Abstract

A suitable cross section incorporating material anisotropy is shown to give circular birefringence in a slowly spun monomode fiber. It is assumed that the fractional variation Δn/n of the refractive index satisfies the weak guidance condition Δn/n ≪1 and that the period (or pitch) p of the spun fiber is large enough so that the fundamental modes remain effectively bound. Under these assumptions the magnitude of the circular birefringence can be calculated from solutions of the scalar wave equation and in any case lies between the limits (0, 4π/p). The value is zero in the absence of material anisotropy. The required material anisotropy could be produced by stress implanted in the core.

© 1988 Optical Society of America

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References

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  1. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 295.
  2. Y. Fujii, C. D. Hussey, Proc. Inst. Electr. Eng. 133, 249 (1986).
  3. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 32.
  4. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 28.
  5. L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Pergamon, New York, 1958), Sec. 18.
  6. G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, 2nd ed. (Cambridge U. Press, Cambridge, 1964), p. 132.
  7. J. D. Love, Electron. Lett. (to be published).

1986 (1)

Y. Fujii, C. D. Hussey, Proc. Inst. Electr. Eng. 133, 249 (1986).

Fujii, Y.

Y. Fujii, C. D. Hussey, Proc. Inst. Electr. Eng. 133, 249 (1986).

Hardy, G. H.

G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, 2nd ed. (Cambridge U. Press, Cambridge, 1964), p. 132.

Hussey, C. D.

Y. Fujii, C. D. Hussey, Proc. Inst. Electr. Eng. 133, 249 (1986).

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Pergamon, New York, 1958), Sec. 18.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Pergamon, New York, 1958), Sec. 18.

Littlewood, J. E.

G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, 2nd ed. (Cambridge U. Press, Cambridge, 1964), p. 132.

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 28.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 32.

J. D. Love, Electron. Lett. (to be published).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 295.

Polya, G.

G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, 2nd ed. (Cambridge U. Press, Cambridge, 1964), p. 132.

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 28.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 32.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 295.

Proc. Inst. Electr. Eng. (1)

Y. Fujii, C. D. Hussey, Proc. Inst. Electr. Eng. 133, 249 (1986).

Other (6)

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 32.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 28.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Pergamon, New York, 1958), Sec. 18.

G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, 2nd ed. (Cambridge U. Press, Cambridge, 1964), p. 132.

J. D. Love, Electron. Lett. (to be published).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 295.

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Figures (2)

Fig. 1
Fig. 1

Core region of fiber cross section.

Fig. 2
Fig. 2

Refractive index distribution seen by (a) x-polarized light and (b) y-polarized light.

Equations (25)

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Δ 1.
[ e ( x , y ) , h ( x , y ) ] and [ e ( x , y ) , h ( x , y ) ] ,
[ e c ( x , y , z ) , h c ( x , y , z ) ] and [ e c ( x , y , z ) , h c ( x , y , z ) ] ,
f c ( x , y , z ) = R θ f ( x cos θ + y sin θ , - x sin θ + y cos θ ) ,
R θ f = ( cos θ f x - sin θ f y , sin θ f x + cos θ f y , f z ) .
θ = ( 2 π / p ) z .
N = ½ d x d y ( e × h ) · z ^ ,
c ( z ) ( e c , h c ) + c ( z ) ( e c , h c ) .
- i ( d c / d z ) = β c - Γ c - Γ c ,
- i ( d c / d z ) = β c - Γ c - Γ c ,
Γ = N - 1 e c , h c - i ( e c / z ) , - i ( h c / z ) ,
Γ = N - 1 e c , h c - i ( e c / z ) , - i ( h c / z ) ,
f 1 , g 1 f 2 , g 2 1 4 d x d y ( f 1 * × g 2 + f 2 × g 1 * ) · z ^ = 1 4 d x d y ( f 1 x * g 2 y - f 1 y * g 2 x + f 2 x g 1 y * - f 2 y g 1 x * ) .
( f c / z ) z = 0 = ( 2 π / p ) ( - f y + y f x / x - x f x / y , f x + y f y / x - x f y / y , y f z / x - x f z / y ) .
e = ( χ , 0 , 0 ) ,             h = ( 0 / μ 0 ) 1 / 2 n ¯ ( 0 , χ , 0 ) ,
e = ( 0 , χ , 0 ) ,             h = - ( 0 / μ 0 ) 1 / 2 n ¯ ( χ , 0 , 0 ) ,
[ 2 / x 2 + 2 / y 2 + k 2 n 2 ( x , y ) - β ˜ 2 ] χ = 0.
i ( d c / d z ) = β c - i ( 2 π / p ) γ c ,
- i ( d c / d z ) = β c + i ( 2 π / p ) γ c ,
γ = d x d y χ χ / ( d x d y χ 2 ) 1 / 2 ( d x d y χ 2 ) 1 / 2 .
2 - 1 / 2 [ ( e c , h c + i ( e c , h c ) ] exp { i [ β + ( 2 π / p ) γ ] z } ,
2 - 1 / 2 [ ( e c , h c - i ( e c , h c ) ] exp { i [ β - ( 2 π / p ) γ ] z } .
( 4 π / p ) ( 1 - γ ) .
0 γ 1.
p ρ / Δ 1 / 2 ,

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