1. Introduction

In a photonic bandgap fiber (PBGF), light is confined within a low index core by a photonic crystal cladding formed from two different materials. In their most spectacular manifestation, PBGFs are formed using silica and air. Silica-air PBGFs can be made so as to trap light in a low-loss mode within a hollow core [1]. Recently, several research groups have reported developing PBGF’s formed using the far lower index contrast available from doped and undoped silica, resulting in solid silica fibers which still exhibit the unusual spectral and dispersive characteristics of PBGF’s [2,3]. Such structures have proved to be an ideal environment in which to explore the basic physics of photonic band gaps in fibers, making it straightforward to form photonic crystal claddings with isolated high-index regions which is not possible when the lower-index material is air. The high-index regions have previously been formed from rods of doped silica that appear as disks in the fiber’s cross-section. The bandgaps are defined by the frequencies at which the higher-order guided modes of the cladding rods are cut off [4]. Away from these cut-off frequencies, the core mode (which has a modal index close to that of the lower-index material) is confined. Although overall attenuation as low as 20dB/km has been reported [3] these fibers have been found to suffer from significant bend loss under certain circumstances, which is not the case with air-silica fibers. Such loss is not uniform across the band gaps, but varies depending on the specific nature of the modes defining each gap.

We have recently shown that the bend losses arise because when the refractive index contrast between the two materials Δn is small, the bandgaps are shallow (Fig. 1). We showed [5] that the losses will be especially high when the band gaps are defined on their high-frequency edge by an LP_lm mode with low azimuthal order l. The reason for this is that low-l rod modes are intrinsically more strongly coupled together than higher-l modes. A natural suggestion arising from our previous work [5] was to suppress these troublesome low-l modes by redesigning the fiber structure. Specifically, by using a 2-d array of tubular high-index regions (which appear as rings in the fiber cross-section) rather than rods in the cladding, the modes of higher radial order m (including the next set of low-l modes with m=2) will be swept away to higher frequencies because there is “less room” in the radial direction for them. The lowest-order (m=1) modes will be affected much less. Our intention in this paper is to report how such a ring fiber can be practically formed, and what effect this has on the optical properties.

2. Computational analysis

In order to demonstrate the effect of substituting rings for solid disks in a PCF cladding cross-section, we have used the fully-vectorial fixed-frequency plane-wave method [6] to calculate the photonic density of states (DOS) of a sequence of cladding structures which vary smoothly from solid rods to thin rings. For these calculations we assume an infinitely-periodic triangular lattice of high-index inclusions (n_H=1.47288) in a background matrix of lower refractive index (n_L=1.457), where we have chosen refractive indices and dimensions of the structure to match our experimental fiber (described in the next section) as closely as possible. Additionally, to assist in comparison with experimental fibers, we use an 8×8 supercell method to determine the locus of the fundamental core-guided mode introduced by the removal of a single high-index inclusion.

Figures 1 and 2 show the DOS for an array of rings with pitch Λ, fixed outer diameter d=0.70Λ and various inner diameters D between D=0 (ie rods) and a maximum of D=0.91d. Figures 1 and 2 cover smaller and larger D (respectively) and are plotted on different scales, to follow features of interest in the plots. In both figures the photonic bandgaps, within which propagation in the cladding is forbidden, are highlighted in red; the regions of non-zero DOS are shown in grayscale with white representing regions of high DOS and black, regions of low DOS. The DOS for the array of rods shown at the top of Fig. 1 is typical of an all-solid PBG cladding; the structure of similar arrays of rods has been shown and discussed elsewhere [2,3,5,7]. The specific modes appearing in Fig. 1 have been identified using numerical computation, as the LP_lm marked at the top of Fig. 1(a). The progressive replacement of high-index material with low-index material causes all modes to shift to higher frequencies, as would be expected from any process that reduces the effective V-value. However, the m>1 modes shift much faster than the m=1 modes, widening the frequency range between the m=1 and m>1 cutoffs of the low-l modes. Continuing the removal of high-index material in figure 2, the DOS in this frequency range is increasingly dominated by narrow m=1 bands with l>1, while the m>1 bands (including the second l=0 band) remain below the cutoff line. At the same time the bandgaps become shallower but broader.

 

Fig. 1. Photonic DOS for a triangular lattice of high-index inclusions (Δn=1.09%) in a low-index background (n=1.457, representing undoped silica). Specific guided modes occurring above the blue line are identified at the top of (a). The vertical axis is effective index n_eff=β/k; the horizontal axis is normalized frequency kΛ. The images to the right show the structure of the inclusions. Where shown, the ‘core line’ (the locus of the fundamental core-guided mode) is yellow.

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3. Fabrication

We fabricated an all-solid PBGF with a high index 2-d ring matrix cladding using a multiple stacking process. Our starting material was a set of germanium-doped silica canes with a thin pure silica jacket (diameter 0.82mm, diameter ratio ~0.88). We formed the ring canes (the unit cell of our photonic crystal cladding) by inserting 49 individual canes to form a ring in the gap between a large silica central rod placed inside an outer silica tube. This structure was then drawn down to form ring canes of ~1.52mm diameter. These canes were stacked in a close-packed array, replacing the central cane with a plain silica cane to create the low-index core. Each ring in the final fiber is therefore actually a ring of closely-spaced rods, spaced by around 0.6µm. The ratio of the outer diameter of the ring to the pitch, d/Λ, of the final fiber was 0.72, and we have measured a nominal ring thickness of ~0.05d. We have estimated the effective index contrast of the ring to be 1.09% by using the average index in the starting rod. The slightly hexagonal nature of the rings which can be seen in Fig. 3(b) arose during the draw. Fibers of several diameters were drawn; the following characterization was carried out on a fiber of outer diameter 200µm, Λ~15µm and core diameter of ~20µm.

