Abstract

A new type of step-index optical fiber, the helically cladded fiber (HCF), in which a conducting sheath helix is introduced at the core–cladding interface boundary, is proposed. By application of the appropriate sheath-helix boundary condition at the core–cladding interface, the modal characteristic equation is determined. The dispersion curves are also obtained. Analysis of the modal characteristic equation and dispersion curves reveals that only hybrid modes are supported, and the lowest-order mode is HE01. The pitch angle of the helix has no effect on the cutoff condition. Its effect is more pronounced in the case of the first odd modes. One retrieves the modal characteristics of the step-index fiber by setting the pitch angle equal to zero. Further, a fact of technical importance emerges: that the HCF behaves as a monomode guide for a comparatively large core radius.

© 1995 Optical Society of America

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References

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  1. A. H. Cherin, An Introduction to Optical Fibers (McGraw-Hill, New York, 1987), Chap. 5, pp. 85–98.
  2. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 14, pp. 248–255 and 311–315.
  3. H. G. Unger, Planer Optical Waveguides and Fibers (Clarendon, Oxford, 1977), Chap. 2, pp. 321–360.
  4. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1982), Chaps. 8–12, pp. 286–516.
  5. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1982), Chap. 2, pp. 60–89.
  6. D. Gloge, "Dispersion in weakly guiding fibers," Appl. Opt. 10, 2442–2445 (1971).
    [CrossRef] [PubMed]
  7. D. Gloge, "Propagation effects in optical fibers," IEEE Trans. Microwave Theory Tech. 23, 106–120 (1975).
    [CrossRef]
  8. D. Gloge, "Weakly guiding fibers," Appl. Opt. 10, 2252–2258 (1971).
    [CrossRef] [PubMed]
  9. A. W. Snyder, "Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric optical waveguide," IEEE Trans. Microwave Theory Tech. 17, 1130–1138 (1969).
    [CrossRef]
  10. D. A. Watkins, Topics in Electromagnetic Theory (Wiley, New York, 1958), Chap. 2, pp. 39–45.
  11. S. Ramo, J. R. Whinnery, and T. VanDuzer, Fields and Waves in Communication Electronics (Wiley, New York, 1984), Chap. 9, pp. 456–485.
  12. J. R. Pierce, Travelling Wave Tubes (Von Nostrand, Princeton, N.J., 1950), pp. 179–183.
  13. S. Sensiper, "Electromagnetic wavepropagation on helical conductors," Proc. IRE 43, 149–161 (1955).
    [CrossRef]
  14. U. N. Singh and O. N. Singh II, "Simplified analysis of a proposed novel optical fiber," in Proceedings of the National Conference on Electrical Circuits and Systems (Tata McGraw-Hill, New Delhi, 1989), pp. 635–637.
  15. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1968), pp. 358–378.

1975 (1)

D. Gloge, "Propagation effects in optical fibers," IEEE Trans. Microwave Theory Tech. 23, 106–120 (1975).
[CrossRef]

1971 (2)

1969 (1)

A. W. Snyder, "Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric optical waveguide," IEEE Trans. Microwave Theory Tech. 17, 1130–1138 (1969).
[CrossRef]

1955 (1)

S. Sensiper, "Electromagnetic wavepropagation on helical conductors," Proc. IRE 43, 149–161 (1955).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1968), pp. 358–378.

Cherin, A. H.

A. H. Cherin, An Introduction to Optical Fibers (McGraw-Hill, New York, 1987), Chap. 5, pp. 85–98.

Gloge, D.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 14, pp. 248–255 and 311–315.

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1982), Chaps. 8–12, pp. 286–516.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1982), Chap. 2, pp. 60–89.

Pierce, J. R.

J. R. Pierce, Travelling Wave Tubes (Von Nostrand, Princeton, N.J., 1950), pp. 179–183.

Ramo, S.

S. Ramo, J. R. Whinnery, and T. VanDuzer, Fields and Waves in Communication Electronics (Wiley, New York, 1984), Chap. 9, pp. 456–485.

Sensiper, S.

S. Sensiper, "Electromagnetic wavepropagation on helical conductors," Proc. IRE 43, 149–161 (1955).
[CrossRef]

Singh, O. N.

