Abstract

In twisted single-mode optical fibers the polarization of light is affected by an elastooptically induced optical activity and by a modification of any linear birefringence present. These effects are discussed theoretically and demonstrated experimentally. The activity/twist ratio is α/τ ≃ 0.13 … 0.16 universally in weakly guiding silica fibers. Twisted fibers may be used as polarization rotators. A fiber with a ±68° double twist operates as a fast/slow mode interchanger, suitable for delay equalization.

© 1979 Optical Society of America

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References

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  1. A. M. Smith, Appl. Opt. 17, 53 (1978).
  2. V. Vali, R. W. Shorthill, M. F. Berg, Appl. Opt. 16, 2605 (1977).
    [CrossRef] [PubMed]
  3. F. P. Kapron, N. B. Borelli, D. B. Keck, IEEE J. Quantum Electron. QE-8, 222 (1972); W. A. Gambling, D. N. Payne, H. Matsumara, in Digest of Topical Meeting on Optical Fiber Transmission II, (Optical Society of America, Washington, D.C., 1977), p. TuD5.
    [CrossRef]
  4. H. Papp, H. Harms, Appl. Opt. 14, 2406 (1975).
    [CrossRef] [PubMed]
  5. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974).
  6. D. Gloge, Appl. Opt. 10, 2252 (1971).
    [CrossRef] [PubMed]
  7. R. Ulrich, Opt. Lett. 1, 109 (1977).
    [CrossRef] [PubMed]
  8. J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1960).
  9. G. N. Ramachandra, S. Ramaseshan, in Handbuch der Physik, S. Flügge, Ed. (Springer, Berlin, 1962), Vol. 25/1.
  10. D. Gray, Ed. American Institute of Physics Handbook (McGraw Hill, New York, 1976), p. 6–236.
  11. G. S. Ranganath, S. Ramaseshan, J. Opt. Soc. Am. 59, 1229 (1969).
    [CrossRef]
  12. S. C. Rashleigh, R. Ulrich, Opt. Lett. 3, 60 (1978).
    [CrossRef] [PubMed]
  13. R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978).
    [CrossRef]
  14. A. Simon, R. Ulrich, Appl. Phys. Lett. 31, 517 (1977).
    [CrossRef]

1978 (3)

A. M. Smith, Appl. Opt. 17, 53 (1978).

S. C. Rashleigh, R. Ulrich, Opt. Lett. 3, 60 (1978).
[CrossRef] [PubMed]

R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978).
[CrossRef]

1977 (3)

1975 (1)

1972 (1)

F. P. Kapron, N. B. Borelli, D. B. Keck, IEEE J. Quantum Electron. QE-8, 222 (1972); W. A. Gambling, D. N. Payne, H. Matsumara, in Digest of Topical Meeting on Optical Fiber Transmission II, (Optical Society of America, Washington, D.C., 1977), p. TuD5.
[CrossRef]

1971 (1)

1969 (1)

Berg, M. F.

Borelli, N. B.

F. P. Kapron, N. B. Borelli, D. B. Keck, IEEE J. Quantum Electron. QE-8, 222 (1972); W. A. Gambling, D. N. Payne, H. Matsumara, in Digest of Topical Meeting on Optical Fiber Transmission II, (Optical Society of America, Washington, D.C., 1977), p. TuD5.
[CrossRef]

Gloge, D.

Harms, H.

Kaiser, P.

R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978).
[CrossRef]

Kapron, F. P.

F. P. Kapron, N. B. Borelli, D. B. Keck, IEEE J. Quantum Electron. QE-8, 222 (1972); W. A. Gambling, D. N. Payne, H. Matsumara, in Digest of Topical Meeting on Optical Fiber Transmission II, (Optical Society of America, Washington, D.C., 1977), p. TuD5.
[CrossRef]

Keck, D. B.

F. P. Kapron, N. B. Borelli, D. B. Keck, IEEE J. Quantum Electron. QE-8, 222 (1972); W. A. Gambling, D. N. Payne, H. Matsumara, in Digest of Topical Meeting on Optical Fiber Transmission II, (Optical Society of America, Washington, D.C., 1977), p. TuD5.
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974).

