Abstract

Surface roughness is normally considered to be the main cause of attenuation in intergrated-optics glass waveguides. Previous analyses have concentrated on scattering of light into the radiation field; in fact, depending on the roughness length scale, scattering can be predominantly in the backward direction, raising the question of how important the coupling with the backward-directed bound mode is. We investigate this effect and show that it can be neglected in most circumstances.

© 1996 Optical Society of America

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References

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  1. D. Marcuse, Bell Syst. Tech. J. 48, 3233 (1969).
  2. J. P. R. Lacey, F. P. Payne, Proc. Inst. Electr. Eng. Part J 137, 282 (1990).
  3. F. Ladouceur, J. D. Love, T. J. Senden, Proc. Inst. Electr. Eng. Part J 141, 242 (1994).
  4. L. H. Koopmans, The Spectral Analysis of Time Series (Academic, New York, 1974).
  5. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  6. F. Ladouceur, J. D. Love, Silica Based Buried Channel Waveguides and Devices (Chapman & Hall, London, 1995).

1994 (1)

F. Ladouceur, J. D. Love, T. J. Senden, Proc. Inst. Electr. Eng. Part J 141, 242 (1994).

1990 (1)

J. P. R. Lacey, F. P. Payne, Proc. Inst. Electr. Eng. Part J 137, 282 (1990).

1969 (1)

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

Koopmans, L. H.

L. H. Koopmans, The Spectral Analysis of Time Series (Academic, New York, 1974).

Lacey, J. P. R.

J. P. R. Lacey, F. P. Payne, Proc. Inst. Electr. Eng. Part J 137, 282 (1990).

Ladouceur, F.

F. Ladouceur, J. D. Love, T. J. Senden, Proc. Inst. Electr. Eng. Part J 141, 242 (1994).

F. Ladouceur, J. D. Love, Silica Based Buried Channel Waveguides and Devices (Chapman & Hall, London, 1995).

Love, J. D.

F. Ladouceur, J. D. Love, T. J. Senden, Proc. Inst. Electr. Eng. Part J 141, 242 (1994).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

F. Ladouceur, J. D. Love, Silica Based Buried Channel Waveguides and Devices (Chapman & Hall, London, 1995).

Marcuse, D.

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

Payne, F. P.

J. P. R. Lacey, F. P. Payne, Proc. Inst. Electr. Eng. Part J 137, 282 (1990).

Senden, T. J.

F. Ladouceur, J. D. Love, T. J. Senden, Proc. Inst. Electr. Eng. Part J 141, 242 (1994).

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Bell Syst. Tech. J. (1)

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

Proc. Inst. Electr. Eng. Part J (2)

J. P. R. Lacey, F. P. Payne, Proc. Inst. Electr. Eng. Part J 137, 282 (1990).

F. Ladouceur, J. D. Love, T. J. Senden, Proc. Inst. Electr. Eng. Part J 141, 242 (1994).

Other (3)

L. H. Koopmans, The Spectral Analysis of Time Series (Academic, New York, 1974).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

F. Ladouceur, J. D. Love, Silica Based Buried Channel Waveguides and Devices (Chapman & Hall, London, 1995).

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Figures (3)

Fig. 1
Fig. 1

Typical experimental measurements of surface roughness along the vertical core/cladding interface of a silica-based waveguide. The curve denotes the deviation from the mean core position of the BCW, denoted by the straight line.

Fig. 2
Fig. 2

Schematic representation of a slab waveguide with roughness present on a distance L. nco and ncl are the core and the cladding indices, respectively, and a+(z) and a(z) are the amplitudes of forward- and the backward-traveling modes.

Fig. 3
Fig. 3

Attenuation coefficient γ calculated from Eq. (14) in decibels per centimeter that is due to backreflection as a function of correlation length Lc. The parameters used here were nco = 1.45, ncl = 1.447, ρ = 5.0 μm, λ = 1.55 μm, and δρ = 0.1 μm.

Equations (14)

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C f ( u ) = δ f 2 exp ( - u / L c ) ,
S f ( σ ) = - + d u C f ( u ) exp ( i σ u ) .
β - k n cl < σ < β + k n cl ,
σ = β - k n cl cos θ .
d a ± ( z ) d z ± i β a ± ( z ) = ± i K ( z ) a ( z ) ,
a - ( 0 ) = - 0 L d z K ( z ) exp ( 2 i β z ) .
R = 0 L d z 0 L d z C K ( z - z ) exp [ 2 i β ( z - z ) ] ,
R = L - 2 L 2 L d x C K ( x ) exp ( 2 i β x ) ,
γ = S ( 2 β ) .
K ( z ) = k 2 n co - + d x [ n 2 ( x , z ) - n - 2 ( x , z ) ] ψ 2 ( x ) ,
n 2 ( x , z ) - n - 2 ( x , z ) ( n co 2 - n cl 2 ) f ( z ) δ ( x - ρ ) .
K ( z ) = f ( z ) [ U 2 W 2 ρ 3 β ( 1 + W ) ] ,
C K ( z - z ) = [ U 2 W 2 ρ 3 β ( 1 + W ) ] 2 C f ( z - z ) .
γ = [ U 2 W 2 ρ 3 β ( 1 + W ) ] 2 δ f 2 L c π 1 1 + 4 β 2 L c 2 .

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