1. Introduction

Standard optical fibers guide light using total internal reflection (TIR). This restricts their optical properties, because only solid or liquid materials can be used for the fiber core. There are no suitable cladding materials which have a sufficiently low refractive index to confine light by TIR in a vacuum or a gas core. Solid or liquid cores limit the fiber transparency, dispersion behavior and nonlinear response to roughly the corresponding values in the bulk materials. This has had a profound influence on the development of fiber optics: for example, the spectral dependence of the attenuation and dispersion of bulk silica led to the development of optical telecommunications in the 1.3 µm and 1.5 µm wavelength bands. We have recently shown that light can be guided through an air core in a hollow optical fiber by using a photonic bandgap material as the fiber cladding [1,2]. Such “hollow-core” fibers are potentially of massive importance, freeing fiber performance from material constraints. A low-loss (13 dB/km) air-core fiber designed for use at 1.5 µm wavelength was recently reported [3].

Photonic bandgap fibers guide light at a low-index “defect” site within the photonic crystal lattice which forms the cladding. At a given frequency, the band gaps appear in a range of values of the propagation constant β in which one would normally expect propagating modes, and they are surrounded at both higher and lower values of β by propagating modes. Band gaps can occur for values of β<k(k is the vacuum wavevector), and so can be used to trap light in an air core. However, the range of k>β for which bandgaps occur is limited. This means that in a photonic bandgap fiber only a limited range of wavelengths can be expected to be guided in the hollow core. Since the first report of hollow-core guidance at visible frequencies corresponding to higher-order bandgaps [2] researchers have concentrated on guidance in fundamental gaps at wavelengths beyond 1 µm [3,4]. In this work we extend the wavelength range of fundamental-bandgap guidance to cover the 850 nm wavelength band. Fabricating fibers for use at 850 nm is more difficult because the dimensions of the fiber microstructure have to be reduced compared to fibers for 1550 nm. The larger draw-down ratio results in more deformation of the fiber structure, while the stronger surface tension forces associated with the smaller features make the structure less stable during drawing. However, fabricating fibers for shorter wavelengths is worthwhile, because the properties of hollow-core fibers should make them useful for delivering ultrashort optical pulses. In this paper, we describe the linear optical properties of the fiber and draw conclusions about possible applications and future designs.

 

Fig. 1. Scanning electron micrograph of the 850 nm air-core fiber used in this work. The outer diameter of the fiber is 85 µm.

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2. Fabrication

Our fibers have been made using the stack-and-draw fabrication technique, in which thin-walled silica tubes are drawn down to form meter-length capillaries, which are then stacked by hand to form the required close-packed array. Seven capillaries were omitted from the center of the stack to form the core in the final fiber, and the entire stack was jacketed before being drawn down to fiber. Before the draw, the preform was purged with nitrogen so that the holes in the final fiber are nitrogen-filled. The outer diameter of the fiber used in the present work was 85 µm, and a protective polymer jacket was applied during the draw. The fiber was drawn in lengths of several hundreds of meters, which were re-spooled for optical measurements.

A scanning electron micrograph of the fiber is shown in Fig. 1. The spacing between the holes in the cladding (the pitch Λ) is 1.94 µm, and the core diameter is 7 µm by 6 µm. The air filling fraction in the cladding is over 85%. There are 7 “rings” of holes between the core and the silica jacket, although those near the inner and outer edges are somewhat deformed. When illuminated from below using a white-light source under an optical microscope, the cladding is brightly lit while the core remains dark, as expected in a fiber designed for 850 nm wavelength.

3. Loss

The optical attenuation of the fiber shown in Fig. 1 was measured with a broadband light source using a cut-back technique. The light source was a tungsten-halogen lamp and the spectral analysis was performed using a commercial optical spectrum analyzer (OSA). The fiber was wound in a single layer on a spool of 16 cm diameter. The measurements were done by holding the fiber in standard bare fiber adaptors connected directly to the light source and the OSA. The fiber length was cut from 56 m to 20 m. The shorter length was chosen to be 20 m because the broadband light source used in this measurement resulted in substantial cladding-mode and surface-mode excitation. The attenuation of the fiber as a function of wavelength is shown in Fig. 2. The fiber guides light in a band of roughly 70 nm width, centered at a wavelength of 850 nm. Outside of this low-loss band, the attenuation increases rapidly. No other low-loss transmission bands were found in a wavelength range spanning 500 nm – 1600 nm. The lowest loss recorded in this fiber was 180 dB/km at a wavelength of 847 nm, although we have measured similar fibers with losses in this wavelength band as low as 130 dB/km: the transmission curve of this lower-loss fiber was not as attractive in terms of symmetry and bandwidth. In principle, it is possible to form fibers with a somewhat broader transmission band than this fiber by improving the fiber structure, and it is certainly possible to form fibers with different central wavelengths in this band.