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1960).

Papp, H.

Pleibel, W.

R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978).
[CrossRef]

Ramachandra, G. N.

G. N. Ramachandra, S. Ramaseshan, in Handbuch der Physik, S. Flügge, Ed. (Springer, Berlin, 1962), Vol. 25/1.

Ramaseshan, S.

G. S. Ranganath, S. Ramaseshan, J. Opt. Soc. Am. 59, 1229 (1969).
[CrossRef]

G. N. Ramachandra, S. Ramaseshan, in Handbuch der Physik, S. Flügge, Ed. (Springer, Berlin, 1962), Vol. 25/1.

Ramaswamy, V.

R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978).
[CrossRef]

Ranganath, G. S.

Rashleigh, S. C.

Shorthill, R. W.

Simon, A.

A. Simon, R. Ulrich, Appl. Phys. Lett. 31, 517 (1977).
[CrossRef]

Smith, A. M.

A. M. Smith, Appl. Opt. 17, 53 (1978).

Stolen, R. H.

R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978).
[CrossRef]

Ulrich, R.

Vali, V.

Appl. Opt. (4)

Appl. Phys. Lett. (2)

R. H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Appl. Phys. Lett. 33, 699 (1978).
[CrossRef]

A. Simon, R. Ulrich, Appl. Phys. Lett. 31, 517 (1977).
[CrossRef]

IEEE J. Quantum Electron. (1)

F. P. Kapron, N. B. Borelli, D. B. Keck, IEEE J. Quantum Electron. QE-8, 222 (1972); W. A. Gambling, D. N. Payne, H. Matsumara, in Digest of Topical Meeting on Optical Fiber Transmission II, (Optical Society of America, Washington, D.C., 1977), p. TuD5.
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Other (4)

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1960).

G. N. Ramachandra, S. Ramaseshan, in Handbuch der Physik, S. Flügge, Ed. (Springer, Berlin, 1962), Vol. 25/1.

D. Gray, Ed. American Institute of Physics Handbook (McGraw Hill, New York, 1976), p. 6–236.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974).

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Figures (9)

Fig. 1
Fig. 1

Twisted optical fiber, schematically. (a) Coordinate systems; (b) arbitrary, but smooth radial distribution of dielectric permeability; (c) transverse fields of the fundamental modes.

Fig. 2
Fig. 2

Birefringent fibers. (a) Due to an elliptically deformed core; (b) due to application of external electric field.

Fig. 3
Fig. 3

Representation of a general state of polarization C on a Poincaré sphere, referring (a) to the base H, V of horizontal and vertical linear polarizations and (b) to the base L, R of circular polarizations.

Fig. 4
Fig. 4

Evolution of polarization C(z) for various kinds of birefringence. (a) Linear; (b) circular; (c) straight elliptical; (d) twisted elliptical.

Fig. 5
Fig. 5

Evolution of polarization in a single-mode fiber, measured electrooptically at two different twist rates. (a) τ = 1.9 rad/m; (b) τ = 6.1 rad/m. The numbers at the curves indicate the position in centimeters along the fiber.

Fig. 6
Fig. 6

Evolution of polarization, recorded magnetooptically. A cross section of the modulating coil is shown in the inset.

Fig. 7
Fig. 7

Determination of the twist-induced optical activity α from the total birefringence Ω(τ), measured according to Fig. 6. According to Eq. (22) the ordinate should be |2 − α/τ|. The dashed line marks α/τ = 0.13.

Fig. 8
Fig. 8

(a) Measured and (b) calculated output polarization C L ° as a function of twist, relative to the principal axes of the fiber. The parameter along the curves is the twist/birefringence ratio (2 − g)τ/β.

Fig. 9
Fig. 9

The ±68° double twist for interchanging the fast and slow mode. (a) Schematically; (b) its operation represented on S °.

