Early work suggested that very large refractive index contrasts would be needed to create photonic bandgaps in two or three dimensionally periodic photonic crystals. It was then shown that in two-dimensionally periodic structures (such as photonic crystal fibres) a non-zero wavevector component in the axial direction permits photonic bandgaps for much smaller index contrasts. Here we experimentally demonstrate a photonic bandgap fibre made from two glasses with a relative index step of only 1%.
©2005 Optical Society of America
A photonic bandgap is a property of some two- or three-dimensionally periodic dielectric structures, whereby light of certain frequencies is forbidden to propagate . It is a common perception that very large refractive index contrasts are needed for bandgaps to occur. For example, a relative index step (index difference/lower index) of over 160% is needed for light propagating perpendicular to an array of rods . However, a fixed but nonzero wavevector component parallel to such a 2-D structure permits bandgaps for much smaller contrasts . Thus bandgap-guiding optical fibres incorporating air [4–6], fluids [7–8] and contrasting glasses  have been reported, where the core is surrounded by a cladding with a 2-D bandgap . For certain wavelengths, light with a wavevector component along the fibre that is consistent with propagation in the core material is forbidden to propagate through the cladding by the bandgap. Light of these wavelengths therefore cannot escape the core, and propagates along it with low loss. Guidance by conventional total internal reflection is prevented if the core has a low refractive index compared to the cladding, so any long-distance guidance of light in such a fibre indicates the presence of a bandgap.
Some of these fibres have isolated high-index rods or “nodes” embedded in a contiguous background material of lower index, a core being formed by omitting one or more nodes [7–9]. Guidance in these fibres has been described as being due to the “ARROW” mechanism [8,11,12], where the bandgaps correspond to antiresonant states of the nodes in isolation. When the nodes are antiresonant, they expel light and so resist its leakage from the core.
However, all previously-reported 2-D bandgap fibres still have substantial index steps of 16% or more , although theoretical treatments have shown that 2-D bandgaps can appear for arbitrarily small steps [13,14]. Here we experimentally demonstrate two-dimensional photonic bandgaps in solid optical fibres with index steps of only 1%. Mostly pure silica, they incorporate raised-index nodes derived from readily-available conventional fibres. Thus as well as illustrating how 2-D bandgaps can appear for any index contrast, they also show how simple it can be to form practical photonic bandgap materials.
So-called Bragg fibres also confine light by a photonic bandgap [15,16], and low-contrast Bragg fibres have been made by the MCVD technique . However, these are coaxial structures with a multilayered cladding so their bandgaps are only one-dimensional. It was long ago recognised  that 1-D and 2-D bandgaps differ in one key respect: 1-D bandgaps appear for normal incidence at arbitrarily small index contrasts, whereas very large contrasts are needed for 2-D “in-plane” bandgaps at perpendicular incidence . Hence 2-D bandgap fibres are not merely generalisations of Bragg fibres and would be expected to have different properties; before their theoretical prediction  it was not obvious that low-contrast 2-D bandgap fibres were possible at all.
To make a low-contrast bandgap fibre with a true 2-D bandgap, we started with a photonic crystal fibre  preform with an outer diameter of 2 mm. Made from pure fused silica, it incorporated an array of air holes big enough to fit a conventional optical fibre inside, Fig. 1(a). Commercial step-index multimode fibre  was inserted into each hole except the central one. The core of the multimode fibre was doped with germanium and so had a slightly higher index than pure silica. Commercial single-mode fibre  was inserted into the central hole, Fig. 1(b). The filled preform was then drawn to fibre in the conventional way [10,20] to reduce the multimode cores from 50 µm to ~2 µm in diameter. The result is a bandgap fibre with isolated nodes of raised-index Ge-doped silica (derived from the cores of the multimode fibre) embedded in a background of lower-index pure silica. The pure silica region around the central lattice site lacks such a node (since the single-mode fibre had a much smaller core than the multimode fibre to begin with) and is the defect that acts as the new fibre’s low-index bandgap-guiding core, Fig. 1(c).
We drew such fibres to different scales. The centre-centre spacing or pitch Λ of the nodes was 6 µm in fibre A and 7.5 µm in fibre B. The ratio of the node diameter d to the pitch, d/Λ, was 0.34 in both fibres. Our bandgap fibre resembled previous ones [7–9] but with a much smaller index contrast. The relative index step calculated  from the numerical aperture quoted in the multimode fibre’s specifications was 1.05%, 16 times smaller than the next smallest reported  and well within the scalar “weak guidance” approximation . This means it behaves as a bandgap fibre with an arbitrarily small index step.
where ρ is the radius of the core and NA is the fibre’s numerical aperture . V quantifies a fibre core’s effectiveness as a waveguide and is normally ~2 for a working single-mode fibre. The diameter of the re-drawn single-mode core in fibre A was ~350 nm. If this was embedded in an infinite pure-silica cladding, its V would be around 0.22 at 560 nm wavelength. Mode field diameter  is a very sensitive function of such small values of V, and our calculations of it ranged from many thousands of km to several Astronomical Units for different credible parameter values. In other words, the residual single-mode core on its own was not effectively a waveguide at all  and could be ignored: the bandgap fibre’s core was indeed effectively pure silica and could not guide light by total internal reflection.
