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Photonic crystal fiber design based on the V-parameter

Martin Dybendal Nielsen and Niels Asger Mortensen

Open Access Open Access

Abstract

Based on a recent formulation of the V–parameter of a photonic crystal fiber we provide numerically based empirical expressions for this quantity only dependent on the two structural parameters—the air hole diameter and the hole-to-hole center spacing. Based on the unique relation between the V–parameter and the equivalent mode field radius we identify how the parameter space for these fibers is restricted in order for the fibers to remain single mode while still having a guided mode confined to the core region.

©2003 Optical Society of America

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Figures (5)
Fig. 1.
Fig. 1. left panel shows V PCF calculated from Eq. (1) for d/Λ ranging from 0.20 (lowest curve) to 0.70 in steps of 0.05. The dashed line indicates V PCF=π. The right panel shows the relative equivalent mode-field radius, w PCF/Λ plotted as function of V PCF for each of the 9 curves in the left panel. The inset shows a schematic drawing of the considered PCF structure.

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Fig. 2.
Fig. 2. The left panel shows curves for constant values of V PCF in a normalized wavelength versus relative hole-size plot. The open circles indicate calculated data points with full lines to guide the eye. Similarly, the right panel shows curves for constant relative equivalent mode-field radius.

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Fig. 3.
Fig. 3. Plot of the parameter space in terms of relative hole size and normalized wavelength divided into three regions by the boundaries defined byV PCF=1 andV PCF=π. In the upper red area the mode penetrates deeply into the cladding region and in lower blue region the structure supports a higher-order mode.

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Fig. 4.
Fig. 4. Plot of V PCF as a function of relative wavelength λ/Λ for d/Λ ranging from 0.20 (lowest curve) to 0.80 in steps of 0.05.

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Fig. 5.
Fig. 5. Plot of V PCF in the λ→0 limit as function of the relative air hole size (open circles). The full red line represents a fit to the data points and the horizontal dash line indicated the ESM limit V PCF=π. The insert shows a close-up of the intersection with the vertical line indicating the air hole size d/Λ≃0.43.

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Equations (7)

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V PCF = 2 π Λ λ n FM 2 ( λ ) − n FSM 2 ( λ )
V PCF = Λ λ λ z c ( λ )
V PCF ( λ Λ , d Λ ) = A ( d Λ ) B ( d Λ ) × exp ⁡ [ C ( d Λ ) × λ Λ ] + 1
A ( d Λ ) = d Λ + 0.457 + 3.405 × d Λ 0.904 − d Λ
B ( d Λ ) = 0.200 × d Λ + 0.100 + 0.027 × ( 1.045 − d Λ ) − 2.8
C ( d Λ ) = 0.630 × exp ⁡ ( 0.755 0.171 + d Λ )
lim λ → 0 V PCF ( λ Λ , d Λ ) = A ( d Λ ) B ( d Λ ) + 1 = π .
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