Abstract

The scattering of optical guided waves by waveguide surface roughness has been analyzed in three dimensions. The scattered fields were determined by satisfying the boundary conditions to first order in the height of the surface roughness. The utility of the theory for practical problems is illustrated by developing explicit formulas for the power radiated by a TE guided wave into the medium above the planar waveguide. These formulas are expressed in terms of the surface autocorrelation function.

© 1981 Optical Society of America

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References

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  1. A recent review was given by J. M. Elson, J. M. Bennett, “Vector scattering theory,” Opt. Eng. 18, 116 (1979).
  2. J. T. Boyd, D. B. Anderson, “Effect of waveguide optical scattering on the integrated optical spectrum analyzer dynamic range,” IEEE J. Quantum Electron. QE-14, 437 (1978).
    [CrossRef]
  3. D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell. Syst. Tech. J. 48, 3187 (1969).
  4. Y. Suematsu, K. Furuya, M. Hakuta, K. Chiba, “Farfield radiation pattern caused by random wall distortion of dielectric waveguides and determination of correlation length,” Electron. Commun. Jpn. 56-C, 62 (1973).
  5. D. G. Hall, “Comparison of two approaches to the waveguide scattering problem,” Appl. Opt. 19, 1732 (1980).
    [CrossRef] [PubMed]
  6. E. Kröger, E. Kretschmann, “Scattering of light by slightly rough films including plasma resonance emission,” Z. Phys. 237, 1 (1970).
    [CrossRef]
  7. J. M. Elson, J. M. Bennett, “Relation between the angular dependence of scattering of the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31 (1979).
    [CrossRef]
  8. See, for example, H. Kogelnik, “Theory of dielectric waveguides” in Integrated Optics, T. Tamir, ed. (Springer-Verlag, New York, 1979), p. 47.

1980 (1)

1979 (2)

1978 (1)

J. T. Boyd, D. B. Anderson, “Effect of waveguide optical scattering on the integrated optical spectrum analyzer dynamic range,” IEEE J. Quantum Electron. QE-14, 437 (1978).
[CrossRef]

1973 (1)

Y. Suematsu, K. Furuya, M. Hakuta, K. Chiba, “Farfield radiation pattern caused by random wall distortion of dielectric waveguides and determination of correlation length,” Electron. Commun. Jpn. 56-C, 62 (1973).

1970 (1)

E. Kröger, E. Kretschmann, “Scattering of light by slightly rough films including plasma resonance emission,” Z. Phys. 237, 1 (1970).
[CrossRef]

1969 (1)

D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell. Syst. Tech. J. 48, 3187 (1969).

Anderson, D. B.

J. T. Boyd, D. B. Anderson, “Effect of waveguide optical scattering on the integrated optical spectrum analyzer dynamic range,” IEEE J. Quantum Electron. QE-14, 437 (1978).
[CrossRef]

Bennett, J. M.

Boyd, J. T.

J. T. Boyd, D. B. Anderson, “Effect of waveguide optical scattering on the integrated optical spectrum analyzer dynamic range,” IEEE J. Quantum Electron. QE-14, 437 (1978).
[CrossRef]

Chiba, K.

Y. Suematsu, K. Furuya, M. Hakuta, K. Chiba, “Farfield radiation pattern caused by random wall distortion of dielectric waveguides and determination of correlation length,” Electron. Commun. Jpn. 56-C, 62 (1973).

Elson, J. M.

Furuya, K.

Y. Suematsu, K. Furuya, M. Hakuta, K. Chiba, “Farfield radiation pattern caused by random wall distortion of dielectric waveguides and determination of correlation length,” Electron. Commun. Jpn. 56-C, 62 (1973).

Hakuta, M.

Y. Suematsu, K. Furuya, M. Hakuta, K. Chiba, “Farfield radiation pattern caused by random wall distortion of dielectric waveguides and determination of correlation length,” Electron. Commun. Jpn. 56-C, 62 (1973).

Hall, D. G.

Kogelnik, H.

See, for example, H. Kogelnik, “Theory of dielectric waveguides” in Integrated Optics, T. Tamir, ed. (Springer-Verlag, New York, 1979), p. 47.

Kretschmann, E.

E. Kröger, E. Kretschmann, “Scattering of light by slightly rough films including plasma resonance emission,” Z. Phys. 237, 1 (1970).
[CrossRef]

Kröger, E.

E. Kröger, E. Kretschmann, “Scattering of light by slightly rough films including plasma resonance emission,” Z. Phys. 237, 1 (1970).
[CrossRef]

Marcuse, D.

D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell. Syst. Tech. J. 48, 3187 (1969).

Suematsu, Y.