Attenuation in hollow-core fibers is expected to be limited by similar mechanisms to those found in conventional fibers: confinement, bend loss, microbending, Rayleigh scattering, and local imperfections. Clearly, the contributions of these to the overall loss, and the level of each of them, will differ from those in conventional fibers, as will their dependence on wavelength. In the current fiber, calculations suggest that the intrinsic cladding thickness is sufficient to reduce confinement loss to well below the observed level. On the other hand, the microstructure forming the cladding is imperfect (see Fig. 1), so that confinement loss is a likely mechanism limiting the fiber loss. Support for this is found in the variation in the fiber loss between nominally identical 50 m lengths of fiber, which can vary in magnitude with very little change in the bandwidth or central wavelength.

 

Fig. 2. Attenuation recorded using a cutback measurement on 56 m of fiber. Outside of this spectral window, no low-loss wavelength bands were observed.

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Bending the fiber macroscopically does not measurably increase the attenuation: in our experiments we have wound 100 turns of fiber around a mandrel of 5 mm diameter, and the additional loss caused by such bending is not measurable. Bending the fiber more tightly does not lead to catastrophic bend loss either, until the fiber snaps at a bend radius less than 2 mm. Rayleigh scattering in hollow-core fibers will be substantially reduced when compared to the bulk scattering from silica, because over 95% of the light of the guided mode is propagating in air. On the other hand, there is an unknown contribution from surface scattering, which will have a different spectral dependence to bulk scattering. Variations in the structure along the fiber over length scales of meters to microns will cause loss and scattering out of the fundamental mode: we know such variations are present (we detect variations in the outer fiber diameter of a fraction of a percent during the draw) but have not quantified their contribution to the overall loss. As in previous air-core fibers [2,3] we believe that variations in the fiber cross-section and along the fiber length are the limiting factors in the samples used in this work.

4. Observed guided modes

We have used near-field imaging to study the guided-mode pattern as a function of wavelength. Light from a Ti:Sapphire laser was introduced into the core of a 60 m length of the fiber using an objective lens, and the output face was imaged (with suitable attenuation) using a 40X objective onto a 12-bit digital camera. The pattern observed at a wavelength of 848 nm (the center of the guiding band) is shown in Fig. 3.

In order to unambiguously identify the relative orientation and scale of the fiber structure, we have illuminated the output face of the fiber with a small portion of the laser beam using a beamsplitter, and so simultaneously imaged the fiber output face. This enables us to place the locations of the holes in the fiber relative to the guided-mode pattern, and a few rings of (not always circular) air holes are shown schematically as orange outlines in the figure. The guided mode is very well confined within the air core, and is roughly Gaussian in shape. Fig. 3(b) shows line scans through this plot on the two principal axes of the elliptical core (plotted on a logarithmic scale). Numerical analysis of Fig. 3(a) shows that more than 90% of the guided mode is in the core. Using photographic film, we recorded the far-field intensity pattern shown in the inset to Fig. 3(b) at a wavelength of 850 nm with no optics between the fiber endface and the film. The film is saturated in the centre to show the far weaker features on the edges, which are more than 20 dB below the main peak. The measured numerical aperture (NA) of this mode was 0.17 at 848 nm, taken at the 5% intensity points.

 

Fig. 3. (a) Near-field pattern of the guided mode, recorded at a wavelength of 848 nm after transmission through 60 m of fiber (linear scale). The location of the first few rings of air holes are represented schematically as the orange outlines. (b) Line plots through the two axes of the elliptical core, in a logarithmic scale, with arrows indicating the positions of the core wall. The inset shows the far-field pattern, as recorded on infrared photographic film.

