 ψ G cos 4 ϕ N , = m = 1 16 T α 2 ( m Δ α ) sin 4 m Δ α ,
2 ϕ N = ½ arctan ( B 4 / A 4 ) ,
2 ψ G = 2 arccos [ ( A 4 2 + B 4 2 ) 1 / 2 ] .

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