Equations (44)

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= 0 + ˜ .
A m ( z ) = a m exp ( i k m z ) .
E t ( x , y , z ) = m A m ( z ) E m t ( x , y ) .
a m ( z ) = i Σ κ m n a n ( z ) exp [ i ( k n - k m ) z ] .
E ( x , y , z ) = [ a 1 ( z ) E 1 ( x , y ) + a 2 ( z ) E 2 ( x , y ) ] exp i k 1 z .
κ m n = [ I m n ( 1 ) + I m n ( 2 ) + I m n ( 3 ) ] / Q m ,
I m n ( 1 ) + I m n ( 2 ) = k k 1 E m * ( ˜ E n ) d x d y ,
I m n ( 3 ) = - i k E m z * ( ˜ E n ) d x d y ,
Q 1 = Q 2 = 4 π n 0 k 1 J 2 r d r .
˜ 4 = - p 44 n 0 4 τ x ;             ˜ 5 = p 44 n 0 4 τ y .
κ 11 = κ 22 = 0 ;             κ 12 = - κ 21 = - i n 0 2 p 44 τ / 2.
˜ ( r , ϕ ) = - η r 0 ( r ) cos 2 ( ϕ - ϕ B ) ,
κ 11 = - κ 22 = ( β / 2 ) cos 2 ϕ B , κ 12 = κ 21 = ( β / 2 ) sin 2 ϕ B . }
β K = 2 π B K E K 2 .
˜ 12 = - ˜ 21 = - 2 i n 0 V H F / k .
κ 11 = κ 22 = 0 ;             κ 12 = - κ 21 = - 2 i V H F .
2 χ = arctan [ ( a 1 / a 2 - 1 ) / ( a 1 / a 2 + 1 ) ] , 2 ξ = arg ( a 1 / a 2 ) . }
C ( z ) = ω ( z ) × C ( z ) ,
ω = ω = [ ( κ 11 - κ 22 ) 2 + 4 κ 12 κ 21 ] 1 / 2 ,
2 χ ω = arctan [ ( κ 11 - κ 22 ) / ( 4 κ 12 κ 21 ) 1 / 2 ] ,
2 ξ ω = arg ( κ 12 ) .
α = g τ ,
ω ( z ) = β ( z ) + α ( z ) .
ω ( z ) = 2 τ × ω ( z ) .
Ω ° = β ° + α - 2 τ ,
Ω = Ω ° = [ β 2 + ( α - 2 τ ) 2 ] 1 / 2 .
C Ω = Ω ° / Ω .
2 ψ n = arctan [ ( α - 2 τ ) / β ] .
β = Ω cos 2 ψ Ω ,
α - 2 τ = Ω sin 2 ψ Ω .
2 δ ϕ ( z ) = 2 V H F ( z ) d z .
α / τ = 0.13 ± 0.01.
C L ° ( τ ) - C L ° ( o ) < 1.63 / N ,
2 E + k 2 ( 0 + ˜ ) E - ( E ) = 0.
( E ) = 0 E + E 0 + ( ˜ E ) = 0.
- t ( E ) = m a m exp ( i k m z ) t [ E m t ] n 0 + U m ] ,
U m = 0 - 1 ( ˜ E m ) + i 0 - 1 k m ( ˜ E m ) z .
m [ 2 i k m a m E m t + a m k 2 ( ˜ E m ) t + a m t U m ] exp ( i k m z ) = 0.
Q m = 2 k m [ E m t × H m t * ] z d x d y ,
I m n ( 1 ) = k 2 [ ( ˜ E n ) t × H m t * ] z d x d y ,
I m n ( 2 ) = k k n E m z * ( ˜ E n ) z d x d y ,
I m n ( 3 ) = - i k E m z * ( ˜ E n ) d x d y .
E 1 = - H 2 / n 0 = { J ( r ) , 0 , ( i / k 1 ) cos ϕ J ˙ ( r ) } ,
E 2 = H 1 / n 0 = { 0 , J ( r ) , ( i / k 1 ) sin ϕ J ˙ ( r ) } .

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