 

Fig. 2. Photonic DOS as shown in Fig. 1, but for a range of rings with D=0.6d to D=0.91d. The diameter of the thinnest rings (D=0.91d) was chosen so as to be similar to our experimental fiber. Note the change of both vertical and horizontal scales relative to Fig. 1; D=0.6d has been repeated here to assist in comparison.

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4. Analysis

In order to obtain efficient coupling to the bandgap-guided mode, a 90cm section of the ring fiber was fusion spliced to a short length of 12µm core diameter “endlessly single mode” photonic crystal fiber (ESM) [8]. Light from a broadband supercontinuum source [9] was coupled into the ESM and the light emerging from the core of the ring fiber was analyzed using an optical spectrum analyzer. Figure 4(a) shows the measured transmission through straight and bent (1 turn of diameter 7.5cm) sections of ring fiber. In order to compare the performance of the ring PBGF with the previous type of all-solid PBGF with high-index rods in the cladding (corresponding in design to the first plot in Fig. 1) we have performed similar measurements on such a “rod fiber” as well. The characteristics of this fiber were Δn=2.03%, pitch ~15µm and d/Λ~0.7. The transmission spectra recorded in a similar way using the rod fiber are shown in Fig. 4(b). By careful identification of the cladding mode patterns at isolated wavelengths between bandgaps (see example in Fig. 5) we were able to unambiguously identify specific high-l mode crossings in the two fibers, and we have adjusted the choice of scale on the x-axes in figure 4 so as to approximately align these high-l modes. The number of lobes (=2l) observed in some of the high-angular momentum modes at specific wavelengths are labeled on the two plots.

 

Fig. 3. The ring fiber. a) Optical micrograph of the fabricated fiber. The outer diameter is 200µm. High-index regions appear lighter in the image. b) Scanning electron micrograph of the rings close to the core. The individual germanium doped rods can just be identified within each ring. c) Near-field image at the fiber output face when the fiber input is illuminated by a broadband supercontinuum source. Fiber length is 90cm.

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Fig. 4. Transmission spectra for a) the ring fiber and b) a rod fiber with a similar pitch and d/Λ. The overall shape of the transmitted spectra is due to the supercontinuum light source used in the experiments. The blue traces are the transmission through straight sections of fiber and the red traces are transmission through fibers with a bend diameter of 7.5cm. The numbers indicate the number of bright lobes measured in the high-l mode crossings at the indicated wavelengths. The peak at 1064 nm in b) and the intensity drop at ~470 nm in a) are due to the supercontinuum pump source and the short wavelength edge of the supercontinuum respectively.

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Fig. 5. Near field images of unconfined modes excited by leakage from the core between bandgaps in the ring fiber (left, at a wavelength of 506 nm) and a rod fiber (right, at 736 nm). The same high-l mode (with 16 lobes; l=8) is observed at these wavelengths in the two structures.

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In each case, in the straight fiber a series of low loss transmission windows can be seen, corresponding to the photonic band gaps. The changes to the cladding mode structure shown in Figs. 1 and 2 lead to significant changes to the locations and widths of the bands. The broad high-attenuation features in the rod fiber are eliminated from the ring fiber, so that the guiding regions in that structure are spectrally wider. The lowest-order bandgaps do not provide robust guidance in the ring fiber (as expected on the basis of the density-of-states calculations in Fig. 2). The crossings of the l=6, 7 and 8 modes in the rod fiber cause the narrow attenuation features marked in Fig. 4(b)). Our experimental observation of these modes is supported by detailed numerical computations (not shown). However, the shape of that transmission spectrum is dominated by the far broader features due to the crossings of lower-l cladding modes. In the ring fiber, these broad attenuation features have been swept away, leaving just the narrow loss regions due to crossings of the same high-l modes. The higher-order bandgaps in the ring structure suffer reduced bend loss when compared to those in the rod fiber. Although the actual wavelengths are a little different in the two cases, it should also be noted that the effective refractive index contrast is lower (by a factor of around 2) in the ring structure, as a result of the fabrication procedure. The improvement in bend loss performance is therefore marked, despite the bandgaps being shallower. We attribute the improvement to the very weak coupling between the core mode and the high-l modes of the cladding nodes.

5. Conclusions

We have modeled, fabricated and characterized an all-solid bandgap fiber with a 2-d ring matrix cladding, with the intention of suppressing higher-order radial modes of the high-index nodes in the cladding. This has the effect of increasing the widths of the photonic band gaps, and decreasing bend sensitivity. We have experimentally verified the improved performance by direct comparison of ring and rod fibers. Our fabrication technique enables fabrication of novel cladding structures in all-solid fibers, enabling us to construct advanced structures inside the unit cell of the photonic crystal. We anticipate that this procedure will lead to other designs of all-solid PBGF’s with enhanced characteristics.