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Simple geometric criterion to predict the existence of surface modes in air-core photonic-bandgap fibers

Michel J. F. Digonnet, Hyang Kyun Kim, Jonghwa Shin, Shanhui Fan, and Gordon S. Kino

Open Access Open Access

Abstract

We propose a simple geometric criterion based on the size of the core relative to the photonic crystal to quickly determine whether an air-core photonic-bandgap fiber with a given geometry supports surface modes. Comparison to computer simulations show that when applied to fibers with a triangular-pattern cladding and a circular air core, this criterion accurately predicts the existence of a finite number of discrete ranges of core radii that support no surface modes. This valuable tool obviates the need for time-consuming and costly simulations, and it can be easily applied to fibers with an arbitrary photonic-crystal structure and core profile.

©2004 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. (a) Example of a surface mode calculated for a triangular-pattern PBF with an air hole radius ρ = 0.47Λ and a core radius of 1.15 Λ, and (b) the highest frequency bulk mode of the same fiber in the absence of core. Both were calculated at kz Λ/2π= 1.7.

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Fig. 2.
Fig. 2. Example of a circular core (a) that intersects corners of the photonic-crystal cladding (surface modes expected), and (b) that intersects only membranes of the photonic crystal (no surface modes expected).

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Fig. 3.
Fig. 3. Schematic of the rod (small black circle) inscribed within a corner of a photonic-crystal cladding (larger open circles), drawn for ρ = 0.47Λ.

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Fig. 4.
Fig. 4. The gray regions represent the ranges of core radii that intersect rods, and thus support surface modes, and the white regions between them the surface-mode-free bands. See text for details.

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Fig. 5.
Fig. 5. Dependence of the number of surface modes on core radius predicted by numerical simulations (dashed curves with triangles) and by the proposed geometric criterion (solid curve).

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Fig. 6.
Fig. 6. Evolution of the surface-mode-free bands with increasing hole radius predicted by the geometric criterion.

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Tables (1)

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Table 1. Location of the 14 bands of core radii that support no surface modes in triangular PBFs with ρ = 0.47Λ (see text for details).

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