Abstract

A simple formalism to estimate modal power loss coefficients for an overmoded rectangular waveguide with rough surfaces is presented. The method is based on small index differences where the true radiation modes are approximated by free space modes. Loss coefficients are important in order to establish more accurate channel models for, e.g., optical backplane communication systems. The theory is validated by comparing the loss coefficients of a squeezed rectangular waveguide with the loss coefficients of a slab waveguide.

© 2004 Optical Society of America

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References

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    [CrossRef]
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  8. D. Lenz, B. Rankov, D. Erni,W. Bächtold, and A.Wittneben, �??MIMO Channel for Modal Multiplexing in Highly Overmoded Optical Waveguides,�?? in International Zurich Seminar on Communications, pp. 196 (Zurich, 2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

Appl. Opt.

Bell Syst. Tech. J.

E. Marcatili, �??Dielectric Rectangular Waveguide and Directional Coupler for Integrated Optics,�?? Bell Syst. Tech. J. 48, 2071�??2103 (1969).

IEE Proc.

J. Lacey and F. Payne, �??Radiation loss from planar waveguides with random wall imperfections,�?? IEE Proc. 137, 282�??288 (1990).

IEE Proc. Optoelectron.

F. Ladouceur, F. Love, and T. Senden, �??Effect of side wall roughness in buried channel waveguides,�?? IEE Proc. Optoelectron. 141, 242�??48 (1994).
[CrossRef]

IEEE J. Quantum Electron.

Z. Wang, �??Free Space Mode Approximation of Radiation Modes for Weakly Guiding Planar Optical Waveguides,�?? IEEE J. Quantum Electron. 34, 680�??685 (1998).
[CrossRef]

IZS 2004

D. Lenz, B. Rankov, D. Erni,W. Bächtold, and A.Wittneben, �??MIMO Channel for Modal Multiplexing in Highly Overmoded Optical Waveguides,�?? in International Zurich Seminar on Communications, pp. 196 (Zurich, 2004).
[CrossRef]

J. Lightwave Technol.

A. S. Sudbø, �??Why Are Accurate Computations of Mode Fields in Rectangular DielectricWaveguides Difficult?�?? J. Lightwave Technol. 10, 418�??419 (1992).
[CrossRef]

S. Lee, D. Mui, and L. Coldren, �??Explicit Formulas of Normalized Radiation Modes in Multilayer Waveguides,�?? J. Lightwave Technol. 12, 2073�??2079 (1194).

Opt. Eng.

J. Moisel, J. Guttmann, H.-P. Huber, O. Krumpholz, M. Rode, R. Bogenberger, and K.-P. Kuhn, �??Optical backplanes with integrated polymer waveguides,�?? Opt. Eng. 39, 673�??679 (2000).
[CrossRef]

Other

D. Marcuse, Light Transmission Optics, 2nd ed. (Krieger, 1982).

D. Marcuse, Theory of Dielectric Optical Waveguides, Quantum Electronics-Principles and Applications, 2nd ed. (Academic Press, Boston, 1997).

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Figures (3)

Fig. 1.
Fig. 1.

Perturbed rectangular waveguide.

Fig. 2.
Fig. 2.

Simulation results in order to illustrate the applicability of the proposed method.

Fig. 3.
Fig. 3.

Radiation patterns for two different correlation lengths D with σ=4×10-9 using a Gaussian ACF (b=d=30 µm).

Equations (20)

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K μ , ρ = ω ε 0 4 i P ( n 2 n 0 2 ) ( E μ t * E ρ t + n 0 2 n 2 E μ z * E ρ z ) d x d y
K μ , ρ = ω ε 0 4 i P ( n 2 ( x , y , z ) n 0 2 ( x , y ) ) E μ x * E ρ x d x d y
α μ = { s = 1 4 K ̂ μ , ρ ( s ) ( κ , σ ) 2 F ( s ) ( β μ β ρ ) 2 } d κ d σ
F ( s ) ( β μ β ρ ) 2 = f ( s ) ( z ) f ( s ) ( z u ) exp [ i ( β μ β ρ ) u ] d u .
K ρ μ = ω ε 0 4 i P 0 b 0 f ( 1 ) ( z ) n f δ n ( n 1 n 2 ) 2 E ρ x * E μ x d x d y Integral I 1 + ω ε 0 4 i P f ( 2 ) ( z ) 0 0 d δ n E ρ x * E μ x d x d y Integral I 2
E μ x = a ( μ ) sin [ k x ( μ ) ( x + ξ ( μ ) ) ] cos [ k y ( μ ) ( y + η ( μ ) ) ] exp ( i β μ z )
P = 1 = 1 2 β μ ω μ 0 E μ x E μ x * d x d y .
E ρ x = u ( ρ ) exp [ i ( σ x + κ y + ρ z ) ] .
1 2 ε 0 ω β k 2 E ρ x ( σ , κ ) E ρ x * ( σ , κ ) d x d y = δ ( σ σ , κ κ )
I 1 = 0 b 0 f ( z ) δ n ( n 1 n 2 ) 2 E ρ x * E μ x d x d y
= δ n ( n 1 n 2 ) 2 u * ( ρ ) a ( μ )
× 0 f ( z ) exp ( i σ x ) sin [ k x ( μ ) ( x + ξ ( μ ) ) ] d x 0 b exp ( i κ y ) cos [ k y ( μ ) ( y + η ( μ ) ) ] d y χ ( k y , η , κ )
= δ n ( n 1 n 2 ) 2 u * ( ρ ) a ( μ ) sin ( k x ( μ ) ξ ( μ ) ) χ ( k y , η , κ ) f ( 1 ) ( z )
I 2 = δ n u * ( ρ ) a ( μ ) cos ( k y ( μ ) η ( μ ) ) ζ ( k x , σ , ξ ) ( f ( 2 ) ( z ) )
K ρ μ ( z ) = K ̂ ρ μ ( 1 ) f ( 1 ) ( z ) + K ̂ ρ μ ( 2 ) f ( 2 ) ( z )
K ̂ ρ μ ( 1 ) = ω ε 0 2 4 i P u * ( ρ ) a ( μ ) δ n ( n 1 n 2 ) 2 χ ( k y , η , κ ) sin ( k x ( μ ) ξ ( μ ) )
K ̂ ρ μ ( 2 ) = ω ε 0 2 4 i P u * ( ρ ) a ( μ ) δ n ζ ( k x , σ , ξ ) cos ( k y ( μ ) η ( μ ) )
χ ( k y , η , κ ) = 0 b exp ( i κ y ) cos [ k y ( μ ) ( y + η ( μ ) ) ] d y
ζ ( k x , σ , ξ ) = 0 d exp ( i σ x ) sin [ k x ( μ ) ( x + ξ ( μ ) ) ] d x
α tot = 1 10 z lg ( Σ P μ ( 0 ) Σ P μ ( 0 ) exp ( α μ z ) ) dB / cm

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