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Ultimate low loss of hollow-core photonic crystal fibres

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell

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Abstract

Hollow-core photonic crystal fibres have excited interest as potential ultra-low loss telecommunications fibres because light propagates mainly in air instead of solid glass. We propose that the ultimate limit to the attenuation of such fibres is determined by surface roughness due to frozenin capillary waves. This is confirmed by measurements of the surface roughness in a HC-PCF, the angular distribution of the power scattered out of the core, and the wavelength dependence of the minimum loss of fibres drawn to different scales.

©2005 Optical Society of America

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Figures (5)
Fig. 1.
Fig. 1. (a) Scanning electron micrograph (SEM) of the 1.7 dB/km HC-PCF with a 20 µm diameter core (the 1.2 dB/km fibre discussed in the text was very similar), (b) a digitised representation used for modelling and (c) a similar but idealised structure with lower predicted loss.

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Fig. 2.
Fig. 2. (solid line) The roughness spectrum measured by AFM along a hole in a HC-PCF. The arrows identify artefacts due to electrical noise. (broken red lines) Roughness spectra calculated from Eq. (2) for three values of surface tension. (inset) SEM of the endface of the HC-PCF with a 19-cell core and an attenuation of 1.7 dB/km at 1565 nm wavelength.

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Fig. 3.
Fig. 3. The power P(n) per unit effective index n scattered from 5.5 mm of HC-PCF into fluid of index nf =1.449, as a function of n and of scatter angle θ. The solid grey curve is from measured data and the broken red curve is a fit to Eq. (5). The vertical origin is arbitrary. (inset) Schematic diagram of the experimental setup.

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Fig. 4.
Fig. 4. (solid orange curve) The low-loss part of the measured attenuation spectrum of a 7-cell HC-PCF, with a minimum of 700 dB/km at λc =550 nm. (left inset) Measured near-field pattern at the output of this fibre at 550 nm. (points) The minimum attenuation of similar HC-PCFs with various transverse scales, versus the wavelength λc of minimum attenuation. (broken red line) A straight-line fit to the points, having a slope of -3.07. (right inset) SEM of a representative of these HC-PCFs, with λc ≈1550 nm.

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Fig. 5.
Fig. 5. Modelled bulk (dotted red lines) and surface (broken blue lines) contributions to the net (solid lines) minimum attenuation of 19-cell HC-PCFs, based on actual and plausible attenuation values at 1620 nm wavelength under the assumptions described in the text. Corresponding values of fa are marked on the bulk attenuation curves.

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Equations (7)

Equations on this page are rendered with MathJax. Learn more.

S z ( κ ) = k B T g 4 π γ κ ,
S z ( κ ) = k B T g 4 π γ κ coth ( κ W 2 ) ,
κ = k ∣ n − n 0 ∣ ,
F = ( ε 0 μ 0 ) 1 ⁄ 2 ∮ hole perimeters dl ∣ E ∣ 2 ∫ cross − sec tion dA E × H * · z ̂ ,
α n ( n ) ∝ F ∣ n − n 0 ∣ ,
u 2 = k B T 4 π γ ( n − n 0 ) coth ( ( n − n 0 ) k W 2 ) δ n
α ( λ c ) ∝ 1 λ c 3 .
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