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Hollow-core PCF for guidance in the mid to far infra-red

G. J. Pearce, J. M. Pottage, D. M. Bird, P. J. Roberts, J. C. Knight, and P. St.J. Russell

Open Access Open Access

Abstract

A major limitation to attaining low-loss single-mode guidance in hollow core photonic crystal fibre (PCF) is surface guided modes that are trapped in the core surround. This is particularly severe when high index (n > 2) glasses are used. By modelling a structure that has the characteristic features of a realistic fibre we show that, by tuning the thickness of the core wall, the influence of these ‘surface’ modes can be minimised. For a refractive index of 2.4 we predict power-in-air fractions of over 95% over a fractional bandwidth of ~ 5%, peaking at over 98%. The designs are appropriate for mid- to far-IR PCFs for which suitable glasses (e.g., tellurites and chalcogenides) have high refractive indices.

©2005 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. Core design of high-index PCF using geometrical shapes, showing air regions in grey (different shades of which are shown for clarity) and glass in white. For simplicity, only the unique 1 12 of the design is given; the remainder may be obtained by applying C 6v symmetry operations. The two large circles lie on the cladding lattice, and the radius s is chosen such that the corresponding circle touches arc A and line B. The adjustable parameters are the cladding hole radius r and the core wall thickness t, which is controlled by the radius R of the central hole; in this paper we consider a fixed hole radius r = 0.4Λ and vary R.

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Fig. 2.
Fig. 2. (a) An SEM image of a typical silica hollow-core fibre (fabricated by Blaze Photonics), and (b) the model design for high-index glass created using geometrical shapes. The core wall thickness in the model design is t = 0.05Λ.

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Fig. 3.
Fig. 3. Mode trajectories for a range of three core wall thicknesses of the PCF design shown in Figs. 1 and 2. The modes are labelled by symmetry according to the notation of [24]; the key to symmetry types is given in Fig. 4. The fundamental air-guided mode is shown by an arrow in each figure.

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Fig. 4.
Fig. 4. Modes of the PCF structure with core wall thickness t = 0.05Λ. The red shaded regions in the top-left and lower-right corners show the band edges, and the air-line is marked with a vertical black line. The fundamental air-guided mode is shown by an arrow.

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Fig. 5.
Fig. 5. Plots of the axial Poynting vector (normalised to unity over the supercell, and shown on a linear scale) for selected surface modes near to the air-line, at frequencies above and below the ‘clean’ region of Fig. 4. Each row of the figure shows two modes of the same symmetry type. The two modes of each doubly-degenerate pair have been added in intensity to show their structure more clearly.

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Fig. 6.
Fig. 6. Plots of the axial Poynting vector (normalised to unity over the supercell, and shown on a linear scale) for the lowest-order air-guided modes of the PCF structure with core wall thickness t = 0.05Λ at frequency k 0Λ = 5.5. The two modes of each doubly-degenerate pair (at βΛ = -0.266,-0.105) have been added in intensity, and the colour scale used is the same as that in Fig. 5.

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Equations (4)

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

{ ∇ t 2 + n 2 k 0 2 + ∇ t ln n 2 × ∇ t × } h t = β 2 h t ,
P ( M − σ I ) w = Pu .
Q ( M ˜ − σ I ) y = Qx ,
P air = ∫ air S . z ̂ d A ∫ S . z ̂ d A ,
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