Abstract

A new algorithm for calculating the confinement loss of leaky modes in arbitrary fibre structures is presented within the scalar wave approximation. The algorithm uses a polar-coordinate Fourier decomposition method with adjustable boundary conditions (ABC-FDM) to model the outward radiating fields. Leaky modes are calculated for different examples of microstructured fibres with various shaped holes.

© 2002 Optical Society of America

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References

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J. Lightwave Technol. (3)

Opt. Lett. (3)

Optical Fiber Communications Conference (1)

T.M. Monro, K.M. Kiang, J.H. Lee, K. Frampton, Z. Yuso., R. Moore, J. Tucknott, D.W. Hewak, H.N. Rutt and D.J. Richardson,�??High nonlinearity extruded single-mode holey optical fibers�??in Optical Fiber Communications Conference 2002 PD-FA1.

Other (2)

C. A. J. Fletcher, Computational Galerkin Methods, (Springer Verlag, 1984).
[CrossRef]

A. W. Snyder and J. D. Love, Optical Waveguide Theory, (Chapman and Hall, 1983) p. 376.

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Figures (4)

Fig. 1.
Fig. 1.

Four different fibre structures investigated with the ABC-FDM. The structures are all to scale and the core radius in structure (a) is 1 micron.

Fig. 2.
Fig. 2.

(a)Fundamental and (b) first higher order mode of 3 hole structure shown in Fig 1(a). (c)Ring mode and (d) hollow core mode of the structure shown in Fig 1(d). The contours are equally spaced at 3 dB intervals. The color indicates phase. The radial phase variation reveals outward propagating waves associated with confinement loss.

Fig. 3.
Fig. 3.

(a) Comparison of leakage loss for 3 and 6 hole structures shown in Fig. 1(a) and (b) as a function of wavelength and air fraction f. (b) Similar comparison of leakage loss for 3 holes with outer radii r = 2.0 and 3.0 μm. (c) Effective index.

Fig. 4.
Fig. 4.

(a) Reconstruction of waveguide from computed solution of Fig. 2(a). (b) Reconstruction of hollow core waveguide from solution shown in Fig. 2(d). (c) Contour map of the same reconstruction as in (b). Dimensions are in microns.

Equations (10)

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2 ψ ( x , θ ) + V 2 ( x , θ ) ψ ( x , θ ) = W 2 ψ ( x , θ ) ,
ψ ( x , θ ) = m B m e imθ K m ( Wx ) .
ψ ( x , θ ) = m , n A mn ψ mn ( x , θ ) .
M μν mn A mn = W 2 N μν mn A mn .
M μν mn = ϕ μν 2 ψ mn + ϕ μν V 2 ( x , θ ) ψ mn ; N μν mn = ϕ μν ψ mn
ψ mn ( x , θ ) = e imθ [ sin ( nπx ) + α mn ( W ) + β mn ( W ) x ]
ϕ mn ( x , θ ) = e imθ sin ( nπx )
α mn ( W ) = δ m , 0 [ 1 + ( 1 ) n 1 W K 0 ( W ) K 0 ( W ) ] ,
β mn ( W ) = δ m , 0 + ( 1 δ m , 0 ) ( 1 ) n W K m ( W ) K m ( W ) K m ( W ) .
f g = 0 2 π 0 1 f ( x , θ ) * g ( x , θ ) dxdθ ,

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