Predicting macrobending loss for large-mode area photonic crystal fibers

M. D. Nielsen; N. A. Mortensen; M. Albertsen; J. R. Folkenberg; A. Bjarklev; D. Bonacinni

doi:10.1364/OPEX.12.001775

Optics Express
Vol. 12,
Issue 8,
pp. 1775-1779
(2004)
•https://doi.org/10.1364/OPEX.12.001775

Predicting macrobending loss for large-mode area photonic crystal fibers

M. D. Nielsen, N. A. Mortensen, M. Albertsen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni

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M. D. Nielsen, N. A. Mortensen, M. Albertsen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, "Predicting macrobending loss for large-mode area photonic crystal fibers," Opt. Express 12, 1775-1779 (2004)

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Abstract

We report on an easy-to-evaluate expression for the prediction of the bend-loss for a large mode area photonic crystal fiber (PCF) with a triangular air-hole lattice. The expression is based on a recently proposed formulation of the V-parameter for a PCF and contains no free parameters. The validity of the expression is verified experimentally for varying fiber parameters as well as bend radius. The typical deviation between the position of the measured and the predicted bend loss edge is within measurement uncertainty.

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Fig. 1. Structural data for the LMA fibers which all have a cross-section with a triangular arrangement of air-holes running along the full length of the fiber.

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Fig. 2. Macro-bending loss for the LMA-20 fiber for bending radii of R=8 cm (red, solid curve) and R=16 cm (black, solid curve). Predictions of Eq. (1) are also included (dashed curves).

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Fig. 3. Macro-bending loss for the LMA-25 fiber for bending radius of R=16 cm (solid curve). Predictions of Eq. (1) are also included (dashed curve).

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Fig. 4. Macro-bending loss for the LMA-35 fiber for bending radius of R=16 cm (solid curve). Predictions of Eq. (1) are also included (dashed curve).

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Equations (6)

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α Λ ≃ \frac{1}{8 \sqrt{6 π}} \frac{1}{n_{S}} \frac{Λ^{2}}{A_{eff}} \frac{λ}{Λ} F ({\frac{1}{6 π^{2}} \frac{1}{n_{S}^{2}} \frac{R}{Λ} (\frac{λ}{Λ})}^{2} V_{PCF}^{3}), F (x) = x^{- 1 ⁄ 2} \exp (- x),

V_{PCF} = Λ \sqrt{β^{2} - β_{cl}^{2}}

\underset{~ 1 ⁄ 4}{\underset{︸}{π^{3} \frac{1}{6 π^{2}} \frac{1}{n_{S}^{2}}}} \frac{R^{*}}{Λ} {(\frac{λ}{Λ})}^{2} ~ 1 \Rightarrow R^{*} \propto \frac{Λ^{3}}{λ^{2}}

α = \frac{\sqrt{π}}{8} \frac{1}{A_{eff}} \frac{ρ}{W} \frac{\exp (- \frac{4}{3} \frac{R}{ρ} \frac{Δ}{V^{2}} W^{3})}{\sqrt{W \frac{R}{ρ} + \frac{V^{2}}{2 Δ W}}}

Δ = \frac{\sin^{2} θ_{c}}{2}, V = β ρ \sin θ_{c}, W = ρ \sqrt{β^{2} - β_{cl}^{2}} .

α Λ ≃ \frac{1}{8} \sqrt{\frac{2 π}{3}} \frac{Λ^{2}}{A_{eff}} \frac{1}{β Λ} F (\frac{2}{3} \frac{R}{Λ} \frac{V_{PCF}^{3}}{{(β Λ)}^{2}})

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