3. Optical properties
White supercontinuum light generated in a photonic crystal fibre using a Nd:YAG microchip laser  was used to illuminate the whole input end-face of a 10 m length of fibre A and spectrally filtered images (using passband filters) of the output end-face were recorded, Fig. 2(a). The nodes can act as conventional index-guiding waveguides but we are interested in guidance in the low-index core, which can confine light only by a photonic bandgap and not total internal reflection. As well as light in the nodes, a bandgap-guided core mode is present for green to orange but not blue and red light.
By focusing the input light using a 60× microscope objective, the core mode could be excited without illuminating the nodes. Fig. 3(a) is the imaged intensity pattern for the bandgap-guiding core of fibre B, which had a larger pitch so transmission was at longer wavelengths than fibre A. The Adjustable Boundary Condition method  was used to calculate the attenuation and mode patterns for our fibres, assuming a perfect structure (circular nodes, hexagonal lattice) with as many nodes as the real fibre, and Fig. 3(b) is the intensity pattern calculated for fibre B. The measured and calculated intensity patterns are similar, including the faint satellite spots around the main lobe.
Figure 2(b) is the measured transmission spectrum of fibre A’s core for 10 m and 0.2 m lengths, together with the calculated transmission through 0.2 m. The spectra were obtained by placing a pinhole in the output image plane to select the light from core alone, which was then coupled to an optical spectrum analyser. The measured and calculated transmission curves match well, the 10% wavelength discrepancy between them being attributable to: measurement uncertainties in key dimensions (taken from micrographs) and the multimode fibre’s numerical aperture (quoted by the manufacturer ); structural deformations such as deviations of nodes from their nominal positions and circularity (their aspect ratio was typically ~0.8) as evident in Fig. 1(c); and nonuniformity along the fibre. (Note added in proof: subsequent direct measurement of the index profile of this fibre does indeed indicate an overestimate of the numerical aperture that is of the order of 10%.)
Medium-term fluctuations in the supercontinuum source prevented accurate direct cutback measurements  of attenuation at the minimum-loss wavelength of 560 nm. Instead we measured the attenuation at 633 nm with a helium-neon laser and extrapolated to 560 nm using the transmission curve of Fig. 2(b), making conservative assumptions to deduce a minimum attenuation of ≤1.3 dB/m. Modelling of confinement loss was sensitive to the fibre parameters, giving results ranging from 0.5 to 1.6 dB/m for different sets of credible parameter values. This compares favourably with the measured attenuation, and can readily be reduced by adding more rings of nodes to the fibre to inhibit tunnelling through the photonic crystal cladding . For example, just one extra ring of nodes is enough to reduce the calculated confinement loss of a fibre like fibre A to below 0.1 dB/m.
Both fibres A and B appeared to be single-moded. According to our calculations, the fibres were guiding in the first (lowest-frequency) bandgap of the cladding at the wavelengths shown in Figs. 2 and 3. For fibre B and larger fibres, guidance in the second bandgap was also observed at short wavelengths. In fact the wavelength positions of the bandgap edges can be predicted quite accurately without recourse to sophisticated modelling, since according to the ARROW picture they lie where the modes of the index-guiding nodes are cut-off . For example, the short-wavelength edge of the first bandgap is defined by V=2.4 and so should lie at 560 nm in fibre A. This is a close match, given the 10% discrepancy that affected our calculation of the transmission spectrum. (The long-wavelength edge of the first bandgap is exceptional because it does not correspond to a cut-off, but we find the short-wavelength edge to be a useful rule of thumb.)
The low attenuation, spectral low-loss bands and agreement with calculations confirm that the light is indeed bandgap-guided. The index step of 1% falls well within the weak guidance approximation of waveguide theory, under which changes in index step imply changes in wavelength or length scales but are otherwise irrelevant . Our results therefore demonstrate experimentally the existence of photonic bandgaps for arbitrarily small index steps and that, contrary to widespread perceptions grounded on early work into photonic bandgaps, large index contrasts are not necessary. Indeed, theoretical work has shown that low-contrast systems can actually have wider bandgaps (relative to centre wavelength) than high-contrast systems, due to polarisation degeneracy . Low-contrast bandgap fibres may therefore be preferable for applications requiring the widest possible bandgaps.
Our work also demonstrates the simplicity of fabricating bandgap fibres using readily-available conventional fibres to provide the raised-index material. Although a photonic crystal fibre preform was used to hold the constituent fibres in place it performed no other function; there was no need to maintain air holes in our all-solid fibre. Fibre drawing equipment is reasonably common and, unlike previous bandgap fibres, our technique can form metre (and potentially kilometre) lengths of bandgap material without the usual stringent steps to control the process. The fibre design is clearly tolerant to imperfections, since the distortion of circular multimode cores into the randomly-oriented elliptical nodes seen in Fig. 1(c) did not stop the fibres guiding light. The fibre is therefore a convenient and effective source of photonic bandgap material in quantity, and we expect at least the dispersion and spectral attenuation properties to find numerous applications  in due course. Furthermore, since confinement loss can be made arbitrarily small by including more nodes in the cladding, and other important loss mechanisms depend on the index contrast and the presence of dopants in the core , it is intriguing to consider that the attenuation of such fibres could potentially be very low indeed.
We thank A.K. George, W.A. Lambson, C.K.W. Cheung, N.Y. Joly, H.R. Perrott and G.J. Pearce for supporting contributions. We acknowledge support from M.C.J. Large and M.A. van Eijkelenborg for A.A.’s visit to Bath. AA acknowledges financial support from the Research and Scholarships Office and the School of Physics, University of Sydney.
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