The angular transmissivity of high numerical aperture air-clad fibres is measured as a function of skewness of the launched light. Within the experimental limits the measured transmissivity of skew rays is significantly lower compared to theoretical predictions for air-clad fibres with uniform cladding surfaces. The discrepancy is attributed to diffractive losses of skew rays from the periodic corrugations at the pump core-cladding air interface.
©2005 Optical Society of America
Optical fibres with a high numerical aperture, (NA), is a research area of considerable interest [1,2]. The research is predominantly aimed at the fabrication of fibres with increased capture efficiency of pump-light, as well as large power handling capacity for double-clad fibre lasers . These fibres are usually fabricated with a low refractive index polymer cladding, in which NA’s of 0.45 are routinely achieved. Another high NA fibre design is the air-clad fibre [4–6]. Guidance in this type of fibre is achieved by nanostructured air holes, usually distributed in a single layered annulus, stretching longitudinally along the length of the fibre. A partial cross-section of this is illustrated in Fig. 1 whilst Fig. 2 (b) shows the full cross section. Theoretical analysis suggests that these fibres can potentially have an NA of 1.06. In practice, however, leakage across the barriers tends to reduce the NA . Research towards the production of higher values of NA in this type of fibres is aimed to reduce leakage of light across the nanostructure by decreasing the barrier width or, if necessary, by increasing the number of barriers. Experimental studies , report experimentally measured NA’s of air-clad fibres to be approximately 15% less than what would be expected theoretically. In this paper, we show this discrepancy relates to diffraction-like losses arising from coherent scattering from the corrugated surface of the pump-core. The losses are shown to be sensitive to the level of skewness and incident angle at which light is coupled into the fibre.
In the experiment, the transmissivity of an air-clad fibre was monitored whilst the corrugated surface of the pump-core was illuminated with different input angles and levels of skewness. The silica air-clad fibre under test was fabricated using standard methods. A preform was prepared by stacking capillaries between a protective tube and an undoped silica rod without an active core. The preform was then drawn under pressure into a fibre with a pump-core of ~180 µm diameter. The pump-core was supported by 59 bridges of ~26µm length with a minimum thickness of ~δ=300 nm (nominal NA=0.55 for λ=633 nm). A close-up of the corrugated surface of the pump-core is shown in Fig. 1. The light source was a HeNe laser operating at λ=632.8nm, and the illumination method is shown schematically in Fig. 2. The HeNe is focused with an NA=0.85 microscope objective, so that only light with a small divergence within the Rayleigh range (zR≈0.7mm) is incident on the inside of the pump-core. The spot-size at the waveguide surface was measured to have a diameter of ~30µm. When analyzing this data we have made the assumption that the divergence does not significantly change the qualitative signal variations observed with changing skewness, and therefore we consider the simplest case of a coherent flat wavefront on a planar grating. The angle γ denotes the incident angle relative to the fibre axis (z-direction), and the symbol ξ denotes how skew (off-center) the ray is when it is incident on the waveguide surface: ξ=0 represents meridional incidence and ξ=1 fully skew incidence. The transmissivity can only be interpreted from a relative perspective and not as an absolute value because after the first reflection, the divergent light is uniformly distributed to a broad range of angles, γ, as well as levels of skewness, ξ. This assumption is supported by the fact that there was no significant difference in the experimental results for different fibre lengths between 0.5m<L<3m. The transmissivity as a function of skewness is shown for four different input angles in Fig. 3. During angular transmissivity measurements, these angles have been measured to have approximate transmissivities of 99%, 95%, 20% and 5% respectively. In the diagram it can be seen that the transmissivity at the input angles γ=10° and 15° are independent of skewness to within experimental error. This is to be expected as light propagating at these angles is well guided. However, at input angles γ=20° and 30° the transmissivity is strongly correlated with the level of skewness at the first reflection. The observed periodic response at 300 has to be treated with care since both divergence and interference of the coherent light needs more comprehensive consideration than is given here. Light launched at 20° experiences a clear transmission peak near ξ=0.15. Generally, within these fibres there is less transmission the more skew the probe-beam is aligned, which is the opposite trend when compared to both theoretical predictions and experimental results made on conventional step-index high-NA fibres with a flat non-corrugated core-cladding interface. In these fibres the loss is the highest at the steepest incidence, i.e. pure meridional illumination [1,8,9]. In plastic fibres with very rough core-cladding interfaces, skew rays have been found to be lossier because skew rays experience a significantly larger net number of reflections than meridional rays . However, these conditions should not apply here because silica fibres have low surface roughness and it is only at the first single reflection in our experiments where all rays have similar skewness and incident angle on the core-cladding interface. Instead we note that within air-clad fibres, the core-cladding interface of the pump-core has a concave distributed high Δn-corrugation with a period of 9.6µm. This suggests it is plausible that it acts analogous to a curved diffraction grating for certain rays.
