Abstract

The angular distribution of the radiation emitted into the far field by TE0 and TM0 optical guided waves was measured and compared with a theory assuming surface roughness to be the source of the scattering. The comparison with theory was made in such a way that a detailed knowledge of the surface under investigation was not required.

© 1982 Optical Society of America

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References

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  1. D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell Syst. Tech. J. 48, 3187 (1969).
  2. G. B. Brandt, “In-plane scattering in glass and niobium oxide waveguides,” Opt. Eng. 20, 150 (1981).
  3. D. W. Vahey, “In-plane scattering in LiNbO3 waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 176, 62 (1979).
  4. F. K. Hopkins, H. E. Jackson, J. T. Boyd, “In-plane scattering measurements in a planar optical waveguide by an integrated technique,” Appl. Opt. 20, 2761 (1981).
    [CrossRef]
  5. Y. Suematsu, K. Furuya, M. Hakuta, K. Chiba, “Far-field radiation pattern caused by random wall distortion of dielectric waveguides and determination of correlation length,” Electron. Commun. Jpn. 56-C, 62 (1973).
  6. M. Gottlieb, G. B. Brandt, J. J. Conroy, “Out-of-plane scattering in optical waveguides,” IEEE Trans. Circuits Syst. CAS-26, 1029 (1979).
    [CrossRef]
  7. T. L. Tsai, H. S. Tuan, “Reflection and scattering by a single groove in integrated optics,” IEEE J. Quantum Electron. QE-10, 326 (1974).
    [CrossRef]
  8. D. G. Hall, “Comparison of two approaches to the waveguide scattering problem,” Appl. Opt. 19, 1732 (1980).
    [CrossRef] [PubMed]
  9. D. J. Walter, J. Houghton, “Attenuation in thin film optical waveguides due to roughness-induced mode coupling,” Thin Solid Films 52, 461 (1978).
    [CrossRef]
  10. See, for example, J. M. Elson, J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31 (1979).
    [CrossRef]
  11. D. G. Hall, “Scattering of optical guided-waves by waveguide surface roughness: three-dimensional treatment,” Opt. Lett. 6, 601 (1981).
    [CrossRef] [PubMed]
  12. The waveguides were provided by J. K. Powers, D. A. Bryan of McDonnell Douglas Astronautics Company, St. Louis, Missouri.

1981 (3)

1980 (1)

1979 (3)

M. Gottlieb, G. B. Brandt, J. J. Conroy, “Out-of-plane scattering in optical waveguides,” IEEE Trans. Circuits Syst. CAS-26, 1029 (1979).
[CrossRef]

D. W. Vahey, “In-plane scattering in LiNbO3 waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 176, 62 (1979).

See, for example, J. M. Elson, J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31 (1979).
[CrossRef]

1978 (1)

D. J. Walter, J. Houghton, “Attenuation in thin film optical waveguides due to roughness-induced mode coupling,” Thin Solid Films 52, 461 (1978).
[CrossRef]

1974 (1)

T. L. Tsai, H. S. Tuan, “Reflection and scattering by a single groove in integrated optics,” IEEE J. Quantum Electron. QE-10, 326 (1974).
[CrossRef]

1973 (1)

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

1969 (1)

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

Bennett, J. M.

Boyd, J. T.

Brandt, G. B.

G. B. Brandt, “In-plane scattering in glass and niobium oxide waveguides,” Opt. Eng. 20, 150 (1981).

M. Gottlieb, G. B. Brandt, J. J. Conroy, “Out-of-plane scattering in optical waveguides,” IEEE Trans. Circuits Syst. CAS-26, 1029 (1979).
[CrossRef]

Bryan, D. A.

The waveguides were provided by J. K. Powers, D. A. Bryan of McDonnell Douglas Astronautics Company, St. Louis, Missouri.

Chiba, K.

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

Conroy, J. J.

M. Gottlieb, G. B. Brandt, J. J. Conroy, “Out-of-plane scattering in optical waveguides,” IEEE Trans. Circuits Syst. CAS-26, 1029 (1979).
[CrossRef]

Elson, J. M.

Furuya, K.

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

Gottlieb, M.

M. Gottlieb, G. B. Brandt, J. J. Conroy, “Out-of-plane scattering in optical waveguides,” IEEE Trans. Circuits Syst. CAS-26, 1029 (1979).
[CrossRef]

Hakuta, M.

Y. Suematsu, K. Furuya, M. Hakuta, K. Chiba, “Far-field 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.

Hopkins, F. K.

Houghton, J.

