Abstract

Photonic crystal fibers are well-known to offer a number of unusual properties, including supercontinuum generation, large mode-areas and controllable dispersion behavior. Their manufacturability would be enhanced by a more detailed understanding of how small perturbations in the fiber’s geometric structure cause variations in the fiber’s fundamental modes. In this paper, we demonstrate that such sensitivity analysis is feasible using highly accurate boundary integral techniques.

© 2004 Optical Society of America

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References

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IEEE Photonics Technology Letters (1)

T.P. Hansen, J. Broeng, S.E.B. Libori, E. Knudsen, A. Bjarklev, J.R. Jensen and H. Simonsen, �??Highly birefringent index-guiding photonic crystal fibers,�?? IEEE Photonics Technology Letters 13, 588-90 (2001).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Express (3)

Science (1)

P.S.J. Russel, �??Photonic crystal fibers,�?? Science 299, 358-362 (2003)
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Quadrature points for the test problem. Each hole has 32 quadrature points. Selected holes are labelled for later reference. Pitch is Λ and hole diameters are 0.7Λ.

Fig. 2.
Fig. 2.

Convergence analysis for the model problem. The vertical axis is absolute value of the difference compared to the calculated result with 40 quadrature points per hole.

Tables (6)

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Table 1. Effective indices for the two modes of interest for the wavelength λ = 1.1 Λ.

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Table 2. Finite difference calculation of third derivative of effective indices with respect to diameter of holes 1 and 11.

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Table 3. Sensitivity of modal effective indices to the diameters of individual holes. Only two significant figures are shown, although the real parts are known more accurately. The units of the derivative are Λ-1.

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Table 4. Sensitivity of modal effective indices to the x-coordinate of individual holes. Only two significant figures are shown, although the real parts are known more accurately. The units of the derivative are Λ-1.

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Table 5. Sensitivity of modal effective indices to the y-coordinate of individual holes. Only two significant figures are shown, although the real parts are known more accurately. The units of the derivative are Λ-1.

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Table 6. Sensitivity of modal effective indices to the oblateness of individual holes. Only two significant figures are shown, although the real parts are known more accurately. The derivative is dimensionless.

Equations (4)

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L = 20 ln ( 10 ) · 2 π λ · ( n eff ) · 10 9 ,
n ( x + h ) n ( x h ) 2 h n x + 1 6 3 n x 3 h 2 + ε h +
d 1 0.7 Λ ~ 2 n d 1 2 n d 1 2 .
( x x 0 ) 2 ( 1 + ε ) 2 + ( y y 0 ) 2 ( 1 + ε ) 2 = r 0 2 .

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