U. N. Singh and O. N. Singh II, "Simplified analysis of a proposed novel optical fiber," in Proceedings of the National Conference on Electrical Circuits and Systems (Tata McGraw-Hill, New Delhi, 1989), pp. 635–637.

Singh, U. N.

U. N. Singh and O. N. Singh II, "Simplified analysis of a proposed novel optical fiber," in Proceedings of the National Conference on Electrical Circuits and Systems (Tata McGraw-Hill, New Delhi, 1989), pp. 635–637.

Snyder, A. W.

A. W. Snyder, "Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric optical waveguide," IEEE Trans. Microwave Theory Tech. 17, 1130–1138 (1969).
[CrossRef]

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 14, pp. 248–255 and 311–315.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1968), pp. 358–378.

Unger, H. G.

H. G. Unger, Planer Optical Waveguides and Fibers (Clarendon, Oxford, 1977), Chap. 2, pp. 321–360.

VanDuzer, T.

S. Ramo, J. R. Whinnery, and T. VanDuzer, Fields and Waves in Communication Electronics (Wiley, New York, 1984), Chap. 9, pp. 456–485.

Watkins, D. A.

D. A. Watkins, Topics in Electromagnetic Theory (Wiley, New York, 1958), Chap. 2, pp. 39–45.

Whinnery, J. R.

S. Ramo, J. R. Whinnery, and T. VanDuzer, Fields and Waves in Communication Electronics (Wiley, New York, 1984), Chap. 9, pp. 456–485.

Appl. Opt. (2)

IEEE Trans. Microwave Theory Tech. (2)

D. Gloge, "Propagation effects in optical fibers," IEEE Trans. Microwave Theory Tech. 23, 106–120 (1975).
[CrossRef]

A. W. Snyder, "Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric optical waveguide," IEEE Trans. Microwave Theory Tech. 17, 1130–1138 (1969).
[CrossRef]

Proc. IRE (1)

S. Sensiper, "Electromagnetic wavepropagation on helical conductors," Proc. IRE 43, 149–161 (1955).
[CrossRef]

Other (10)

U. N. Singh and O. N. Singh II, "Simplified analysis of a proposed novel optical fiber," in Proceedings of the National Conference on Electrical Circuits and Systems (Tata McGraw-Hill, New Delhi, 1989), pp. 635–637.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1968), pp. 358–378.

D. A. Watkins, Topics in Electromagnetic Theory (Wiley, New York, 1958), Chap. 2, pp. 39–45.

S. Ramo, J. R. Whinnery, and T. VanDuzer, Fields and Waves in Communication Electronics (Wiley, New York, 1984), Chap. 9, pp. 456–485.

J. R. Pierce, Travelling Wave Tubes (Von Nostrand, Princeton, N.J., 1950), pp. 179–183.

A. H. Cherin, An Introduction to Optical Fibers (McGraw-Hill, New York, 1987), Chap. 5, pp. 85–98.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 14, pp. 248–255 and 311–315.

H. G. Unger, Planer Optical Waveguides and Fibers (Clarendon, Oxford, 1977), Chap. 2, pp. 321–360.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1982), Chaps. 8–12, pp. 286–516.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1982), Chap. 2, pp. 60–89.

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Figures (7)

Fig. 1
Fig. 1

(a) Model case of a sheath-helix cladded fiber. (b) Possible realization of the sheath-helix model.

Fig. 2
Fig. 2

Normalized frequency V = (U2 + W2)1/2 versus the core parameter U = k1a at various helix pitch angles at core radius a = 5 μm and operating wavelength λ = 0.86 μm. The modal indices are shown for the curves corresponding to ψ = 3°. Other curves can be similarly indexed.

Fig. 3
Fig. 3

Normalized frequency V = (U2 + W2)1/2 versus the core parameter U = k1a at various helix pitch angles at core radius a = 50 μm and operating wavelength λ = 1.55 μm. The modal indices are shown for the curves corresponding to ψ = 3°. Other curves can be similarly indexed.