Previously, in single-mode or few moded photonic crystal fibres with more than one ring, a one-dimensional transverse cross section of the periodic structure is sufficient to analyze the role of diffractive propagation within the waveguide , even when bending is introduced . However, in this case, we have a single ring and a large number of modes represented by a large range of skewness within the waveguide. Therefore, incidence with the grating at angles other than the plane of the grating axis needs particular consideration. A rigorous modal analysis including higher order modes and mode classes with significant skew ray components is computationally intensive and outside the scope of this paper. However, the conical diffraction grating equation can be used to analyze the prospect of diffraction when the incident beam is not perpendicular to the grooves of the grating :
where m is the diffraction order, λ the wavelength, d the period, α the angle of the projection of the light path onto the plane perpendicular to the corrugations and the normal of the core-cladding interface, β the conical diffraction angle and ε the angle between the light path and the plane perpendicular to the corrugations. With the definitions given in the schematic of the experimental setup in Fig. 2, Eq. (1) can be rewritten as:
Equation (2) can be used to investigate if there are orders that are diffracted into less guided angles. The diffraction grating is curved with few gratings illuminated during the experiments, so first order diffraction should be the strongest. The first order diffraction (m=+1 and m=-1) are plotted as a function of skewness for incident light of γ=20°, d=9.6µm and λ=632.8nm, in Fig. 4. In the diagram we find that the angle, β, of the first diffraction order (m=+1), decreases approximately linearly from 10° to -50° for 0.0<ξ<1.0, passing 0° at ξ=0.15. The diffraction angle of the first negative order (m=-1) decreases in an approximately linearly fashion from -10° to -90° for 0.0<ξ<0.6. When β=0, the diffraction order is aligned with the gratings, i.e. along the fibre axis. This indicates that a local loss minimum for light of skewness, ξ=0.15, is to be expected for the first (m=+1) diffraction order and that light of an increasing or decreasing level of skewness experiences proportionally more loss. Experimentally the light launched at this angle, γ=20°, over the skewness range, 0.0<ξ<1.0, does indeed show a peak transmissivity in accordance with Equation 2 (the dotted line in Fig. 3). Further, localized far-field light spots identified as possible diffraction orders were observed emerging from the side of the fibre when the transmission was low through the fibre. An example is shown in the inset of Fig. 3. The apparent lobe structure of these diffraction spots are aligned in the same direction of the fibre indicating that we do not have a perfectly collimated beam beyond the Rayleigh range inside the fibre. We believe interference is the most likely cause of this structure and this is currently the subject of a more detailed study. The spots were also elongated vertically, which can be attributed mostly to the divergence of the beam as well as to some lens-like effects of the curved surface of the waveguide wall.
The immediate implications of diffractive scattering are important and could potentially be far reaching. Figure 3 indicates that under certain conditions only diffraction-assisted coupling can be present, something not possible in conventional step-index waveguides. Exploratory experiments also indicate that light launched at normally non-guided extreme angles, γ > γmax, can be coupled into well-guided angles by the diffractive properties of the core-cladding interface. An example of this is shown in Fig. 5, which shows a graph of the far-field output of the fibre for light launched at an angle outside the NA. The light was in a collimated beam and had a wavelength of 1550 nm. For this wavelength the fibre has an NA of 0.75. The corresponding angle for 5% transmissivity where the NA is measured is 48°. The collimated beam was launched into the fibre (L=1m) at an angle well outside the NA of γ=60° and the far-field output were recorded with a vidicon camera. In the graph in Fig. 5 it can be seen that there is no significant light emerging from the fibre at angles larger than the cut-off angle γmax≈50°, which is consistent with the NA of the fibre. For angles below the cut-off angle there is a sudden increase in the light intensity that occurs due to random scattering. This light decreases in intensity for lesser angles, and is common for all fibre types. However, at angles 30°, 22° and 15° there are clear transmission bands visible, which are not found with standard smooth core-cladding interface fibres. These rings can be attributed to diffraction orders that are coupled into well-guided angles.
Likewise, a corresponding diffractive loss at other normally well-guided angles is also possible. This may reduce the effective NA of these fibres, and could, for example in high power fibre lasers lead to the loss of pump-light which is scattered out of the fibre before being absorbed by the doped core. On the other hand, this angular selectivity may form the basis of refining other features and potentially enabling new devices. For example, the selective loss mechanism could be used to filter out modes with unwanted effective refractive indices, thus enabling fibres with low focal ratio degradation (FRD) for astronomical applications .
Quite apart from considering beam divergence, given the regimes that are potentially able to be covered and that the index contrast between air and glass is sufficiently high, a more rigorous approach to analyzing scattering, including grazing incidence angle scattering  and so-called extreme angle scattering , will eventually be required. High NA, highly multimode air-clad fibres may be ideal test vehicles for many of these unusual scattering regimes that have been theoretically identified. In the context of air-clad applications, future theoretical waveguide models will need to incorporate these structures, along with the exact launching conditions since it is often not possible to launch with a planar wavefront.
In conclusion, the transmissivity of a high-NA air-clad fibre has been experimentally measured as a function of skewness of the launched light. Results show larger losses of skew rays compared to what is predicted in theoretical models of high-NA fibres with a uniform cladding surface. The losses are attributed to diffractive-like coherent scattering processes occurring at the periodic corrugations of the surface boundaries of the pump-core. The results qualitatively agree to a first approximation with the diffraction grating equation, and are further supported by the apparent diffraction orders emerging from the side of the fibre. These results show that whilst previous analyses have focused on meridional rays since they are easier to implement theoretically, in practice the full spectrum of launch conditions needs consideration, particularly if the input light has a non-planar wavefront, typical of a number of significant applications such as high power fibre lasers. Whilst this is currently a challenging area of research from a numerical perspective, future experimental work will evaluate in more detail the responsible phenomena that distinguish these fibres from conventional double-clad fibres and their relative contributions.
The authors would like to thank Justin Digweed for help with fabrication of the air-clad fibres and Nader Issa for useful discussions. The work was funded by Australian Research Council Discovery Projects.
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