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References

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  1. D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969).
  2. J. T. Boyd, D. B. Anderson, IEEE J. Quantum Electron. QE-14, 437 (1979).
  3. D. Marcuse, Bell Syst. Tech. J. 48, 3233 (1969).
  4. T. L. Tsai, H. S. Tuan, IEEE J. Quantum Electron. QE-10, 326 (1974).
    [CrossRef]
  5. Y. M. Chen, J. Math. Phys. 9, 439 (1968).
    [CrossRef]
  6. J. M. Elson, Opt. Eng. 18, 116 (1979).
    [CrossRef]
  7. D. G. Hall, A. J. Braundmeier, Phys. Rev. B: 17, 1557 (1978).
    [CrossRef]
  8. J. M. Elson, Phys. Rev. B: 12, 2541 (1975).
    [CrossRef]
  9. E. Kretschmann, Opt. Commun. 5, 331 (1972).
    [CrossRef]

1979 (2)

J. T. Boyd, D. B. Anderson, IEEE J. Quantum Electron. QE-14, 437 (1979).

J. M. Elson, Opt. Eng. 18, 116 (1979).
[CrossRef]

1978 (1)

D. G. Hall, A. J. Braundmeier, Phys. Rev. B: 17, 1557 (1978).
[CrossRef]

1975 (1)

J. M. Elson, Phys. Rev. B: 12, 2541 (1975).
[CrossRef]

1974 (1)

T. L. Tsai, H. S. Tuan, IEEE J. Quantum Electron. QE-10, 326 (1974).
[CrossRef]

1972 (1)

E. Kretschmann, Opt. Commun. 5, 331 (1972).
[CrossRef]

1969 (2)

D. Marcuse, Bell Syst. Tech. J. 48, 3233 (1969).

D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969).

1968 (1)

Y. M. Chen, J. Math. Phys. 9, 439 (1968).
[CrossRef]

Anderson, D. B.

J. T. Boyd, D. B. Anderson, IEEE J. Quantum Electron. QE-14, 437 (1979).

Boyd, J. T.

J. T. Boyd, D. B. Anderson, IEEE J. Quantum Electron. QE-14, 437 (1979).

Braundmeier, A. J.

D. G. Hall, A. J. Braundmeier, Phys. Rev. B: 17, 1557 (1978).
[CrossRef]

Chen, Y. M.

Y. M. Chen, J. Math. Phys. 9, 439 (1968).
[CrossRef]

Elson, J. M.

J. M. Elson, Opt. Eng. 18, 116 (1979).
[CrossRef]

J. M. Elson, Phys. Rev. B: 12, 2541 (1975).
[CrossRef]

Hall, D. G.

D. G. Hall, A. J. Braundmeier, Phys. Rev. B: 17, 1557 (1978).
[CrossRef]

Kretschmann, E.

E. Kretschmann, Opt. Commun. 5, 331 (1972).
[CrossRef]

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 48, 3233 (1969).

D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969).

Tsai, T. L.

T. L. Tsai, H. S. Tuan, IEEE J. Quantum Electron. QE-10, 326 (1974).
[CrossRef]

Tuan, H. S.

T. L. Tsai, H. S. Tuan, IEEE J. Quantum Electron. QE-10, 326 (1974).
[CrossRef]

Bell Syst. Tech. J. (2)

D. Marcuse, Bell Syst. Tech. J. 48, 3233 (1969).

D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969).

IEEE J. Quantum Electron. (2)

J. T. Boyd, D. B. Anderson, IEEE J. Quantum Electron. QE-14, 437 (1979).

T. L. Tsai, H. S. Tuan, IEEE J. Quantum Electron. QE-10, 326 (1974).
[CrossRef]

J. Math. Phys. (1)

Y. M. Chen, J. Math. Phys. 9, 439 (1968).
[CrossRef]

Opt. Commun. (1)

E. Kretschmann, Opt. Commun. 5, 331 (1972).
[CrossRef]

Opt. Eng. (1)

J. M. Elson, Opt. Eng. 18, 116 (1979).
[CrossRef]

Phys. Rev. B (2)

D. G. Hall, A. J. Braundmeier, Phys. Rev. B: 17, 1557 (1978).
[CrossRef]

J. M. Elson, Phys. Rev. B: 12, 2541 (1975).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Normalized far-field radiation pattern from a symmetric waveguide with an irregular surface. Angle α is measured in the x-z plane from the forward direction, and the parameter values are 2d = 0.35 μm, λ = 0.84 μm, σ = 0.5 μm, and n0 = 1.5.