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Fig. 4. Near-field patterns observed after transmission through 60 m of fiber on the edges of the guided wavelength range at 790 nm (left) and 898 nm (right), plotted on a linear scale. The locations of the air holes in the first few rings around the core are shown schematically.

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The observed patterns do not change as the input is varied, nor as the fiber is moved about. We have scanned the wavelength over the guiding band, and find only rather small changes in the modal field pattern over the 100 nm band centered on 850 nm, as shown in Fig. 4. We can couple more than 60% of the power of our Ti:Sapph laser beam into this “fundamental” mode at 850 nm, and this could probably be increased with more precise matching of the NA.

When this experiment is repeated using a shorter length of fiber (1 m) and a higher power coupling lens (numerical aperture roughly 0.3), a range of different output field patterns can be seen (Fig. 5). We attribute these to excitation of higher-order guided modes, which experience higher loss than the “fundamental” mode because of larger overlap with the silica, and a higher transverse k-vector. The fiber is not intrinsically single-mode, and computations on similar structures using the FDTD method reveal that one can expect several localized modes to be within the bandgap. However, the differential loss is found to be substantial, and as in strongly-guiding solid-core photonic crystal fibers [5], the bend-induced coupling between the low-loss mode and the higher modes is very weak. It is worth noting that the high differential loss means that bend-induced modal coupling would manifest as transmission loss through a long piece of fiber, which is not observed in our bending experiments. Unlike previous work at longer wavelengths [6,7], we can not observe higher-order mode patterns in lengths of longer than a few meters. Consequently, the fiber can be used as if single-mode.

 

Fig. 5. Near-field patterns of higher-order modes excited in a short piece of fiber (1 m length) at a wavelength of 882 nm, plotted on a linear scale. The two plots correspond to different excitation conditions. The locations of the air holes in the first few rings around the core are shown schematically.

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5. Properties of the low-loss mode: birefringence

The fiber used in these experiments has an elliptical core (ratio of axes 0.85:1) due to unintentional but uniform deformation during the drawing process. The ellipticity is accommodated mainly by deformations in the innermost ring of air holes surrounding the core. The deformations are apparent in Fig. 1, and the effect of ellipticity on the modal field patterns is visible in Figs. 3 – 5. It is of interest to consider the polarization-mode splitting of the fundamental mode which arises as a result of this deformation, and the extent to which light introduced into one polarization mode of the fiber is coupled to the other by bends and twists along the fiber length. To this end we have measured the polarization beat length, by introducing a localized mechanical deformation of the fiber cross-section. We used a waveplate to excite both polarization modes equally at the fiber input, and a polarizer at the output. We then introduced localized mode coupling by sliding an object of around 1 mm diameter along the fiber length, with a force of a few Newtons. We observed high-visibility oscillations in the light transmitted through the polarizer as shown in the inset to Fig. 6. By repeating this measurement at different wavelengths, we found that the beat length ranges from 4 mm to 13 mm over the guiding band (Fig. 6). We confirmed the measurement at long wavelengths by cutting the fiber back in short lengths of approximately 1 mm, and studying the output polarization state, which gave results in good agreement with the mechanical perturbation method.

The observed level of mode splitting for a significant ellipticity suggests that changes in the fiber design rather than simply deformation of existing designs will be required in order to make a very highly birefringent air-core fiber without an elliptical mode [8], although the observed level of mode splitting is already significant.

 

Fig. 6. Measured beat length for the fundamental polarization modes as a function of wavelength across the guiding wavelength band. Inset shows an example of the data used to measure the beat length, showing the intensity transmitted through the polarizer as the mechanical disturbance is slid along the fiber length. The fringes are not uniformly spaced only because the speed of the mechanical disturbance was not constant.

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6. Properties of the low-loss mode: dispersion

We have studied the dispersion of the guided mode through the low-loss region using a combination of low-coherence and time-domain methods. The low-coherence measurements were performed using a white-light source and 10 nm or 3 nm bandpass filters with a Michelson interferometer. We measured the group index of the two fundamental polarization modes at a number of different wavelengths, in a fiber of length 30 cm. Some of these measurements are presented in Table 1. As expected, the group index is close to but slightly above unity. It can be deduced that the change in the group velocity with wavelength – the group velocity dispersion (GVD) – was small on the short-wavelength side of the transmission band, and far larger and positive (anomalous dispersion) on the long-wavelength side. More detailed experiments with smaller wavelength steps showed that both modes passed through zero GVD between 800 nm and 850 nm, with anomalous dispersion between 850 nm and 900 nm.