Y. Suematsu, K. Furuya, M. Hakuta, K. Chiba, “Farfield radiation pattern caused by random wall distortion of dielectric waveguides and determination of correlation length,” Electron. Commun. Jpn. 56-C, 62 (1973).

Appl. Opt. (1)

Bell. Syst. Tech. J. (1)

D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell. Syst. Tech. J. 48, 3187 (1969).

Electron. Commun. Jpn. (1)

Y. Suematsu, K. Furuya, M. Hakuta, K. Chiba, “Farfield radiation pattern caused by random wall distortion of dielectric waveguides and determination of correlation length,” Electron. Commun. Jpn. 56-C, 62 (1973).

IEEE J. Quantum Electron. (1)

J. T. Boyd, D. B. Anderson, “Effect of waveguide optical scattering on the integrated optical spectrum analyzer dynamic range,” IEEE J. Quantum Electron. QE-14, 437 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

A recent review was given by J. M. Elson, J. M. Bennett, “Vector scattering theory,” Opt. Eng. 18, 116 (1979).

Z. Phys. (1)

E. Kröger, E. Kretschmann, “Scattering of light by slightly rough films including plasma resonance emission,” Z. Phys. 237, 1 (1970).
[CrossRef]

Other (1)

See, for example, H. Kogelnik, “Theory of dielectric waveguides” in Integrated Optics, T. Tamir, ed. (Springer-Verlag, New York, 1979), p. 47.

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Figures (3)

Fig. 1
Fig. 1

Geometry for the calculation.

Fig. 2
Fig. 2

Optical factors V(α, ϕ = 0°) and V(α, ϕ = 90°). ϕ = 0° corresponds to the xy plane; ϕ = 90° corresponds to the xz plane. Parameter values are given in the text.

Fig. 3
Fig. 3

Normalized radiation patterns for ϕ = 0° and ϕ = 90°. These plots were constructed using V(α, ϕ) from Fig. 2 and a Gaussian autocorrelation function with σ = 0.5 μm.

Equations (22)

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x = h + η ζ ( y , z ) ,
A I = A i I + n = 1 η n A s n I , x > h ,
A II = A i II + n = 1 η n A s n II , 0 x , h ,
A III = A i III + n = 1 η n A s n III , x 0 .
n ̂ = [ 1 + ( η ζ y ) 2 + ( η ζ y ) 2 ] 1 / 2 ( x ̂ y ̂ η ζ y z ̂ η ζ z ) .
A i I | x = h = A i II | x = h ,
A i I x | x = h = A i II x | x = h ,
x ̂ × ( A s 1 I A s 1 II ) | x = h = 0 ,
x ̂ × ( × A s 1 I × A s 1 II ) | x = h = ζ ( y , z ) y ̂ ( 2 A i II x 2 | x = h 2 A i I x 2 | x = h ) ,
A i II | x = 0 = A i III | x = 0 ,
A i II x | x = 0 = A i III x | x = 0 ,
x ̂ × ( A s 1 II A s 1 III ) | x = 0 = 0 ,
x ̂ × ( × A s 1 II × A s 1 III ) | x = 0 = 0 ,
A s 1 I ( x , y , z ) = ( 1 2 π ) 2 Q ( q ) e i q c x e i q · R d q y d q z ,
A s 1 II ( x , y , z ) = ( 1 2 π ) 2 [ R ( q ) e i q f x + S ( q ) e i q f x ] e i q · R d q y d q z ,
A s 1 III ( x , y , z ) = ( 1 2 π ) 2 T ( q ) e i q s x e i q · R d q y d q z ,
A I ( r , α , ϕ ) = η k 0 2 π r sin ( α ) Q ( q y , q z ) exp [ i ( k 0 r π / 2 ) ] ,
d P d Ω = δ 2 λ 4 V ( α , ϕ ) g ( q y , q z β ) ,
V ( α , ϕ ) = 8 π 2 ( n f 2 N 2 ) ( n f 2 1 ) υ g N h eff | V 1 ( α , ϕ ) V 2 ( α , ϕ ) | 2 ,
V 1 ( α , ϕ = 0 ° ) = 2 π q f q c ( 1 + q y 2 / q c 2 ) 1 / 2 λ ( q f q c ) ( q y 2 q f q c ) sin ( α ) × [ e i q f h ( q f + q s q f q s ) ( q y 2 + q f q s q y 2 q f q s ) e i q f h ] ,
V 2 ( α , ϕ = 0 ° ) = e i q f h ( q f + q c q f q c ) ( q y 2 + q f q c q y 2 q f q c ) × ( q f + q s q f q s ) ( q y 2 + q f q s q y 2 q f q s ) e i q f h ,
g ( q y , β q z ) = π 2 σ 2 exp { [ q y 2 + ( β q z ) 2 ] σ 2 / 4 } ,

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