Fig. 2
Fig. 2

Normalized angular prefactor F(α) used in the calculation of the radiation pattern shown in Fig. 1.

Fig. 3
Fig. 3

Normalized angular prefactor F(α) for an asymmetric waveguide with the parameters n0 = 1.56, ns = 1.47, 2d = 0.35 μm, and λ = 0.84 μm.

Fig. 4
Fig. 4

Normalized far-field radiation pattern from an asymmetric waveguide with the same parameter values as those in the caption of Fig. 3. Note that the peak intensity is located near α = 24°, whereas that in Fig. 1 is near α = 16°.

Equations (19)

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2 E y x 2 + 2 E y z 2 + ( n 0 2 + Δ n 2 ) E y = 0 ,
E y = n C n ( z ) E n + 0 g ( ρ , z ) E ( ρ ) d ρ ,
g ( ρ , z ) = C ( ρ ) + D ( ρ ) exp ( 2 i β z ) + 1 2 i β × 0 { exp [ 2 i β ( z ζ ) ] 1 } G ( ρ , ζ ) d ζ ,
G ( ρ , z ) = β k 2 2 ω μ P [ n C n ( z ) E * ( ρ ) Δ n 2 E n d x + 0 d ρ g ( ρ , z ) E * ( ρ ) Δ n 2 E ( ρ ) d x ] ,
G ( ρ , z ) = β k 2 2 ω μ P E * ( ρ ) Δ n 2 E 0 d x ,
G ( ρ , z ) = β k 2 2 ω μ P ( n 0 2 1 ) [ f ( z ) d ] E * ( ρ , d , z ) E 0 ( d z ) .
| E y | 2 = [ k 3 ω μ P ( n 0 2 1 ) 2 cos 2 ( K 0 d ) π ( β 0 d + β 0 / γ 0 ) r ] F ( α ) | ϕ ( β 0 β ) | 2 ,
ϕ ( β 0 β ) = 0 L [ f ( z ) d ] exp [ i ( β 0 β ) z ] d z ,
F ( α ) = | sin ( α ) { sin ( α ) sin ( 2 kdq ) i q cos ( 2 kdq ) [ n 0 2 + sin 2 ( α ) cos 2 ( α ) ] sin ( 2 kdq ) 2 i q sin ( α ) cos ( 2 kdq ) } | 2 ,
x = d [ 1 + u ( z ) ] ,
E ys = n = 1 n E n ( x , z ) ,
( E y i + E y s ) I = ( E y i + E y s ) II ,
n ̂ ( E y i + E y s ) I = n ̂ ( E y i + E y s ) II ,
n ̂ = { 1 + [ d u ( z ) z ] 2 } 1 / 2 { x [ d u ( z ) z ] z } ,
E y = 2 d A k 2 ( n 0 2 1 ) cos ( K 0 d ) T ( β ) ϕ ( β 0 β ) × exp [ i ξ 0 ( x 2 d ) ] exp ( i β z d β ) ,
T ( β ) = cos ( 2 ξ 1 d ) i ( ξ 1 / ξ 0 ) sin ( 2 ξ 1 d ) 2 ξ 0 cos ( 2 ξ 1 d ) ( 1 / ξ 1 ) ( ξ 1 2 + ξ 0 2 ) sin ( 2 ξ 1 d ) .
| E y | 2 = [ k 3 ω μ P ( n 0 2 1 ) 2 cos 2 ( K 0 d ) π ( β 0 d + β 0 / γ 0 ) r ] F ( α ) | ϕ ( β 0 β ) | 2 ,
f ( z ) d = h exp ( z 2 / σ 2 ) ,
F ( α ) = | sin ( α ) { q cos ( 2 kdq ) i q s sin ( 2 kdq ) q [ sin ( α ) q s ] cos ( 2 kdq ) i [ q + q s sin ( α ) ] sin ( 2 kdq ) } | 2

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