Table 1. Modal index for the two polarization modes measured on a short (30 cm) length of fiber using low-coherence interferometry. The group velocity dispersion is seen to be strongly anomalous between 850 nm and 900 nm.

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Measurements of the GVD were also obtained directly by measuring output pulse length as a function of wavelength. We used an autocorrelator to measure pulse lengths using 200 fs input pulses from a mode-locked Ti:sapphire laser. In order to maintain a measurable output pulse length, we used a fiber length of 0.67 m. In deriving dispersion values from output pulse lengths, we assumed that the pulse propagation was linear, consistent with our observation that there were no observable spectral changes in the output at the powers used. We also found that the measured autocorrelation trace width was independent of the input power. In order to derive an output pulse length from the autocorrelation trace we assumed that the actual pulse lengths were 0.6 times the autocorrelation length, and used the measured bandwidth. This assumption affects the scale of the GVD curve, but to first order the shape of the curve is not affected.

 

Fig. 7. Group velocity dispersion curves measured for the two polarization modes using the time-domain technique. Output pulse lengths were measured with an autocorrelator, and the sign of the dispersion was obtained from the low-coherence data. The attenuation curve is shown here for ease of reference.

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The pulses were measured independently for the two polarization modes of the fiber, by using a half-wave plate between the laser and the fiber. The resultant GVD curves are shown in Fig. 7. As a check on the validity of the above assumptions, we have verified that the resultant curve is in overall agreement with the GVD estimates obtained by taking 2-point differences of the low-coherence data. Differences could be due to variations between the different pieces of fiber used in the two measurements, or the assumptions made in the time-domain measurement. The GVD curves are similar to those predicted and previously observed [6] for hollow-core fibers in the 1300 nm wavelength region, demonstrating the independence of the dispersion from that of bulk silica. The dispersion is far less than that in solid-core bandgap fibers which include isolated islands of high-index material [9]. The GVD crosses zero within the low-loss window, and is anomalous over much of the guiding band. The dispersion slope around the minimum-loss wavelength is less than 10 ps/nm²/km for both modes, comparable to that previously reported at 1300 nm [6]. This slope may be reduced through refinements in fiber design, suggesting that linear transmission of ultrashort pulses through lengths of many meters of fiber with low dispersion will be feasible. In our preliminary experiments, we have transmitted 200 fs, 4 nJ pulses through 20 meters of fiber at the zero-GVD wavelength. The autocorrelation width of the output pulse was then broadened to roughly 3.5 times the input pulse, partly due to modest spectral deformation. Improvement can be expected by working away from the zero-GVD wavelength and using a compensation or pre-chirping scheme. The fact that the GVD is anomalous over much of the wavelength range is expected to enable the formation of solitons in the fiber at relatively high peak powers [10,11] and we are currently investigating this using our Ti:Sapph laser source.

7. Conclusions

Photonic bandgap air-core fibers can be fabricated for operation at wavelengths as short as 850 nm. Losses in these fibers are already at an acceptable level for many applications, and are expected to fall further with improvement in the fabrication processes. The lowest-loss mode has a quasi-Gaussian field pattern, and is strongly peaked in the air core. Higher-order modes can be observed in short fiber lengths, but have substantially higher losses. Coupling from the fundamental to the higher-order modes is weak, even when the fiber is bent or twisted. The core ellipticity of 10–15% causes a splitting between the fundamental polarization modes of the order of a few times 10^-4.

The width of the bandgap in these fibers makes them suitable for delivery of ultrashort optical pulses from laser systems in this wavelength band. The group-velocity dispersion of the low-loss mode is low and anomalous over most of the low-loss band, passing through zero towards the shorter-wavelength edge of the band gap. Although higher-order dispersion will ultimately limit linear delivery of ultrashort pulses down PCFs with simple structures, it is likely that more sophisticated designs exist where higher-order dispersion can be controlled.