Abstract

We present theoretical and experimental results on an interference effect caused by boundary reflections on the optical scattering loss in high-index-contrast planar waveguides. Analytical expressions for the polarization-dependent scattering loss are derived using a surface Green’s function. For high-index-contrast waveguides of submicrometer dimensions a significant deviation from accepted theory arises, including scattering loss suppression owing to a thin-film interference effect. Our theoretical predictions are confirmed by loss measurements on silicon-on-insulator channel waveguides.

© 2008 Optical Society of America

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References

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  1. D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969).
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2005 (1)

1998 (1)

1990 (2)

J. P. R. Lacey and F. P. Payne, IEE Proc.-J: Optoelectron. 137, 282 (1990).
[CrossRef]

C. Martijn de Sterke and J. E. Sipe, J. Opt. Soc. Am. A 7, 636 (1990).
[CrossRef]

1987 (1)

1969 (1)

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

Bell Syst. Tech. J. (1)

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

IEE Proc.-J: Optoelectron. (1)

J. P. R. Lacey and F. P. Payne, IEE Proc.-J: Optoelectron. 137, 282 (1990).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

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Figures (3)

Fig. 1
Fig. 1

Left, slab waveguide with a randomly rough surface profile s ( z ) with s max λ . Right, the roughness layer is modeled as a thin radiating sheet with a polarization P ( z ) proportional to the average susceptibility χ ¯ as defined in the text and the unperturbed mode field at the surface. Owing to the presence of the waveguide below, the scattered field E s above and below the slab is modified by thin-film interference.

Fig. 2
Fig. 2

Scattering loss of a silicon slab waveguide with SU-8 cladding according to a numerical integration of Eqs. (5, 6) compared with the PL result (valid for TE) for the roughness parameters indicated.

Fig. 3
Fig. 3

Experimental loss of 1.5 - mm -long Si waveguides as a function of the waveguide width compared with the theoretical result [Eqs. (5, 6), solid curves]. The dashed curves indicates simulated taper loss as explained in the text.

Equations (7)

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2 E + n 2 ( y ) k 0 2 E = 4 π k 0 2 P ,
P ( k z ) = ( n 2 2 n 1 2 ) 4 π s max s ̃ ( k z β ) ( x ̂ x ̂ + n 1 2 n 2 2 y ̂ y ̂ + z ̂ z ̂ ) E 0 ,
E ( y , k z ) = s max [ g + ( k z ) e i w ( k z ) y + r ( k z ) g ( k z ) e i w ( k z ) y ] P ( k z ) for y > d + s max ,
E ( y , k z ) = s max t ( k z ) g ( k z ) e i w ( k z ) ( y + d ) P ( k z ) for y < 0 .
g ± ( k z ) = 2 π i k 0 2 w ( k z ) [ s ̂ s ̂ + p ̂ ± ( k z ) p ̂ ± ( k z ) ] ,
α TE = k 0 3 4 π n eff ( n 2 2 n 1 2 ) 2 ( Φ 0 x ) 2 0 π ( ( 1 + r s ( θ ) ) 2 + t s 2 ( θ ) ) R ̃ ( β + n 1 k 0 cos θ ) d θ ,
α TM = ( n eff k 0 3 4 π ( n 2 2 n 1 2 ) 2 b ) 0 π ( n 1 2 n 2 2 E 0 y ( 1 + r p ) cos θ E 0 z ( 1 r p ) sin θ 2 + n 1 2 n 2 2 E 0 y t p cos θ + E 0 z t p sin θ 2 ) R ̃ ( β + n 1 k 0 cos θ ) d θ ,

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