D. J. Walter, J. Houghton, “Attenuation in thin film optical waveguides due to roughness-induced mode coupling,” Thin Solid Films 52, 461 (1978).
[CrossRef]

Jackson, H. E.

Marcuse, D.

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

Powers, J. K.

The waveguides were provided by J. K. Powers, D. A. Bryan of McDonnell Douglas Astronautics Company, St. Louis, Missouri.

Suematsu, Y.

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

Tsai, T. L.

T. L. Tsai, H. S. Tuan, “Reflection and scattering by a single groove in integrated optics,” IEEE J. Quantum Electron. QE-10, 326 (1974).
[CrossRef]

Tuan, H. S.

T. L. Tsai, H. S. Tuan, “Reflection and scattering by a single groove in integrated optics,” IEEE J. Quantum Electron. QE-10, 326 (1974).
[CrossRef]

Vahey, D. W.

D. W. Vahey, “In-plane scattering in LiNbO3 waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 176, 62 (1979).

Walter, D. J.

D. J. Walter, J. Houghton, “Attenuation in thin film optical waveguides due to roughness-induced mode coupling,” Thin Solid Films 52, 461 (1978).
[CrossRef]

Appl. Opt. (2)

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, “Far-field 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)

T. L. Tsai, H. S. Tuan, “Reflection and scattering by a single groove in integrated optics,” IEEE J. Quantum Electron. QE-10, 326 (1974).
[CrossRef]

IEEE Trans. Circuits Syst. (1)

M. Gottlieb, G. B. Brandt, J. J. Conroy, “Out-of-plane scattering in optical waveguides,” IEEE Trans. Circuits Syst. CAS-26, 1029 (1979).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

G. B. Brandt, “In-plane scattering in glass and niobium oxide waveguides,” Opt. Eng. 20, 150 (1981).

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

D. W. Vahey, “In-plane scattering in LiNbO3 waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 176, 62 (1979).

Thin Solid Films (1)

D. J. Walter, J. Houghton, “Attenuation in thin film optical waveguides due to roughness-induced mode coupling,” Thin Solid Films 52, 461 (1978).
[CrossRef]

Other (1)

The waveguides were provided by J. K. Powers, D. A. Bryan of McDonnell Douglas Astronautics Company, St. Louis, Missouri.

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Figures (4)

Fig. 1
Fig. 1

Geometry for the calculation.

Fig. 2
Fig. 2

Measured radiation patterns P(θ) from TE0 and TM0 guided waves. The peak intensity has been normalized to unity in each case.

Fig. 3
Fig. 3

Surface function g(βk0 cos θ) obtained from the data of Fig. 2 using Eqs. (6) and (8).

Fig. 4
Fig. 4

Surface function g(βk0 cos θ) obtained from data taken at a different location on the same waveguide as that used for Fig. 2. This result represents the case of worst agreement for all locations analyzed.

Equations (13)

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x = h [ 1 + η f ( z ) ] ,
E y j = E y i j + m = 1 η m E s m j ,
E y I | B = E y II | B
n ˆ · E y I | B = n ˆ · E y II | B ,
n ˆ · = [ 1 + ( η h d f d z ) 2 ] 1 / 2 ( x η h d f d z z ) .
P TE ( θ ) = N 1 A TE ( θ ) g ( β TE cos θ ) ,
A TE ( θ ) = | [ cos ( ξ f h ) i ( ξ s / ξ f ) sin ( ξ f h ) ] sin θ ( ξ c + ξ s ) cos ( ξ f h ) [ 1 i ξ f 2 + ξ c ξ s ξ f ξ c + ξ f ξ s tan ( ξ f h ) ] | 2 ,
ξ f = k 0 ( n f 2 cos 2 θ ) 1 / 2 , ξ s = k 0 ( n s 2 cos 2 θ ) 1 / 2 ,
P TM ( θ ) = N 2 A TM ( θ ) g ( β TM k 0 cos θ ) ,
A TM ( θ ) = | ( α f ξ c ) 1 ( A 1 A 2 A 3 ) sin θ | 2 ,
A 1 = α f ( α f α s ) exp ( i ξ f h ) i ( α f 2 + ξ c α s ) sin ( ξ f h ) ( ξ c α f + α s α f ) cos ( ξ f h ) ,
A 2 = ( β k 0 / n f 2 ) cos θ i ξ c ( β 2 k 0 2 ) 1 / 2 ,
A 3 = ( β k 0 / n f 2 ) cos θ + i α f ( β 2 k 0 2 ) 1 / 2 ,

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