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The effects of randomly occurring nonuniformities on propagation in photonic crystal fibers

Kristen Lantz Reichenbach and Chris Xu

Open Access Open Access

Abstract

The effects of random imperfections in the lattice of a photonic crystal fiber on the propagation of the fundamental mode are analyzed using numerical simulations based on the multipole method. Lattice irregularities are shown to induce significant birefringence in fibers with large air holes but to cause a negligible increase in the confinement loss for low loss fibers. The dispersion is shown to be robust if the percentage of variation in the fiber parameters is less than 2% and the structure does not fall within a cutoff region. The coupling behavior in two-core structures with large air holes demonstrates high sensitivity to fiber nonuniformities. Understanding the discrepancies between the properties of simulated and fabricated fibers is an important step in leveraging the unique properties of PCFs.

©2005 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. An example of the geometry analyzed including definitions of important parameters and variations.

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Fig. 2.
Fig. 2. The calculated birefringence for two different fibers with Λo=2.5 µm and λ=1.55 µm: (a) do=2.25 µm therefore do/Λo=0.90 and (b) do=1.75 µm therefore do/Λo=0.70. Markers indicate the average birefringence for a data set of 30 random structures for each percentage variation and each type of variation, while the bars represent the spread or standard deviation. The fit is linear. Insets display the fundamental mode for the fibers calculated.

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Fig. 3.
Fig. 3. Loss plotted versus the percentage variation; the solid line is the predicted loss for the structure with a perfect lattice. The markers represent the values for the loss calculated from 30 random structures for each percentage variation and type of variation. The X indicates the average loss for the data set. Inset is an image of the fundamental mode of the fiber with Λo=2.5 µm and do=2.25 µm, λ=1.55 µm.

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Fig. 4.
Fig. 4. The two zero dispersion wavelengths for a fiber with do/Λo=0.70 and Λo=0.8 µm are plotted versus percentage variation. The markers indicate the values calculated for 30 randomly generated structures for each percentage variation and for two types of variations. The X represents the mean of the data and the solid line indicates the value for the perfect structure. The insets display the fundamental mode for the fiber at the respective wavelength.

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Fig. 5.
Fig. 5. The markers represent the calculated beat lengths for the x and y polarizations in (a) and (b), respectively; the X indicates the average for the data set. The solid lines are the predicted values for the structure with a perfect lattice. 30 random structures were simulated for each percentage variation for each type of variation. The inset in (a) displays the fundamental mode for the fiber calculated with Λo=2.5 µm and do=2.25 µm, therefore do/Λo=0.90, and λ=1.55 µm.

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Fig. 6.
Fig. 6. The beat lengths for the x and y polarizations are plotted versus percentage variation for two fibers when λ=1.55 µm: for (a) and (b), do=1.75 µm and do/Λo=0.70, while for (c) and (d), do=1.45 µm and do/Λo=0.58. The solid lines are the predicted values for the structure with a perfect lattice. The markers represent the calculated values for the coupling length while the X indicates the average for the data set; 30 random structures were simulated for each percentage variation for each type of variation. Insets display the fundamental mode for the fiber calculated.

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Tables (1)

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Table 1. Summary of the fiber structures used in the two-core simulations

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Equations (2)

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Loss ( d B ⁄ k m ) = 20 ln ( 10 ) 2 π λ ℑ ( n eff ) × 10 9 ,
D = − λ c ∂ 2 n eff ∂ λ 2
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