Abstract

An original numerical method is presented for the determination of mode propagation constants of inhomogeneous optically anisotropic optical fibers. The method is first checked for an isotropic step-index fiber and then applied to uniaxial anisotropic cases.

© 1983 Optical Society of America

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References

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  1. D. Marcuse, Quantum Electronics (Academic, New York, 1974), Chap. 2.
  2. M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977), Chap. 6.
    [CrossRef]
  3. T. Okoshi, Optical Fibers (Academic, New York, 1982), Chap. 5.
  4. See Ref. 2, Chap. 4.
  5. U. C. Paek, C. R. Kurkjian, J. Am. Ceram. Soc. 58, 330 (1975).
    [CrossRef]
  6. D. Marcuse, Bell Syst. Tech. J. 54, 985 (1975).
  7. T. Tamir, Ed., Integrated Optics (Springer, Berlin, 1975), Chap. 2.6.

1975 (2)

U. C. Paek, C. R. Kurkjian, J. Am. Ceram. Soc. 58, 330 (1975).
[CrossRef]

D. Marcuse, Bell Syst. Tech. J. 54, 985 (1975).

Ghatak, A. K.

M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977), Chap. 6.
[CrossRef]

Kurkjian, C. R.

U. C. Paek, C. R. Kurkjian, J. Am. Ceram. Soc. 58, 330 (1975).
[CrossRef]

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 54, 985 (1975).

D. Marcuse, Quantum Electronics (Academic, New York, 1974), Chap. 2.

Okoshi, T.

T. Okoshi, Optical Fibers (Academic, New York, 1982), Chap. 5.

Paek, U. C.

U. C. Paek, C. R. Kurkjian, J. Am. Ceram. Soc. 58, 330 (1975).
[CrossRef]

Sodha, M. S.

M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977), Chap. 6.
[CrossRef]

Bell Syst. Tech. J. (1)

D. Marcuse, Bell Syst. Tech. J. 54, 985 (1975).

J. Am. Ceram. Soc. (1)

U. C. Paek, C. R. Kurkjian, J. Am. Ceram. Soc. 58, 330 (1975).
[CrossRef]

Other (5)

T. Tamir, Ed., Integrated Optics (Springer, Berlin, 1975), Chap. 2.6.

D. Marcuse, Quantum Electronics (Academic, New York, 1974), Chap. 2.

M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977), Chap. 6.
[CrossRef]

T. Okoshi, Optical Fibers (Academic, New York, 1982), Chap. 5.

See Ref. 2, Chap. 4.

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Figures (7)

Fig. 1
Fig. 1

(a) Ideal step index, (b) real step-index profile, and (c) gradient-index profile.

Fig. 2
Fig. 2

Solutions for two consecutive values of βt. The functions have been truncated in the cladding.

Fig. 3
Fig. 3

Dispersion characteristics of an isotropic step-index fiber.

Fig. 4
Fig. 4

Qualitative illustration of the different dependence of TE and TM modes on the anisotropy.

Fig. 5
Fig. 5

Calculated BTMBTE as a function of n r 2 = n φ 2.

Fig. 6
Fig. 6

Normalized propagation constants as a function of n r 2.

Fig. 7
Fig. 7

Dispersion characteristics for (a) nr = 0.054 and (b) nr = 0.108.

Equations (6)

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̅ ̅ ( r ) = 0 [ ( n 2 ( r ) 0 0 0 n 2 ( r ) 0 0 0 n 2 ( r ) ) ± ( n r 2 ( r ) 0 0 0 n ϕ 2 ( r ) 0 0 0 n z 2 ( r ) ) ] ,
Ē ( r ̅ , t ) = Ē ( r ) · exp [ i ( ω t β z + ν ϕ ) ] , H ¯ ( r ̅ , t ) = H ¯ ( r ) · exp [ i ( ω t β z + ν ϕ ) ] ,
d 2 E z dr = C 11 d E z dr + C 12 E z + C 13 d H z dr + C 14 H z , d 2 H z dr = C 21 d H z dr + C 22 H z + C 23 d E z dr + C 24 E z ,
C 11 = ω 2 μ a r ω 2 μ 0 r β 2 ( ln r ) 1 r , C 12 = ω 2 μ 0 r β 2 r ( ν 2 r 2 ϕ ω 2 μ 0 ϕ β 2 z ) , C 13 = ν β r ω r ( ω 2 μ 0 r β 2 ω 2 μ 0 ϕ β 2 1 ) , C 14 = ν β r ω r ω 2 μ 0 r ω 2 μ 0 r β 2 , C 21 = ω 2 μ 0 ϕ ω 2 μ 0 ϕ β 2 1 r , C 22 = ( ω 2 μ 0 ϕ β 2 ) ( ν 2 r 2 1 ω 2 μ 0 r β 2 1 ) , C 23 = ν β μ 0 ω r ( ω 2 μ 0 ϕ β 2 ω 2 μ 0 r β 2 1 ) , C 24 = ν β μ 0 ω r ω 2 μ 0 ϕ ω 2 μ 0 ϕ β 2
2 π λ n m β t 2 π λ n M ,
B = β λ 2 π n 2 n 1 n 2 ; V = 2 π a λ ( n 1 2 n 2 2 ) 1 / 2 ,

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