Fig. 4
Fig. 4

Normalized frequency V = (U2 + W2)1/2 versus the normalized propagation constant b = (W/V)2 at core radius a = 50 μm and operating wavelength λ = 0.86 μm at various helix pitch angles. The modal indices are shown for the curves corresponding to ψ = 6°. Other curves can be similarly indexed.

Fig. 5
Fig. 5

Normalized frequency V = (U2 + W2)1/2 versus the normalized propagation constant b = (W/V)2 at core radius a = 50 μm and operating wavelength λ = 1.55 μm, for various helix pitch angles. The modal indices are shown for the curves corresponding to ψ = 3°. Other curves can be similarly indexed.

Fig. 6
Fig. 6

Normalized frequency V = (U2 + W2)1/2 versus the fractional power η at core radius a = 50 μm and operating wavelength λ = 0.86 μm for various helix pitch angles. The modal indices are shown for the curves corresponding to ψ = 6°. Other curves can be similarly indexed.

Fig. 7
Fig. 7

Normalized frequency V = (U2 + W2)1/2 versus the fractional power η at core radius a = 50 μm and operating wavelength λ = 1.55 μm for various helix pitch angles. The modal indices are shown for the curves corresponding to ψ = 3°. Other curves can be similarly indexed.

Equations (19)

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E z = E ( r , ϕ ) exp [ j ( ω t - β z ) ] ,
H z = H ( r , ϕ ) exp [ j ( ω t - β z ) ] ,
E z 1 = A J ν ( k 1 r ) exp [ j ( ω t - β z + ν ϕ ) ] ,
H z 1 = B J ν ( k 1 r ) exp [ j ( ω t - β z + ν ϕ ) ] ,
E z 2 = C K ν ( k 2 r ) exp [ j ( ω t - β z + ν ϕ ) ] ,
H z 2 = D K ν ( k 2 r ) exp [ j ( ω t - β z + ν ϕ ) ] ,
E ϕ 1 = - j k 1 2 [ β r A j ν J ν ( k 1 r ) - μ ω B k 1 J ν ( k 1 r ) ] × exp [ j ( ω t - β z + ν ϕ ) ] ,
H ϕ 1 = - j k 2 2 [ β r B j ν J ν ( k 1 r ) + ω 1 A J ν ( k 1 r ) ] × exp [ j ( ω t - β z + ν ϕ ) ] .
E ϕ 2 = - j k 2 2 [ β r C j ν K ν ( k 2 r ) - μ ω D k 2 K ν ( k 2 r ) ] × exp [ j ( ω t - β z + ν ϕ ) ] ,
H ϕ 2 = - j k 2 2 [ β r D j ν K ν ( k 2 r ) + ω 2 C K ν ( k 2 r ) ] × exp [ j ( ω t - β z + ν ϕ ) ] .
E z 1 sin ψ + E ϕ 1 cos ψ = 0 , E z 2 sin ψ + E ϕ 2 cos ψ = 0.
E 1 = E 2 , E z 1 cos ψ - E ϕ 1 sin ψ = E z 2 cos ψ - E ϕ 2 sin ψ .
H 1 = H 2 .
H z 1 sin ψ + H ϕ 1 cos ψ = H z 2 sin ψ + H ϕ 2 cos ψ .
[ J 0 2 ( k 1 a ) K 0 ( k 2 a ) K 1 ( k 2 a ) k 2 + K 0 2 ( k 2 a ) J 0 ( k 1 a ) J 1 ( k 1 a ) k 1 ] × sin 2 ψ - [ J 1 2 ( k 1 a ) K 0 ( k 2 a ) K 1 ( k 1 a ) k 1 2 k 2 μ ω 2 1 + K 1 2 ( k 2 a ) J 0 ( k 1 a ) J 1 ( k 1 a ) k 2 2 k 1 μ ω 2 2 ] cos 2 ψ = 0.
J 0 ( k c a ) J 1 ( k c a ) = 0.
P t = ½ Re 0 0 2 π [ E × H * ] · I ^ z r d r d ϕ ,
P co P t = 1 - ( U / V ) 2 { 1 - [ K 0 ( W ) K 1 ( W ) ] 2 } ,
P cl P t = ( U / V ) 2 { 1 - [ K 0 ( W ) K 1 ( W ) ] 2 } ,

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