Abstract

The radiation losses of the HE11 mode of a fiber with sinusoidal radius fluctuations are calculated in the weak guidance approximation. The loss formula is derived by means of the volume current method and also by using coupled mode theory. The result presented here extends earlier results to the case of radiation escaping nearly perpendicular to the fiber axis.

© 1975 Optical Society of America

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References

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  1. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), p. 155
  2. A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-18, 608 (1970).
    [Crossref]
  3. E. G. Rawson, Appl. Opt. 13, 2370 (1974).
    [Crossref] [PubMed]
  4. Ref. 1, p. 66, Eqs. (2.2-28) and (2.2-30).
  5. Ref. 1, p. 70, Eq. (2.2-42).
  6. A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1138 (1969).
    [Crossref]
  7. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 428, Eq. (26).
  8. Ref. 1, Eq. (3.4-19), p. 115 and Eq. (4.2-24), p. 138.
  9. Ref. 1, Eq. (4.7-5), p. 168.
  10. Ref. 1, Eq. (4.7-1), p. 168.

1974 (1)

1970 (1)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-18, 608 (1970).
[Crossref]

1969 (1)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1138 (1969).
[Crossref]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), p. 155

Rawson, E. G.

Snyder, A. W.

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-18, 608 (1970).
[Crossref]

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1138 (1969).
[Crossref]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 428, Eq. (26).

Appl. Opt. (1)

IEEE Trans. Microwave Theory Tech. (2)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-18, 608 (1970).
[Crossref]

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1138 (1969).
[Crossref]

Other (7)

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 428, Eq. (26).

Ref. 1, Eq. (3.4-19), p. 115 and Eq. (4.2-24), p. 138.

Ref. 1, Eq. (4.7-5), p. 168.

Ref. 1, Eq. (4.7-1), p. 168.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), p. 155

Ref. 1, p. 66, Eqs. (2.2-28) and (2.2-30).

Ref. 1, p. 70, Eq. (2.2-42).

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Figures (3)

Fig. 1
Fig. 1

Fiber core with sinusoidal radius variation.

Fig. 2
Fig. 2

Comparison of Eq. (22) (solid curve, with ρa replaced by σa) with the approximate theory of Ref. 1 (dotted curve) for n1 = 1.6, n2 = 1.5, ka = 10, V = 5.57.

Fig. 3
Fig. 3

Plot of the unmodified Eq. (22) for n1 = 1.515, n2 = 1.5, V = 2.4.

Equations (31)

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E x = B J 0 ( κ r ) exp ( i β z ) ,
E z = i κ B β 0 J 1 ( κ r ) cos ϕ exp ( i β z ) ,
κ = ( n 1 2 k 2 β 0 2 ) 1 / 2 .
B 2 = 2 ( μ 0 / 0 ) 1 / 2 γ 2 P π a 2 n 2 ( n 1 2 n 2 2 ) k 2 J 1 2 ( κ a ) .
γ = ( β 0 2 n 2 2 k 2 ) 1 / 2 .
r = a + b cos θ z .
× H = i ω n 2 0 E ,
× E = i ω μ 0 H ,
E = E 0 + E s H = H 0 + H s .
× H s = J + i ω n 0 2 0 E s ,
× E s = i ω μ 0 H s .
J = i ω 0 ( n 2 n 0 2 ) E 0 .
A ( x , y , z ) = μ 0 4 π J ( x , y , z ) r exp ( i n 2 k r ) d x d y d z
r = [ ( x x ) 2 + ( y y ) 2 + ( z z ) 2 ] 1 / 2 .
A ( x , y , z ) = i ω 0 μ 0 4 π ( n 1 2 n 2 2 ) a b 0 2 π d ϕ L 2 L 2 E 0 ( a , ϕ , z ) × exp ( i n 2 k r ) r cos θ z d z .
A = i ω 0 μ 0 a b ( n 1 2 n 2 2 ) B 2 r 0 sin ( β 0 β θ ) ( L / 2 ) β 0 β θ exp ( i n 2 k r 0 ) [ e x J 0 ( κ a ) J 0 ( ρ a ) e z κ β 0 cos ϕ J 1 ( κ a ) J 1 ( ρ a ) ] .
β = n 2 k cos ψ
ρ = n 2 k sin ψ
cos ψ = ( z / r 0 ) .
2 α = ( Δ P / P L ) .
Δ P = 0 2 π d ϕ 0 π sin ψ r 0 2 S r d ψ = i ω r 0 2 2 0 2 π d ϕ 0 π sin ψ e r [ A × ( × A * ) ] d ψ .
2 α = π b 2 n 2 k γ 2 [ n 1 n 2 1 ] 4 J 1 2 ( κ a ) { J 0 2 ( κ a ) J 0 2 ( ρ a ) + [ ( cos ψ r ) J 0 ( κ a ) J 0 ( ρ a ) + κ β 0 ( sin ψ r ) J 1 ( κ a ) J 1 ( ρ a ) ] 2 } .
β 0 β θ = 0 ,
cos ψ r = β 0 θ n 2 k .
2 α = π 2 | β | ρ i | K ̂ i | 2 .
E z = C j J ν ( ρ r ) [ cos ν ϕ sin ν ϕ ] ; H z = C j F j J ν ( ρ r ) [ sin ν ϕ cos ν ϕ ] ; E r = i C j ρ [ β J ν ( ρ r ) + ω μ 0 ν ρ r F j J ν ( ρ r ) ] [ cos ν ϕ sin ν ϕ ] ; E ϕ = i C j ρ [ ν ρ r β J ν ( ρ r ) ω μ 0 F j J ν ( ρ r ) ] [ sin ν ϕ cos ν ϕ ] ; H r = i C j ρ [ n 2 ω 0 ν ρ r J ν ( ρ r ) + β F j J ν ( ρ r ) ] [ sin ν ϕ cos ν ϕ ] ; H ϕ = i C j ρ [ n 2 ω 0 J ν ( ρ r ) + ν ρ r β F j J ν ( ρ r ) ] [ cos ν ϕ sin ν ϕ ] .
F 1 = n ( 0 / μ 0 ) 1 / 2 F 2 = n ( 0 / μ 0 ) 1 / 2 .
F 1 F 2 = n 2 ( 0 / μ 0 )
1 2 [ E ( ρ ) × H * ( ρ ) ] e z dxdy = P δ ( ρ ρ )
C j 2 = ρ 3 P π n 2 ω 0 β j = 1 , 2 .
ρ = ( n 2 k 2 β 2 ) 1 / 2 .

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